Experimental particle physics without accelerators

EXPERIMENTAL PARTICLE PHYSICS WITHOUT ACCELERATORS

J. RICH, D. LLOYD OWEN and M. SPIRO DPhPE, CEN Saclay, F-91191 Gif-sur-Yvette, France

NORTH-HOLLAND AMSTERDAM -

PHYSICS REPORTS (Review Section of Physics Letters) 51 Nos. S & 6 (1967) 239-364. North-Holland. Amsterdam

EXPERIMENTAL PARTICLE PHYSICS WITHOUT ACCELERATORS J. RICH. D. LLOYD OWEN* and M. SPIRO DPhPE, (‘EN Sac/ar. F-OJ /91 Gif-sur-Yvetic, France

Received February 1967 Con tents:

Introduction 2. Neutrinos 2.1. Introduction 2.2. Direct neutrino-mass measurements 2.3. Neutrino oscillations 2.4. Double-beta decay 3. Neutrons 3.1. Introduction 3.2. 7 violation and the neutron electric dipole moment 3.3. Neutron oscillations 4. Proton decay 4.1. Introduction 4.2. Proton decay in Grand Unified Theories 4.3. Proton-decay experiments 4.4. The future of proton-decay experiments 5. Atomic parity-violation experiments 5.1. Introduction 5.2. Phenomenology 5.3. Optical-rotation experiments 5.4. Stark experiments in forbidden transitions 5.5. Atomic-hydrogen experiments 5.6. The future 6. Time variation of the fundamental constants 6.1. Introduction 6.2. Current variations 6.3. Past variations 6.4. Future variations 7. Cosmic-ray physics 7.1. Introduction 7.2. The primary cosmic-ray spectrum

241 244 244 245 249 265 269 269 2711 273 275 275 276 278 282 283 283 283 289 292 294 294 294 294 295 297 299 299 299 299

7.3. Experimental techniques 7.4. Particle physics in cosmic-ray experiments 7.5. Cygnus X-3 8. Magnetic monopoles 8.1. Phenomenologv of GUT nionopoles 8.2. Hcavv-monopole detectors 9. Fractionally charged particles 9.1. Introduction 9.2. Cosmic-ray searches i),3, Searches for fractional charges residing on hull~ matter 1)4, FCP extraction experiments 9.5. Future prospects 0. Heavy particles bound in nuclei 1(1.1. Introduction (1.2. Experimental searches II. Medium-range forces 11.1. Introduction 11.2. Limits on a and A 11.3. The composition dependence of MRF’s 11.4. Recent developments 12. Galactic dark matter 12.1. Introduction 12.2. The cosmographs of dark matter 12.3. Axions 12.4. Light neutrinos 12.5. Heavy weakly interacting particles 2.6. Quark nuggets References Notes added in proof

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351 362

Present address: Lahoratoire de lAccélérateur Linéaire. (‘entre dOrsay, F-9I405 ()rsav. France

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J. Rich et al., Experimental particle physics without accelerators

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Abstract: We review the phenomenology, the techniques, and the results of particle-physics experiments that are performed beyond the confines of accelerator laboratories.

Introduction Particle accelerators have, for the past 30 years, been the sine qua non of experimental elementaryparticle physics, and progress in accelerator design has been the key to successive advances in our understanding of elementary particles. During the two decades following the construction of the first accelerator by Cockcroft and Walton in 1932, the contributions made to particle physics by acceleratorbased experiments grew steadily in importance. By the late 1950’s, the dominant role of accelerators was firmly established: the discovery of parity violation in nuclear beta decay was the last major discovery to be made by an experiment not performed at an accelerator. Since then, all the fundamental discoveries from which the standard SU(3) x SU(2) X U(1) model has been forged have been made at accelerators. Recently, however, elementary-particle physicists have found their attention drawn with increasing frequency towards experiments performed beyond the perimeters of accelerator laboratories, experiments for the most part addressing issues beyond the Standard Model. By way of illustration, let us recall some of these instances. First, there is the field of “underground physics” (the term itself is a 1980’s neologism coined to denote the activity of increasing numbers of high-energy physicists). From 1982 onwards, several dedicated proton-decay detectors came into operation, and, as their exposures increased, became the intermittent focus of attention of an expectant public. By 1985 or thereabouts, it was becoming apparent that the proton was more stable than it should have been according to the simplest of Grand Unified Theories, but a new surprise was in store for us: two experiments reported sightings of Cygnus X-3 that were of a decidedly perplexing character and that would have considerable ramifications within particle physics if confirmed. Between 1977 and 1981, a magnetic-levitation experiment accumulated growing evidence of the existence of fractional charges residing on superconducting niobium balls. In 1982, an experiment using a superconducting current loop reported an event that was consistent with having been caused by a magnetic monopole. Non-accelerator neutrino experiments have reported several tantalizing results. Neutrinos originating in the Sun were not detected on Earth in sufficient numbers; those emanating from the core of a nuclear reactor appeared to oscillate; and those emitted in the beta decay of tritium bound in valine molecules were reported to be massive. Lastly, in early 1986, a re-evaluation of the original Eotvos experiment suggested that the existence of fifth fundamental interaction, a hypothesis supported by the results of a group studying the variation of the acceleration due to gravity with depth below the Earth’s surface. This catalogue of often provocative experimental reports is not meant to typify the manifold branches of “non-accelerator particle physics” (another deplorable but convenient term!). It does, however, manifest some features common to many of the particle-physics experiments that can be performed without accelerators. One feature that we wish to emphasize is the scope of such physics: the diversity of experimental questions that can be raised without recourse to accelerators is, as we shall see, substantially greater than the above list indicates. Another feature, which is amply demonstated by

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the examples we have cited, is that experiments performed without the benefit of accelerators sometimes have the potential to change our perception of elementary particles in a profound way. A corollary of the latter feature is that non-accelerator experiments are often speculative in their goals or serendipitous in their discoveries. It is not surprising, therefore, that end results are usually negative, or that preliminary findings, when positive, remain unconfirmed or are contradicted by other experiments. This does not mean that non-accelerator experiments are in any way less reputable than the generally less speculative experiments performed at accelerators. There is, though, a tendency on the part of accelerator-based physicists towards a certain degree of skepticism in their acceptance of the findings of non-accelerator physicists. It is, therefore, one of the aims of this review to ensure that the many solid contributions made to particle physics by non-accelerator experiments are not masked by rare reports of sensational observations which later proved to be untenable, and which are partially responsible for the skepticism mentioned above. The idea of a negatively defined review encompassing many disparate areas of particle-physics research evolved from a series of lectures given by one of us (M.S.) at the 1985 Cargèse Summer School. The response elicited by the topics discussed made it clear that the diversity of non-accelerator physics and the novelty and ingenuity of the techniques used in its execution represented a refreshing change of pace in the School’s program. We hope that this is reflected in these pages. We realized, at the outset, that any attempt at completeness in reviewing such a diverse and rather arbitrarily defined field would not only he of dubious value but far beyond the bounds of our competence and patience. We, therefore, assigned ourselves the more pleasurable task of performing an eclectic survey intended to convey the breadth and diversity of the field and the relevance of the results that have been and can be obtained without the use of accelerators. It turned out that most non-accelerator experiments could be classified under one (or more) of eleven broad headings, and that we could, without omitting too many specific research topics, organize our subject matter into eleven self-contained chapters. We have, in general, opened each chapter with discussion of the phenomenology underlying the area of research concerned in order to highlight the potential rewards of experimental efforts in that area. We have then described the experiments that are current or planned more by outlining the techniques involved than by presenting the specific details of individual experiments. We have closed each chapter with a summary of the results that we were aware of at the time of writing and with an indication of what might reasonably be achieved in the future. The first three chapters deal with measurements of the properties of known particles: Chapter 2 Neutrinos Three categories of experiments are discussed: (1) Direct mass measurements, in which the mass of the neutrino (antineutrino) is inferred from the shape of the energy spectrum of the observed particles in a particular beta decay. (2) Neutrino-oscillation experiments, in which the neutrino source is either cosmic rays, a nuclear reactor, a supernova, or the Sun. In the latter case, we give particular attention to the recent theoretical discovery that the presence of matter may strongly affect the propagation of neutrinos. (3) Double-beta-decay experiments, which may be capable of determining whether neutrinos are Dirac or Majorana particles as well as being sensitive to their mass. Chapter 3 Neutrons Here two categories of experiments are discussed: (I) attempts to measure a T-violating electric dipole moment; and (2) attempts to observe baryon-number violation through neutron oscillations. Chapter 4 Protons The status and the future of the search for proton decay is reviewed. —

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The next two chapters are concerned with experiments addressing the properties of known interactions: Chapter 5 Atomic parity violation We discuss two types of experiments those based on optical rotation, and those based on Stark-induced forbidden transitions both of which are sensitive to parameters of the Weinberg— Salam—Glashow theory. Emphasis is given to the general phenomenology of parity-violating effects in atoms. Chapter 6 Time variations of the fundamental constants We discuss the present limits on time variations of coupling constants and the relevance of these limits for dynamical theories of coupling constants (Superstring and Kaluza—Klein theories). The next chapter is a bit of a mixed bag, embracing topics more loosely connected than in other chapters. Chapter 7 Cosmic-ray physics We begin with a description of what is known and what is conjectured about the primary cosmic-ray spectrum. There follows a description of some of the experimental techniques used to exploit its existence as well as to determine more about its characteristics. Modern aspects of the traditional role of cosmic rays in particle physics, i.e., as a “beam”, are then discussed and illuminated by examples of current research work. The remaining portion of the chapter is a fairly full account of recent observations connected with Cygnus X-3. The last five chapters are devoted to searches for hypothesized new particles of one sort or another. Chapter 8 Magnetic monopoles We concentrate on the two techniques induction loops and specific-ionization detection currently used to search for non-relativistic GUT monopoles. Chapter 9 Fractionally charged particles The status of three types of searches are briefly treated: (1) cosmic-ray searches; (2) searches for such particles residing in bulk matter; and (3) attempts to extract them from bulk matter and then detect them. Chapter 10 Heavy particles bound in nuclei In this chapter we consider experiments searching for very massive charged particles, which might have come into being during the early stages of the Big Bang, and which may be detectable as relics of that earlier epoch bound in nuclei. Chapter 11 Medium-range forces We discuss the phenomenology of a hypothetical interaction mediated by a boson of small but non-zero mass, and present existing limits on the parameters of such an interaction. Chapter 12 Galactic dark matter The evidence for its existence is reviewed; the candidates proposed as its constituent are discussed; and detection methods are described. A glance’ at the chapter titles reveals two broad classes of experiments, each with its own reason for not being performed at an accelerator. In experiments of the first class (chapters 7, 8, 9, 10 and 12) the energy range of interest is above that accessible with current accelerator technology. In the case of cosmic-ray “fixed-target” physics, this is only just the case the gap between the top accelerator and primary-flux energies is closing. In the case of the other investigations, the particles sought could now only exist as relics of the Big Bang. In experiments of the second class (chapters 2, 3, 4, 5, 6 and 11) the effects sought are small, and it is a large accumulation of particles that is required rather than high-energy beams of particles. Not only —

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J. Rich et a!. - Experimental particle physics without accelerators

would high energy be a nuisance, but, at least in the case of atomic-parity-violation experiments, the whole point is complementarity with high-energy experiments through the investigation of a different energy regime. We note that while these experiments are “low-energy” experiments, some (like proton-decay experiments) deal with virtual effects of hypothesized super-massive particles. As mentioned earlier, Nature has apparently decided not to reveal herself to us in any fundamentally new guise through the medium of non-accelerator experiments at least for the time being. With the exception of a handful of experiments (on atomic parity violation or on cosmic rays), the results of the experiments that we have discussed are or may be expected to be negative, yielding only constraints on current and future conjecture. While such results are, of course, valuable, leading, as they do to the elimination of some speculations (e.g., SU(5)) and to the development of new hypotheses (e.g., quark confinement), it would be tremendously encouraging if a positive result were to reward the efforts of non-accelerator particle physicists a little more frequently. It is, nevertheless, clear that non-accelerator particle physics has a very active future, as is witnessed by the growing number of such experiments that are in preparation or planned and by the growing number of high-energy physicists who are foresaking the accelerator laboratories (albeit often on a part-time basis) to participate in them. Before starting with the physics we shall make some comments about references. Because of the vast nature of the subject, much attention has been payed to providing a list of references that will guide the reader to the relevant details. Priority has been placed on specialized reviews and the most recent work in the field. This may have resulted in some slighting of authors who did the pioneering work in a given field, and we apologize to these people in advance. —

Acknowledgments In the preparation of this review, we have learned much from conversations with a whole host of specialists. Special thanks goes to R. Barloutaud, R. Bland, M.-A. Bouchiat, J. Bouchez, D. Caplin, G. Chardin, M. Cribier, W. Hampel, T. Kirsten, W. Kolton, W. Kundig, J. LoSecco, W. Mampe, A. Messiah, G. Morpurgo, T. Quinn, B. Sadoulet, A.Yu. Smirnov, P. Smith, C. Speake, F. Stacey and D. Vignaud. Needless to say, these people are not responsible for errors and omissions. For help in the final preparation of the manuscript, we would also like to thank the technical staff of the D.Ph.P.E., Saclay, especially M. Bertevas, D. Breisch, 0. Lebey, H. de Lignieres and J. Mazeau.

2. Neutrinos 2.1. Introduction Thirty years after the discovery of the electron antineutrino in nuclear beta decay, basic questions about the nature of this particle and of its antiparticle remain unanswered. While we know that its mass is less than 40 eV, we do not know what that mass is. We do not know if beta decay produces only one kind of neutrino, or if the “va” is really a mixture of more than one kind, each with its own mass. We do not know if the neutrino and antineutrino are distinct particles (as is the case for other fermions) or are the same particle (as is the case, for example, with the neutral pion). This unfortunate state of affairs is, of course, due to the smallness of the physical parameters involved (masses and mixing angles). As we shall see, there are few known effects that are sensitive to neutrino masses or mixing angles not too far below present upper limits. Further experimental progress

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will depend, then, not only on the improved precision brought by technological progress, but also on the discovery of new effects that depend on these parameters. Currently popular theories (see the reviews of Langacker [1981],Kayser [1985]and Vergados [1985]) give a little guidance. Though Grand Unified Theories (GUT’s) seem to prefer neutrinos that are identical to their antineutrinos (Majorana neutrinos), our lack of understanding of fermion mass generation prevents the prediction of masses and mixing angles, or even of their orders of magnitude. It is worth noting, however, that in “seesaw” mechanisms for the generation of neutrino masses, small values of neutrino masses and mixing angles are due to the existence of particles of very large masses, e.g., mGUT 1014 GeV. Neutrino experiments could, therefore, give information about physics at energy scales beyond those accessible with accelerators. Recent reviews of neutrino physics were given by Boehm [1984],Boehm and Vogel [1984], Ching and Ho [1984], Morrison [1985] and Winter [1985]. Here, we shall discuss the three types of experiments that are most likely to give information on neutrino masses and mixings. The first type attempt to measure the masses of beta-decay neutrinos via their influence on the form of the electron spectra (so-called “direct mass measurements”). In addition to discussing recent experiments in this field, we give a brief introduction to the phenomenology necessary for their interpretation. The nature of this introduction is intended to emphasize the similarities between neutrino physics and quark physics and the relationship between direct mass measurements and the second type of experiment, neutrino-oscillation experiments. Our phenomenological introduction to neutrino oscillations emphasizes Mikheyev and Smirnov’s recent discovery [1985,19861 that the presence of matter may strongly effect the propagation of neutrinos. The effect may be most dramatic in the Sun, where solar Ve can be transformed almost completely into v~during their voyage out of the Sun. This will make possible the investigation of a new range of neutrino mass differences and mixing angles, and is an example of a “new effect” alluded to earlier. Possible solar-neutrino experiments are discussed in some detail, as well as experiments using neutrinos from nuclear reactors, cosmic rays and supernovae. Finally, we discuss experiments on nuclear double-beta decay. In addition to providing information on neutrino masses, these experiments attempt to determine whether neutrinos and antineutrinos are distinct (Dirac particles) or identical (Majorana particles). A fourth class of experiments that could clarify the neutrino-mass issue comprises those that attempt to detect cosmological relic neutrinos. Such experiments will be discussed in the chapter on galactic dark matter. Here we only mention that, if a stable neutrino with a mass between 40 eV and 2 GeV were to exist, then the mass density of relic neutrinos would exceed the observed density of the universe [Cowsikand McClelland 1972, Lee and Weinberg 1977, Dicus et al. 1977]. This implies an upper limit of 40 eV on the mass of any light neutrino, a limit that is comparable with the laboratory limits on the mass of Ve~Indeed, it is the possibility that the neutrino is cosmologically important that has stimulated so much interest in experiments sensitive the masses in the eV range. 2.2. Direct neutrino-mass measurements* The most direct information on neutrino masses comes from measurements of the energies or momenta of the charged particles involved in the neutrino-producing decay. Studies of pion and kaon decay yield an upper limit of 250 keV for the neutrinos normally emitted in these decays (v~)[Abela et *See also Note added in proof.

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J. Rich et a!., Experimental particle physics withow accelerator,s

al. 1984]. Studies of T decay give an upper limit of 70 MeV for the tau-neutrino mass [Albrecht 1985]. Here, we consider only the process that gives the lowest limits: nuclear ~3decay. A general theoretical analysis of the information that can be gained from such spectra was made by Shrock [1980](see also the review of Vergados [1986]for subtleties that we will ignore in the following paragraphs). In general, the electron can couple to a number of neutrinos with different coupling constants. In the case of two neutrinos, the electronic weak charged current that couples to the W boson is then expected to be of the Cabibbo form: J~=éy~(1+y5)(~1cos8+~2sin8),

(2.1)

where e, and i~, are the fields of the electron and of the two neutrinos of masses m1 and m~,and the ratio between the coupling of the electron to the two types of neutrinos is simply tan 0. The linear combination of v~and v, that couples to the electron, r’~cos 0 + i-’2 sin 0. is called v~.If the “GIM” mechanism operates for neutrinos, we expect another charged lepton (e.g., the muon) to couple to the orthogonal combination of v1 and v2, i.e., x-~= r’~sin U + i-’2 cos 0. We can choose 8 by convention, in which case v~is “mostly” v~,and is identical with v1 in the case of the electron coupling to only one neutrino (0 0). Studies of electron spectra, as well as neutrino-oscillation experiments, give information on the three parameters m1, m2 and 0. Since we know that there are at least three neutrinos (Ve, v and vi), we expect the weak electron current to be more general than that of eq. (1) and to involve at least three massive neutrinos. The current would then be parametrized by the Kobayashi—Maskawa mixing angles. Nevertheless, eq. (2.1) is sufficient for a phenomenological analysis of the experiments discussed here. This is due, in part, to the fact that there is, at present, no confirmed evidence for non-zero values of m1, m-, or 0. We now consider nuclear 1~decay: ~-‘~

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where mz and mz+i are the initial- and final-state nuclear masses. Experimentally, one looks for the kinks in the electron spectra which should appear at the end point corresponding to a particular neutrino. Of course, the form of the kink will be modified by experimental resolution, and, if the nuclei are bound in atoms, by the spectrum of final atomic states. Historically, most interest has been centered on the high-energy tail of the electron spectra, corresponding to the end points for any light neutrinos. Recently, however, Simpson [19851reported an anomaly in the tritium ~3 spectrum at low energy. The deviation of the~spectrumfrom that expected for one massless neutrino could be explained by the emission of a heavy neutrino (17 keV) with a branching ratio corresponding to sin2 0 0.03. This effect was not confirmed in the spectra of other disintegrations [Ohi et al. 1985; Altzitzoglou et al. 1985; Markey and Boehm 1985] (see, however, [Simpson 1986]), and the anomaly may be due to atomic effects [Haxton 1985; Lindhard and Hansen 1986]. Nevertheless, the original report of Simpson serves to emphasize the point that it is not only the tail of the electron spectrum that is interesting. Interest in the high-energy end of the spectrum was greatly stimulated by the measurements of the Moscow group of the tritium 13 spectrum [Boris et al. 1985]. Their results were consistent with a single neutrino with a mass between 20 and 45 eV. Their group used an axial-field magnetic spectrometer to measure the momenta of electrons emitted from tritium bound in valine molecules. Tritium decay was studied because its low Q value (17 keV) gives a high sensitivity to low neutrino masses. Figure 2.1 shows their measured spectrum near the end point compared with the curves expected for neutrino masses of 0 eV and 30 eV. The Moscow result has been extensively discussed and criticized in the literature [Bergkvist 1985a, b; Ching and Ho 1984]. The difficulty in interpreting their results come from the fact that the measured neutrino mass, the experimental resolution, and the energy of the excited atomic states are all of the same order of magnitude. In contrast to the effect of a non-zero neutrino mass, the experimental resolution tends to lessen the slope of the Kurie plot. This is why the much awaited kink is absent from the slope in fig. 2.1. In this case, a measured mass depends critically on the estimate of the resolution for electrons near the end point. This resolution is estimated by using conversion electrons, but the procedure has been criticized [Bergkvist 1985b; Bennett et a!. 1985]. Another problem with the Moscow result concerns the final atomic states. In beta decay, conservation of energy applies to the system (atomic, molecular, crystalline) as a whole, and the final-state excitations must be taken into account in the calculation of the end point. In general, a discrete spectrum of states will be produced, each with its own end point and branching ratio. The spectrum is easy to calculate for atomic tritium, but difficult for the valine molecule. The problems involved are discussed by Ching and Ho [1984],Fackler et al. [1985]and Jeziorski et al. [1985]. A large number of new experiments to check the Moscow result are now in progress (see [Moriond 1986] for examples). Most use magnetic or electrostatic spectrometers. The Zurich experiment [Fritschi et al. 1986] has already published an upper limit for the neutrino mass (18 eV) that is barely compatible with the Moscow result. A different approach to the problem of the tritium spectrum is to use high-resolution calorimetry. This approach was pioneered by Simpson [1981], who measured the decay spectrum of tritium deposited in a silicon crystal. Since the energy of the ~3electron and of the photons from atomic de-excitations are deposited in the crystal, this method largely avoids the problem of excited states as well as those due to energy loss in the 13 source. Using a crystal with an energy resolution of 250 eV, he was able to set an upper limit of 60 eV on the neutrino mass. Further progress in this field will depend on the development of new calorimetry techniques. Superconducting tunnel junctions [Barone et al. 1985; Kraus et al. 1986] and bolometers [Coron et al. 1985] are possibilities. -~

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The best measurements of the neutrino mass have come from 13 emitters (yielding the antineutrino mass) since electron capture dominates for low-Q 13~ emitters. De Rujula [1981]pointed out that the photon spectrum in radiative electron capture: e +(A, Z)—*(A, Z— 1)+V+~,

is also sensitive to neutrino masses. The ratio of the capture rates from different atomic orbitals also depends on the neutrino mass, if the mass is not much larger than the Q value of the capture [Bennett et al. 1981]. 93pt (Q = 56.6 keV) yielded a limit of Measurements of the photon spectrum in the EC decay t come from the study of lower-Q 500eV for the neutrino mass [Ravn 1983]. Better limits ofmay transitions. The lowest ground-state-to-ground-state transition occurs in the EC decay of toAHo (Q = 2.58 keV), and this decay is, therefore, the subject of much study [Bennett et al. 1981; Hartmann

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and Nauman 1985; Yasumi et al. 1986]. Raghavan [1983]claimed to have observed the EC decay of to an excited state of ts8Gd with a Q of only 156 eV. While this claim was not supported by further investigation [LoSecco et al. 1985a; von Dincklage et al. 1985], it emphasizes the possibility of finding rare decay modes that may be sensitive to the neutrino mass. As in the study of tritium 13 decay, the study of electron capture should improve with the development of new calorimetry techniques. 2.3. Neutrino oscillations * 2.3.1. Vacuum oscillations In addition to looking at the charged lepton emitted in a decay, one can also detect the neutrino itself, or, more precisely, the particles recoiling from a subsequent neutrino collision. For example, one can observe: (A, Z)—s’(A, Z + 1) eli 12,

(2.4a)

followed by: v12+p—*e+fl.

(2.4b)

Once again, we shall use the current given by eq. (2.1) to2 discuss phenomenology. Reaction (2.4a) 0, and the produces 1i2 with a branching ratio produces i’~with a branching ratio proportional to cos proportional to sin2 8. Similarly i’~scatters via reaction (2.4b) with a cross section proportional to cos2 0, and li 2 0. If the experimental arrangement is such that 2 scatters with a crosswas section proportional to sin by the time of flight between decay and scatter), we can tell which neutrino produced (for example, the total rate for reaction (2.4b) is then proportional to cos4 0 + sin4 U = 1 ~sin2 20 (we neglect phase-space factors that favor the lighter-mass neutrino). This rate is less than the rate correspondingto no mixing (0 = 0). If ii 1 and ii2 couple to another charged lepton (e.g., the muon) through a coupling orthogonal to that of eq. (2.1), the deficit in rate will be compensated by the production of the other charged lepton, as long as the neutrino energy is above the production threshold (not the case in 3 decay). Neutral-current reactions would proceed at the normal rate if these couplings are, as expected, flavor independent. For small neutrino masses and in normal experimental configurations, the uncertainty principle prevents a determination of the species of neutrino emitted in reaction (2.4a) and absorbed in reaction (2.4b) [Kayser 1981]. For example, while the difference in mass of 1i1 and li2 results in a different velocity for the two neutrinos, if the neutrino detector is too close to the decay region, the wave packets will still overlap at the detector resulting in no significant difference in time of flight. In this case, the amplitude for li1 scattering interferes with the amplitude for 1i2 scattering (since the final-state particles are the same). Owing to the difference in the masses of the two neutrinos, their wave functions get out of phase by (m~ m~)lI2pduring their transit from the decay region to the scattering target (lis the decay-target separation and p is the momentum of the neutrino). This leads to a scattering rate that is an oscillating function of 1, and which is usually interpreted as the probability, P(Ve Ve), for the Ve from the source to be observed as a Ve after a distance I. It is given by the well-known formula: 2 20(1 cos 2irlIl~), (2.5a) P(Ve ~ = 1 ~sin —

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.

where ~m2 = m~ m~.Far from the neutrino source, the cos term in eq. (2.5a) will be averaged out —

due to a variety of effects: the width of the neutrino energy spectrum and the energy resolution of the detector, the spatial extent of the neutrino source, and, eventually, the separation of the wave packets for the two neutrinos of different mass. P(v 0-_*v~) then reduces to the result of the preceding paragraph. Neutrino oscillations are observed either by comparing the interaction rate of the neutrinos at two different distances from the source or, if the initial flux is known, by comparing the interaction rate at one distance with the rate calculated assuming no oscillations. Experiments that observe the production of the “normal” charged lepton are called “disappearance” experiments, and yield limits on P(Va~~v~), where a is the flavor of the v beam (a = e, p.. ‘r). Experiments that search for the production of the “abnormal” charged lepton are called “appearance” experiments and yield limits on P(v~—*v0) 2 20 and (=1 through P(V~_*V~) ~m2 eqs. assuming (2.5). two neutrinos). Knowledge of the V energy then yields limits on sin Figure 2.2 is a summary of published experimental results on vacuum oscillations obtained using a variety of v~and v~ beams. All experiments shown have given negative results apart from one experiment at CERN [Bernardi et al. 1986] and another at the Bugey nuclear reactor [Cavaignacet al. 1984]. Interpretations of the limits in the framework of models with three massive neutrinos have been made by Kleinknecht [1986](see also Ushida et al. [1986]). As is clear from eqs. (2.5) and fig. 2.2, in order to be sensitive to small ~ one must use low-energy neutrinos with the detector at the greatest distance from the source consistent with reasonable counting statistics. Table 2.1 shows average energies and maximum distances for six neutrino sources, as well as —

Table 2.1 Mean neutrino energy, source-target distance, and minimum measureable ~m2 for some past and future vacuum oscillation experiments Neutrino beam and reference Past experiments High energy accelerators [Ahrens et al. 1985J [Angelini Ct al. 1986) Fission reactors [Zacek et al. 1986] Cosmic rays [LoSeccoet al. l985b] Future experiments Meson factories [Moriond 1986) Solar neutrinos [Kirsten1986] Supernovae [Reinartz and Stodolsky 1985)

~E)

L (m)

~

1.2GeV 1.5 GeV

96 825

4x ID 7 x 10

2MeV

64.7

2 + 1))

1 GeV

6 x l0~

2 x 10

30MeV

24

3 x 10

300 keV

1.5 x ID

1(1’

10MeV

3 X l0~

10’ 211

(ev’)

251

J. Rich et a!., Experimental particle physics without accelerators

1000.0

100.0

—

J

I I [KARtI

BNL_-.-~ 734

1/

I

-

j

‘i\

BC’-’~”

10.0

‘..~.

‘~—--~

(\\PS191 I //

E BEBC

c

—

~

“.-.

10-

CFR

I

~ fi’ I’BHL

-—

i I

ROVNO

/ I

Ps—v~

Nt

\

~

SRP/

.1

BUGEY

‘

/ GOSIEN

.01 .001

.01

0.1 2

sin

1.0

(2~)

Fig. 2.2. Some experimental limits on the vacuum oscillation prameters for v, —f yr oscillations. The regions to the right of the lines are excluded; the shaded regions are preferred by the Bugey and PS191 experiments. BNL734 [Ahrens et al. 1985]; BNLBC [Baker et al. 1981], CHARM [Bergsmaet al. 19841; CCFR [Stockdaleet al. 1984]; CDHS [Dydak et al. 1984]; PS191 [Bernardi et al. 19861; BEBCPS [Angeliniet al. 1986]; ROVNO [Moriond 1986]; SRP [Sobel 1986]; BUGEY ~Cavaignacet al. 1984]; GOSGEN [Zacek et al. 1986].

the minimum value of ~.m2 to which the associated experiments are sensitive. Experiments using accelerator neutrinos, reactor neutrinos, and cosmic-ray neutrinos have produced significant results on vacuum oscillations; those using solar and supernovae neutrinos are sensitive to the smallest mass differences, but have yet to yield unambiguous results. In order to be sensitive to small mixing angles, it is statistically advantageous to perform appearance experiments. Unfortunately, this is not possible for the low-energy beams from reactors, from the Sun or from supernovae, since their low-energy ~e are below the threshold for producing p. or -r. Hence, the experiments most sensitive to small mixing angles [Ahrens et al. 1985; Zeitnitz 1985] are at accelerators, but they are sensitive only to rather large mass differences. An alternative way to be sensitive to small angles is to use the Mikheyev—Smirnov—Wolfenstein effect, the subject of the next section.

252

J. Rich et al.. Experimental particle physics without accelerators

2.3.2. The Mikheyev—Smirnov—Woifenstein effect

As Wolfenstein [1978] observed, the presence of matter modifies the propagation of neutrinos because of the effects of coherent forward elastic scattering. Z°-exchangediagrams (figs. 2.3a and 2.3b) contribute equally to the elastic-scattering amplitudes for all kinds of neutrinos, whereas the Wexchange diagram for neutrino scattering from electrons (fig. 2.3c) is operative only for Ve~This results in an index of refraction for v~that is different from that for v~and itt. In the case of two neutrinos, V~and v~,the combined effects of mass and index of refraction on the propagation of two wave packets p1(t) and v,(t), centered at x = ct, is determined by the equation [Wolfenstein 1978; Bethe 1986; Halprin 1986]:

(~

d ((m~/2p)+V~Gpcoc0 ‘dt ~PJ~ V~Gpsin0cos0 —

\/~Gpsin0cos0 ~ (m~/2p)+~Gpsin20!~i-~)

76

(~.

where p is the neutrino momentum, G is the Fermi constant,inand p is electron in the 2/2p take into account the difference mass andthe lead, for p =density 0, to vacuum medium. The factors of zXm oscillations. The factors of Gp take into account the forward scattering of Ve in its four channels: 2 0)

V~e-_Av

(amplitude cc Gcos

1e V

(ccGcosesine);

1e—*v2e

(cxGcos0sin0): and 2 0) v2e v2e (xG sin The v,~scattering then allows transitions between V V2e—*v1e -~

1 and v-, and gives the off-diagonal terms in the matrix of eq. (2.6). (We have made the transformation —G—-~’~/~ G from the formula appearing in Wolfenstein’s paper; see [Bethe 19861.) Equation (2.6) is a “Schrödinger” equation for a two-state system, so, in solving it, one can use all the normal results of quantum mechanics. The eigenstates of propagation are related to v~and through the density-dependent mixing angle Urn: =

cos Urn

~irn~

+ sin Urn

~“2m~

(2.7) =

—sin Urn a)

ktm)

+

cos

Urn k’2m)

b)

Fig. 2.3. Diagrams for neutrino elastic scattering on electrons and nuclei. The w-exchange diagram is operative only for

i’,,.

J. Rich et al., Experimental particle physics without accelerators

with

Urn

253

determined by the relation:

tan 20m

=

sin 20/(cos 20 + l~Il~)

(2.8)

,

where l,~,is the vacuum oscillation length given by eq. (2.5b), and 10 is the coherent-forward-scattering length of v~due to the W-exchange graph: 10= 2irI(V’~Gp) = 1.624 x io7 meters 6.02 x 10

cm

(2.9)

For zero density, 0m is equal to U and the propagation eigenstates are the mass eigenstates. At infinite density, Urn is equal to zero (if m 1 > m2) or rrI2 (if m2 > m1) so the eigenstates are ~~‘eand v1~.In fig. 2.4 we have plotted the eigenvalues corresponding to ~1m and P2m versus the density for the second case. Of primary importance for what follows is that, at infinite density, tie is the state with the higher eigenvalue. Equation (2.6) can be easily solved if p is constant. A Ve entering a region of constant electron density will oscillate between Ve and vp, with the probability of observing a Ve at a distance 1 given by: 2 28m (1— COS2IT1/lm), (2.lOa) P(Ve~t’Ve)= 1— ~sin where lm is the matter oscillation length given by: lm =

{1 + 2 (l~Il~) cos20 + (l~/lo)2}t/2

(2.lOb)

For zero density, eqs. (2.lOa) and (2.lOb) reduce to eqs. (2.5a) and (2.5b) for vacuum oscillations.

P res

Electron Density

Fig. 2.4. The eigenvalues of the matrix in eq. (2.6) as a function of the electron density p. The values are calculated for the case m 2 > m1 and for sin0

~K1.

The upper curve corresponds to the eigenvalue for

i’~,,and

the lower curve to the elgenvalue for v, ~

254

J. Rich ci al.. Experimental particle physics without accelerators

Mikheyev and Smirnov [1985,1986] identified two interesting phenomena that occur if zXm2 is negative (i.e., m 2> m1). This corresponds to the electron coupling predominantly to the lighter of the two neutrinos, and is the mass ordering observed in the weak interactions of quarks (i.e., m5 > md). The two phenomena are referred to collectively as the “MSW effect”. For m2 > m1, L,. is negative and eq. (2.8) says there exists a densiy, PreS’ where Urn = —~m I MeV/c 23cm3 =657 10~eV2

(~11)

Pres

-.

6.02x10 The resonant density. marked in fig. 2.4, corresponds to the density where the two states,

i-’tm

and

ti 2,1,

would be degenerate in the absence of vacuum mixing (i.e.,and for 0(2.11) = 0 in eq. an (2.6)). At thislength density,of:the 2 20rn, is unity. Equations (2.lOb) give oscillation oscillation amplitude, sin 6 —

m~Pres)

—6

2

2.48 xsin20 10 meters 1MeV/c p 10—~m2 eV -

2 12

For the 1 GeV/c neutrinos produced in the atmosphere by the decay of cosmic rays, these conditions are realized at terrestrial densities if —i~m— i0~eV2. The oscillation length is then comparable to the radius of the Earth (if sin 20 is not too small) and would result in a difference in the upward- and downward-going cosmic-ray neutrino fluxes [LoSecco 1986; Carlson 1986]. An even more spectacular effect may occur with solar neutrinos in the Sun. Here the density is not even approximately constant along the neutrino trajectory but falls slowly from higl~density (p —~100), where Ve are produced, to zero at the surface of the Sun. At each point along its trajectory, the neutrino state, v(t)), is some linear combination of the local propagation eigenstates, ~ and v —‘-

2m~: =

a(t)

tiirn~

+ b(t)

~2rn)

(2.13)

Since the neutrino is produced as v~,a(0) = cos Urn and b(0) = sin UrnS where £1~, is calculated for the density at the production point. As the neutrino travels outwards, the density falls to zero, and a(t) and b(t) evolve in accordance with eq. (2.6). The neutrino then leaves the Sun as some combination of V~and v~.A particularly simple case occurs when the density changes “slowly”. In this case, the magnitudes of the coefficients a(t) and b(t) remain constant in time: =

Ia(0)~ ,

b(t)I

=

b(0)~.

(2.14)

The phenomenon is well known to students of quantum mechanics as an application of the adiabatic approximation (see, e.g. [Messiah 1986]): if the Hamiltonian of a system changes slowly, the basis vectors change, but no transitions are induced between states. If a system started in a given eigenstate. it remains in that (time-dependent) eigenstate. In the standard quantum mechanical calculation, “slowly” means (d0m/dt) <(C/lm). The mixing angle changes most rapidly near the resonant density where it goes from 7r/2 to 0. The above condition on the time derivative then translates to a condition on the density gradient at the resonant density: I dp pdr —

—<

~m’~

2p

tan2Osin2U.

(2.15)

J. Rich et a!., Experimental particle physics without accelerators

In the Sun, we have p1(dp/dr) P

-~

255

1.3 X 10_8 meter1, so this becomes


Pmax =

200(MeV/c) sin 20 tan 20 (—~m2I106eV2).

(2.16)

Neutrinos with momenta below Pmax satisfy the “adiabatic condition”, and develop according to eq. (2.14). For higher momenta, the development is more complicated, but an analytic solution has been given [Parke 1986]. For p > 10Pmax’ the neutrino is essentially unaffected by the solar matter and leaves the Sun as The interesting case occurs if the adiabatic condition is satisfied and if the density at the point where the neutrino is produced is higher than the resonant density given by eq. (2.11). Equation (2.8) then tells us that the neutrinos are produced primarily as V 2m (Urn i’r/2 at the point of origin). Going to the surface, the neutrinos remain in this (density-dependent) eigenstate and emerge as v2. Referring to fig. 2.4, the neutrino has stayed along the upper curve (corresponding to the higher eigenvalue) its 10Pmax)’ neutrino will shift during from the trajectory. If the adiabatic condition is badly broken (p> upper curve to the lower curve as it passes through the resonant region. The condition that the central density be greater than the resonant density can be written: P

(2.17)

>Prnin’

Pmin = 0.075

(MeV/c) cos 2U(—~m2/106eV2).

Equations (2.16) and (2.17) give the momentum range in which solar Ve’S emerge from the Sun as v 2, 2 0. The suppression function is shown as the equivalent to a suppression of the Ve flux by a factor sin solid lines in fig. 2.5. Of course, if Pmin > Pmax’ there is no region of suppression. This sets a lower limit on sin2 20 of i0” for the neutrino transition to occur. Under the conditions of maximum Ve suppression, no oscillations occur between the Sun and Earth because i-’ 2 is a mass eigenstate. When this beam of v2 passes through the Earth to the neutrino detector we have a situation that is analogous to K~regeneration when a KL beam passes through matter, Since i-’2 is not an eigenstate in matter, there will be oscillations between v2 and v1. Since v1 is mostly v~ this will regenerate a Ve flux. For a medium of constant density, the probability for a v2 beam to yield a Ve after a distance d is given by: 2 0 + sin 20m sin 2(Orn — 0) sin2(lrd/lrn). (2.18) P(v2—* Ve) = sin While the density profile of the Earth is not constant, we would expect the regeneration effect to be important if the angles Urn and (Urn 0) for typical terrestrial densities are large and if the ratio between lrn at these densities and the diameter of the Earth (12.5 X 106 m) is not too large. These conditions give [Bouchez et al. 1986]: —

sin2 20 > 0.01

(2.19)

p---2(MeVIc)(—~m2/106eV2).

(2.20)

and

256

1

1. Rich ci a!.. Experimental particle phvsic.s without accelerators

~

/

12.11

/

10’

~

S

51

-,

10’

I

.

..~,..,1

10’

//

10’

106

6 .

__

/ / /

I

““I~

.

.

.

/7

/

am

II

~H~,IH.~=/

106

am

1”’’”’,’

/

1

S~

2 am

0

4.

106

/

,

/

101

,

,

/

midnight

~ ,

/

2

1

[

1

~.

10’

________

lo’

106

10’

Fig. 2.5. Probability P(v~—~v) that a solar v,2). produced nearlines thecorrespond center of the still effect a v~ when reaches a detector on Earth. The probability is The solid to Sun the is solar aloneit (day observation). The dotted lines are for the a function of p/sm (pin MeV/c, .~m’in eV winter solstice at different hours between midnight and dawn, and at latitude 42°N.

The range of neutrino energies defined by eqs. (2.19) and (2.20) is generally contained in the range defined by eqs. (2.16) and (2.17). Therefore, regeneration effects would be important only if the MSW transition has occurred in the Sun. The regeneration is, in general, an oscillating function of p~and the local time since it depends critically on the ratio between the oscillation lengths typical of terrestrial densities and the length of material traversed. Figure 2.5 shows an example of the Ve suppression as a function p/~m2at various times during the night of the winter solstice (dotted curve) [Cribier et al. 1986a]. The latitude was taken to be 42°N which corresponds more or less to the Gran Sasso, Homestake, and Baksan laboratories. The full curve is the suppression function due to the Sun only (day observation) and reflects the values of Pmin and Prnax for the given value of sin2 20. The effects of regeneration in the Earth are superimposed on the Sun suppression function for various times during the night, If the Earth had a uniform density profile, the minima in the suppression would correspond to values of p/sm for which the path length was an integral number of oscillation lengths. The magnitude of the regeneration would be determined by the magnitude of the momentum-dependent mixing angle for this density. Measurement of the form of the suppression would serve to determine ~m2 and sin2 20 through eqs. (2.19) and (2.20). The situation is more complicated in the case of the Earth’s actual profile, but could yield the same information.

J. Rich et a!., Experimental particle physics without accelerators

257

The MSW effect in the three-neutrino case was studied by Kuo and Pantaleone [1986a,b], Baldini and Giudice [1986], and Smirnov [1987]. The level diagram analogous to fig. 2.4 now involves three level crossings (one at super-high density due to radiative corrections to v~and v~scattering). As in the two-neutrino case, a neutrino will leave the Sun in the highest-mass state if the density at the production point is sufficiently high and if the adiabatic condition is fulfilled. This happens if the momentum falls in an interval determined by two equations like (2.16) and (2.17). If the neutrino momentum is not in this range, it will leave as the second most massive neutrino if its momentum falls in another similar momentum interval. Outside these two intervals, the neutrino will leave the Sun in the lowest-mass state (the one that presumably couples strongly to electrons, i.e., mostly Ve). Thus, we expect two regions of suppression of the Ve flux. If the regions overlap, the situation becomes rather complicated. Nevertheless, the essential features of the two-neutrino case remain, i.e., an energydependent Ve suppression and regeneration of Ve during the passage through the Earth. 2.3.3. Solar-neutrino experiments The Sun is a source of Ve produced in the thermonuclear reactions in the solar interior. Figure 2.6 shows the spectrum of solar neutrinos calculated according to the “Standard Solar Model” [Bahcall et al. 1982, 1985; Bahcall 1986a]. The spectrum is dominated by neutrinos from proton fusion, the so-called “pp” neutrinos: p+p-~*2D+e~+ve.

(2.21)

This reaction produces a continuum of neutrinos with energies up to 420 keV. Other neutrinos come from electron capture in 7Be, from electron capture by two free protons (pep—* 2DVe), and from the beta decay of 8B, t3N and 150 Up to now, no experiment has detected pp neutrinos. Since, to good approximation, the Earth—Sun distance is fixed, a neutrino-oscillation experiment using solar neutrinos must compare the measured flux with the calculated flux. This requires that the calculated flux be independent of non-verifiable details of the solar model. This is the case for the pp neutrinos, whose flux is determined essentially by the observed solar luminosity. The flux of neutrinos f—I

huhll

I

lhhIIIj

.,~ii

t°crE x

9.

13r~j~

.—

o~

~j6~

~Be

-pep 8B

5. ‘l ~., 0.1

,

0.3

—

....i....i....I..

1

Ii

3

il 10

Neutrino Energy (MeV) Fig. 2.6. The solar-neutrino spectrum vs. neutrino energy (MeV) according to Bahcall et al. [19821.For line sources the flux is in cm’ continuous sources in cm’ s’ MeV~.

s~’,and for

J. Rich

258

et a!.. Experimental particle physics without accelerator.s

from other reactions is dependent on details of the solar interior. They are, however, useful to oscillation experiments if the oscillations result in a deformation of the spectrum of a given component, or if a neutral-current reaction can be used to determine the total (v~+ v~+ v1) flux. From the previous section, suppression of the tie flux may arise from vacuum oscillations between the Sun and the Earth or from the MSW effect in the Sun and the Earth. the case 5 km, theWe fluxfirst of consider pp neutrinos (E of vacuum Since the Earth—Sun 1.5 x that i0 since the neutrino energy spectrum 300 keV)oscillations. will be depressed if ~m2~ >10~distance eV2. (Weis note extends to zero, there is a suppression for any ~m2 in some part of the Spectrum.) If L\m2~> 10~’eV2, the extent of the solar core results in a Ve flux uniformly suppressed by a factor (1 ~sin2 20). Since the neutrinos are below the threshold for muon production, we can only perform disappearance experiments. This limits the sensitivity of solar-neutrino vacuum-oscillation experiments to rather large mixing angles (sin2 0>0.1). If z~m2is negative, the MSW effect will lead to a suppression of the v~flux in the momentum range given by eqs. (2.16) and (2.17). Within this range, one must also consider regeneration in the Earth, which, though a smaller effect, could lead to a higher ti~ flux during the night than during the day. To detect low-energy neutrinos we can use the reaction: —

(2.22)

V+n—Kp+e.

Since free neutrons are not available we must use neutrons bound in nuclei. Hence, we use a nucleus with Z protons and (A Z) neutrons: —

v+(Z,A)—A(Z+1,A)+e (+y).

(2.23)

Photons will be present in the final state if the nucleus (Z + 1. A) is left in an excited state which de-excites immediately by gamma emission. Since (Z, A) is, in most cases, stable. (Z + 1, A) will then decay back to (Z, A) via electron capture or I3~ emission with a lifetime typical of the weak interactions. The use of nuclear targets to detect low-energy neutrinos involves, at least, three problems. First, there is a non-zero threshold for neutrino capture given by the Q value for electron capture in (Z + 1, A). Thresholds are typically 1 MeV. excluding the detection of pp solar neutrinos. 7tGa is an exception, with a threshold of 233 keV. The second problem is that while the capture cross section to the ground state of (Z + 1. A) can be calculated from the electron-capture lifetime, the cross sections for neutrino capture resulting in excited nuclear states are not directly measurable. Techniques for estimating these cross sections have been discussed by Bahcall [19781,Mathews et al. [1985],Grotz et al. [1986]and Krofcheck et al. [1985].The target masses needed to detect a single solar-neutrino event per day range from several tons to hundreds of tons. The third problem is that, since the recoil nucleus has little kinetic energy, it is not observable with conventional detectors. This means that a real-time experiment will see only coincident photons and electrons. Experimentally, this signature is not sufficient to distinguish neutrino capture from the Compton scattering of gammas from the decays of radioactive impurities in the target. Even for materials of high purity, the rate of this reaction is much higher than the rate of solar-neutrino capture. A better signature results if the excited nuclear state of (Z + 1, A) has a lifetime longer than the time resolution of the apparatus (ins at best). This is the case for tt5In, where the state of ttSSn that is

J. Rich ci a!., Experimental particle physics without accelerators

259

reached by solar neutrinos (threshold = 130 keV) has a lifetime of 3.3 p.s. This experiment would allow a direct measurement of the solar-neutrino spectrum, since all the neutrino’s energy (except for the known threshold) is taken by the observed electron. Unfortunately, efforts to exploit this target have been hampered by the fact that ~5In is itself radioactive (T112 = 1015 yr), giving a rate of indium beta decay nine orders of magnitude greater than the rate for capture of solar neutrinos. That this experiment has still not been performed 10 years after its proposal by Raghavan [1976]bears witness to the difficulty of observing low-energy neutrinos in the presence of even small rates of radioactivity. The only proven techniques for observing solar neutrinos that avoid the third problem (though not the first and second) are radiochemical techniques based on the extraction of the produced nucleus, (Z + 1, A), from the target and its detection in a proportional counter via its disintegration by electron capture. Since the transmitted nucleus is now observed, the background comes not from gamma rays but from much rarer protons of energy greater than —~5MeV via (p, n) reactions: p+(Z,A)—A(Z+1,A)+n.

(2.24)

Such protons may be secondary products of cosmic-ray interactions, of (n, p) reactions, or of (a, p) reactions due to a’s from radioactive impurities. Hence, radiochemical experiments must be performed underground with low-radioactivity materials. Since the recoil electron is not observed, radiochemical experiments give only a total capture rate, which determines the integral of the flux above the threshold, weighted by the energy-dependent cross section. A combination of experiments with different thresholds [Bahcall 1978; Hurst 1984, 1985] could, in principle, determine the flux of the different components of the solar spectrum. It would, however, be difficult to observe deformations of individual components due, for example, to the MSW effect. The only solar-neutrino experiment so far performed is the radiochemical experiment of Davis et al. [Rowley et al. 1984]. The experiment uses the reaction: 37Cl—~37Ar+e. (2.25) v+ The threshold for this reaction is 814 keV, though most of the cross section corresponds to excited states of 37Ar with thresholds above 3 MeV. Hence, the experiment is sensitive mostly to the solar neutrinos from the beta decay of 8B. The 37Cl is in the form of 600 tons of C 2C16. According to the Standard Solar Model [Bahcallet al. 1985], this would give a neutrino capture rate of about 1 per day, or 6 Solar-Neutrino-units (1 SNU = 10_36 captures/s target atom). Since argon is volatile, it can be easily extracted by bubbling helium through the tank of C2C16. This is done once a month, after which the argon is separated from 37Ar the helium and concentrated into a small proportional counter where the electron capture of (T 1/2 = 34 days) can be observed through the detection of the characteristic Auger electrons. The extraction efficiency can be verified by the injection of a known quantity of non-radioactive argon. The experiment has measured a rate three times lower than the predicted rate. As was discussed above, this can be interpreted either as evidence for neutrino oscillations or as a failure of the Standard Solar Model. The various proposed solutions of this “solar neutrino puzzle” were reviewed recently by Haxton [1986a].Besides the neutrino-oscillation solutions discussed below, other solutions of importance to particle physics include those involving hypothesized weakly interacting particles in the Sun [Spergeland Press 1985; Faulkner et al. 1986; Gelmini et al. 1987], heavy charged particles in the Sun (see the chapter on heavy particles bound in nuclei), neutrino decay [Bahcall et al. 1986a], and large neutrino magnetic moments [Voloshinand Vysotsky 1986; Okun et al. 1986]. .

260

J. Rich ci a!.. Experimental particle physics without accelerators

If the disagreement is due to vacuum oscillations, there must be maximal mixing between three neutrino flavors, or between two flavors if the Earth happens to be positioned at a minimum of P(Ve~3Ve). A more plausible explanation is the MSW effect [Mikheyevand Smirnov 1985, 1986; Bethe 1986; Barger et al. 1986; Rosen and Gelb 1986; Kolb et al. 1986; Haxton 1986c; Bouchez et al. 1986; Parke and Walker 1986]. In fig. 2.7 [Bouchez et al. 1986; Cribier et al. 1986a], we show, in ~m2—sin220 space, the region (delimited by the solid line) where the MSW suppression would make the observed solar Ve flux consistent with the initial v~flux calculated by Bahcall et a!. The shape of the roughly triangular region is easily understood using eqs. (2.16) and (2.17). If the neutrino-oscillation parameters fell in the upper band, eq. (2.17) would give Prnin —‘2MeV, and above this energy the Ve flux would be suppressed by a factor sin2 0 1. In this case, the 37C1 experiment would see only the low-energy 8B neutrinos and those from 7Be electron capture. Along the diagonal side, eq. (2.16) gives Pmax -‘—6MeV so, if the parameters fell in this region, the chlorine experiment would see primarily the high-energy part of the 8B spectrum. If the parameters fell in the vertical band, the entire spectrum to which the chlorine experiment is sensitive would be within the part of the spectrum delimited by pm~and Prnax’ yielding an energy-independent suppression of about 1/3. Without the effects of the Earth, this region would be centered on a vertical line at sin2 U = ~. However, the Ve component is partially regenerated in the Earth, so the band is bent in to smaller angles to compensate. ‘~

I

11111111

rc~1mn

-—

1~TmrflrS~fl1mrn

E I

10.2

iB~

/

,~

/

-

-

-

c~ç~ io~’~

0.1 0.25

-----

-

N,

0.75 II

I 1/

IIIII!.~.

I

2

111111111

0. 1

niH

1

I iY 5

Fig. 2.7. The parameter space defined by —~m2and sin2 20. For parameters between the two solid contours, the initial solar v flux determined by the Standard Solar Model combined with the time averaged MSW suppression yields the observed counting rate for the chlorine experiment. The dashed and dotted contours show the suppression of the rate for an experiment using gallium.

J. Rich ci a!., Experimental particle physics without accelerators

261

To determine whether the chlorine result is due to a failure of the Standard Solar Model or to the MSW effect we will need some new experimental input. There are several possibilities: the observation of a suppression of the low-energy model-independent flux of pp neutrinos; the observation of a modulation in the solar Ve flux with the time of day or with season indicating Ve regeneration in the Earth; an independent measurement of the 8B solar neutrino (~e+ + v2) flux using a flavorindependent neutral-current reaction;inorthetheMSW observation 8B or pp) as expected effect. of a deformation of one of the continuous spectra of Ve ( We now discuss several proposed experiments that may be capable of observing these effects. Whether or not a given experiment can resolve the issue depends on the values of ~m2 and sin2 20. Two radiochemical experiments plan to observe the Ve from proton—proton fusion, using the reaction: v+StGa~~*7tGe+e_.

(2.26)

The threshold for this reaction is 233 keV, so about 60% of the anticipated capture rate (—125 SNU in the Standard Solar Model calculation [Bahcall 1968a]) would be due to pp neutrinos. In an experiment to be located in the Gran Sasso underground laboratory, the 71Ga is in the form of 100 tons of GaCl 3—HC1 solution [Kirsten 1986]. This yields a solar-neutrino capture37C1 rateexperiment. of 1 per dayOf in the Standard Solar Model. The detection method is essentially the same as in the great importance is that it may be possible to calibrate the experiment with a neutrino source of known activity. The source could consist of 100 kg of neutron-activated chromium which gives two monoenergetic neutrino lines through the electron capture of StCr [Cribier et al. 1986b]. The use of four such sources, each of an activity of 800000 Curies, would result in a calibration precision of 10%, well matched to the expected statistical error in the solar-neutrino capture rate after a four-year run. An experiment planned for the Baksan underground laboratory in the USSR [Barabanov et al. 1984] is similar, but the gallium is in the form of 60 tons of liquid metallic gallium. A combination of the gallium and chlorine results will further constrain ~m2 and sin2 20 assuming that the MSW effect is the cause of the low chlorine rate. In fig. 2.7 we have superimposed on the allowed region from the 37C1 experiment, the contours for the rate suppression in the gallium experiment. If the gallium rate is low (suppression by a factor of 0.6) only the MSW effect (or large vacuum oscillations) can explain the two experiments since modified solar models always give rates higher than this. The gallium experiment could, then, verify the presence of the MSW effect if —z~.m2is less than i05 eV2. A second way of verifying the MSW interpretation of the chlorine experiment would be the observation of a flux dependent on the time of day or on the season [Bouchez et al. 1986; Baltz and Weneser 1986; Cribier et al. 1986a, 1987; Dar and Melina 1986]. These effects are important if ~m2 and sin2 20 fall in the regions defined by eqs. (2.19) and (2.90). The chlorine experiment is not sensitive to a diurnal modulation because argon is extracted only once every two months. The experiment is, however, sensitive to a seasonal effect, and the lack of such an effect was used by Cribier et al. [1987]to exclude the region shown in fig. 2.8 where the December/June counting ratio should be greater than 1.5. As discussed by the authors, this ratio is rather insensitive to the flux calculated by the solar model. The forthcoming gallium experiments should see such an effect if the oscillation parameters fall in a region displaced toward smaller values of ~m2 by about an order of magnitude. Proposed real-time experiments (see below) are, of course, sensitive to a day/night effect. This effect is about twice as big as the seasonal effect for the same values of oscillation parameters.

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J, Rich ci a!., Experimental particle physics without accelerators

1 ~—3 A

C 1~

~—

\ \

108 i

lb

1o’

ill!

io~

I

i.__. .~

—

11l

I

10

o.i

2 28

6

Fig. 2.8. Same as fig. 2.7 except that, for parameters inside the solid line, theSinratio between the December and June counting rates for the chlorine experiment is greater than 1.5. The curve is calculated for the spectrum of the Standard Solar Model.

The last two ways of verifying the MSW interpretation of the chlorine experiment, the use of neutral-current reactions and measurements of the form of the v~spectrum, require real-time experiments. As discussed previously, such experiments are difficult because of the background from ambient radioactivity. Because of this and because of the need to understand the result of the chlorine experiment, present efforts are directed towards the detection of the high-energy neutrinos from 8B decay (end point —14 MeV) where the background from radioelements may become small. An experiment combining both a neutral-current reaction and a measurement of the form of the neutrino spectrum was discussed by Chen [1985]and Sinclair et a!. [1986]. It uses deuterium as a target for the reactions: v

+

2D—~ppe

(threshold =

1.44

MeV)

v

+

2D

(threshold

2.2 MeV).

and —~

pnv

=

The first reaction measures the solar v~energy spectrum (above the threshold) via a measurement of the electron energy, whereas the second measures the total solar-neutrino flux above the higher threshold. The deuterium would be contained in a heavy-water Cherenkov detector. About 50 tons would be necessary to detect one event per day. In the neutral-current reaction the neutron is identified through its radiative capture by another deuterium nucleus. The background for this reaction due to the capture of thermal neutrons from several sources makes it extremely difficult to observe. Other experiments using charged-current/neutral-current pairs of reactions were discussed by Raghavan et al. [1986]. Information about the 8B v spectrum may also come from studies of neutrino—electron scattering

J. Rich et a!., Experimental particle physics without accelerators

263

(see the review of Bahcall [1986b]): ye —~ve

This reaction proceeds through flavor-independent Z°-exchangediagrams and through a W-exchange diagram operative only for Ve• This results in a cross section for Ve about seven times larger than that for neutrinos of other flavors. Since the solar neutrino’s energy is shared by the final-state electron and neutrino, the solar-neutrino energy can be measured only if the scattering angle is determined. The effects of vacuum neutrino oscillation on the electron recoil spectrum were discussed by Krauss and Wilczek [1985].The MSW effect as it pertains to elastic scattering experiments was discussed by Cribier et al. [1986a] and Bahcall et al. [1986b]. An appropriate detector for observing neutrino—electron elastic scattering might be a solid- or liquid-argon time projection chamber [Baldo-Ceolin 1986]. The track length is long enough to be observed only for the neutrinos from 8B, and the rate is rather small: 1 event per day for 1000 tons of argon. For these “high-energy” (5 MeV) neutrinos, the electron track would point towards the Sun, thus providing a means to reject background and proof that the neutrinos really do come from the Sun. Another possible type of detector is the large water-Cherenkov detector as used in proton-lifetime experiments. In the 3000-ton Kamiokande II experiment [Hirata et al. 1986], the energy threshold is 10 MeV, and the experiment may soon reach the sensitivity necessary to see the high-energy part of the 8B spectrum. Besides these experiments designed to detect the 8B neutrinos, there are at least two proposals for real-time experiments to detect the neutrinos. The first uses the previously mentioned reactions in indium. Because of the extreme background problems due to the radioactivity of indium, the possibility of using this extremely attractive target depends on the development of new techniques based on superconducting detectors. Possibilities are superconducting tunnel junctions with massive indium electrodes [Booth 1984] and metastable superconducting grains [Waysand 1984]. A second possibility was discussed by Cabrera et al. [1985]who proposed the use of super-cold silicon bolometers to detect elastic scattering of neutrinos on electrons. The experiment would exploit the fall in specific heat with temperature. For example, a deposition of 100 keV in a 1-kg block of silicon at 1 mK would raise its temperature to 4 mK, a rise that could be observed as a heat pulse by a thermistor. (See, however, [Keyes 1986].) As discussed above, this type of experiment is extremely difficult because of the background from ambient radioactivity, but the authors hope to exploit the high purity of commercially available silicon. The bolometer experiment could also observe 8B neutrinos through the observation of nuclei recoiling from neutrino—nucleus elastic scattering. This reaction could also be observed with superconducting grain detectors [Drukier and Stodolsky 1984]. Finally, we note two planned geophysical experiments. The first [Henning et al. 1984] is sensitive to pp neutrinos: +

205Tl—+ 205Pb + e

(threshold = 43 keV).

The second [Haxton 1986b] is sensitive mainly to 8B neutrinos: v + 98Mo—~9tTc + e

(threshold

=

1.5 MeV).

These experiments measure the concentration of the final-state isotopes in deep underground deposits

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J. Rich ci a!., Experimental particle physics without accelerators

of the initial-state element. Since the lifetimes of 20~Pband 96Tc are several million years, the experiments measure the average solar-neutrino flux over such a period. These experiments are long-term versions of the gallium and chlorine experiments and check, for instance, if the low flux measured by the chlorine experiment is due to variations in solar-neutrino production over periods of millions of years. Both experiments suffer from a lack of direct measurements of the neutrino-capture cross section. 2.3.4. Supernova-neutrino experiments Supernovae are another neutrino source that could give information on neutrino masses and mixings. Supernovae are generally believed [Schinder et al. 1982; Freedman et al. 1977] to be an intense source of neutrinos through a v~pulse from electron capture by protons (neutronization) lasting 50 to 100 ms and containing neutrinos of energies between 7 and 17MeV. This v~pulse may be distorted, during propagation towards the Earth, through a variety of mass-related effects [Reinartz and Stodolsky 1985]. The subluminal velocities of massive neutrinos will separate the v~pulse into pulses for each mass eigenstate, and, within each pulse, there will be a correlation between energy and arrival time. The v~ will also be transformed into other flavor neutrinos via vacuum oscillations or the MSW effect in the supernova. These interesting effects may, however, be difficult to observe because of the rarity of observable supernovae (—1 per 20 yr). In addition, the pulse structure may be washed out because, after the neutronization pulse, the remaining stellar material is not completely neutronized, and one expects further neutronization to take place over a longer time scale (of the order of 500 ms) accompanied by additional bursts of v~.Other species of neutrinos (~, v~,i/~,v, i/f) are emitted mainly through e e annihilation. The fluxes of these neutrinos are more uncertain. Experiments are unlikely to be sensitive to the arrival times, to the energies, and to the species of the neutrinos. Existing experiments use ‘—‘100 tons of liquid scintillator and are sensitive to supernovae less than a few kpc far away. Since liquid scintillator is primarily sensitive to i~(see the section on reactorantineutrino experiments), these experiments are not sensitive to the v~from the neutronization pulse. The detectors are located at Homestake [Cherry et al. 1986], Mt. Blanc [Aglietta et al. 1986]. and Baksan [Alexeyev et al. 1986]. Future large experiments are planned in the Gran Sasso laboratory: the LVD detector [Alberini et al. 1986] will employ —‘1000 tons of liquid scintillator (which could, in principle, also detect elastic scattering of neutrinos on electrons making this experiment sensitive to ~ The ICARUS experiment [Baldo-Ceolin 1986] will use a 3000-ton liquid-argon time-projection chamber. Finally, experiments using coherent scattering on nuclei [Drukier and Stodolsky 1984] are attractive because of their large event rates. However, the feasibility of such detectors has not yet been established. -

2.3.5. Reactor-antineutrino experiments Nuclear reactors are powerful sources of i/c’s through the ~3 decay of the neutron-rich fission products. The detection of low-energy (—1—8 MeV) antineutrinos is now a well-established art based on the pioneering work of Reines [Reines and Cowan 1953]. The method uses on the reaction: -

v + p~

e~+ n.

If the protons are contained in liquid scintillator, the positron gives a prompt signal proportional to the neutrino energy less the reaction threshold (1.80 MeV). The recoil neutron is thermalized and performs a random walk to the edge of the scintillator container, where it can be absorbed in a neutron counter,

J. Rich et al., Experimental particle physics without accelerators

265

normally a 3He proportional counter. This gives a delayed, monochromatic pulse through the reaction: n + 3He—~p + 3H. The delay between the positron and neutron pulses is determined by the geometry of the detector, and is about 100 p.s for typical experiments. Currently, two experiments have published results of roughly equal sensitivity to neutrino oscillations. One was at the Gosgen power reactor in Switzerland [Zacek et al. 1985, 1986] and the other at the Bugey reactor in France [Cavaignacet al. 1984]. Both used about 3501 of liquid scintillator as the target, yielding event rates from 5 to 20 per hour depending on the detector’s distance from the reactor core. Neutron-detection efficiencies were about 25% in both experiments. The Gosgen experiment compared positron spectra and rates at positions 37.9, 49.9 and 61 meters from the reactor core. Their results were consistent with no oscillations and ruled out the area in the ~m2—sin2 20 plane shown in fig. 2.2 (the calculated flux is used to set the limit). The Bugey reactor compared spectra and rates at two positions 13.6 and 18.3 meters from the reactor core. They observed a difference in rate that was consistent with neutrino-oscillation parameters in the shaded region of fig. 2.2. Planned experiments at the Bugey reactor [Cavaignac1986], at Rovno in the U.S.S.R. [Afonin et a!. 1985], and at the Savannah River reactor in the U.S.A. [Sobel 1986] should resolve the existing experimental discrepancy. The new experiments will use a larger volume of liquid scintillator to increase the event rate. New neutron detectors using Li- and Gd-loaded scintillator should increase the neutron-detection efficiency to about 60%. These improvements should lower the minimum mixing angle to which the experiments are sensitive by a factor of —5. 2.3.6. Cosmic-ray neutrino experiments Cosmic-ray neutrinos result from the decay in the atmosphere of cosmic-ray pions, kaons and muons. Their mean energy is calculated [Gaisser et al. 1986] and observed [Haines et a!. 1986] to be near 1 GeV. Muon neutrinos dominate, but there is an important component of electron neutrinos from muon and kaon decay. The 1MB proton-lifetime experiment observed the interactions of these neutrinos and was able to set a limit on neutrino oscillations by comparing neutrinos coming from above (originating —1000 m above the detector) with those coming from below (originating i07 m from the detector). A change in the electron-neutrino content would be observed, since electrons give more visible energy in their detector than muons. In addition, muons can give a delayed signal from their decay after stopping in the detector. Their results [LoSeccoet al. 1985b] eliminate .~m2between i0~ and i0~eV2 for sin2 20 greater than 0.2 (assuming vacuum oscillations only). A better knowledge of the neutrino flux would allow them to extend their limit to higher values of dm2. The effects of possible resonant MSW oscillations on cosmic-ray neutrinos was calculated by Carlson [1986],Dar et al. [1986]and LoSecco [1986].Preliminary results from the 1MB collaboration [LoSecco 1987] require sin2 20 <0.08 for i0~<~m2< i0~.These results are interesting because they explore part of the region that solves the solar-neutrino problem (fig. 2.7).

2.4. Double-beta decay* 2.4.1. Phenomenology Interest in double-beta decay (for reviews see [Haxton and Stephenson 1984; Doi et a!. 1985]) has been stimulated in recent years with the realization that this reaction is the only known reaction sensitive to whether a neutrino and its antineutrino are identical particles (Majorana neutrinos) or *See also Note added in proof.

266

J. Rich

Ci a!., Experimental particle

physics without accelerators

distinct particles (Dirac neutrinos). In general, any particle with a charge or magnetic moment is distinct from its antiparticle, since its charge or magnetic moment will be opposite to that of its antiparticle. Since the neutrino is neutral and its magnetic moment is, for the moment, unmeasured, the two possibilities exist. It might be expected that we could use the weak interactions of neutrinos and antineutrinos to distinguish the two cases. Since we know that laboratory neutrinos scattering on stationary targets produce negative leptons and laboratory antineutrinos scattering on stationary targets produce positive leptons, we might say that this proves that neutrinos are not the same as antineutrinos. On the other hand, we also know that laboratory neutrinos are primarily left-handed and antineutrinos right-handed since they are produced in decays governed by V—A weak interactions. The fact that neutrinos produce negative leptons could be due to the fact that negative leptons couple to left-handed neutrinos and positive leptons couple to right-handed neutrinos (what we are accustomed to calling antineutrinos). If the neutrino is massive we can, in principle, distinguish the two possibilities by chasing the neutrino with a target going in the same direction as the neutrino but faster. In the rest frame of this target, one sees a right-handed neutrino coming toward a stationary target. If neutrinos are Majorana particles, a collision will result in the production of a positive lepton. If neutrinos are Dirac particles a collision will result in the production of a negative lepton, but the cross section for such a collision 2 to that for a left-handed neutrino. would be suppressed by a factor (m~/E~)relative The above gedanken-experiment illustrates the difficulty in telling whether the neutrino is a Dirac or a Majorana particle. If the neutrino has a mass of I eV and we take a laboratory neutrino of 1 GeV, a chasing proton would have to have an energy of more than lots GeV to see a I GeV right-handed neutrino coming toward it. Kayser [1985]has discussed several other possibilities. All experiments are hopelessly unrealistic with the exception of neutrinoless double-beta decay. Double-beta decay is a second-order weak process that may exist in two varieties, the 2v mode:

(Z,A)~(Z±2,A) and the neutrinoless mode: (Z, A)~(Z ±2, A)

:~:.

Other, more exotic, transitions involving the emission of hypothetical particles (e.g., the Majoron) are also possible [Caldwell 1987]. Double-beta decays are observable when the decay of (Z, A) to (Z ±2, A) is energetically allowed, but the normally much faster, direct, single-beta decay to (Z ± I, A) is energetically forbidden. Such is sometimes the case when both Z and A are even, since the nucleon-pairing interaction may give (Z, A) a greater binding energy than (Z ±1, A). The 2v decay is allowed in the normal Fermi theory of weak interactions, since it consists basically of the simultaneous decay of two neutrons in the nucleus. Lifetimes for the 2v 1~~3 decay are calculated to be in the range of lots to 1025 yr for the various nuclei subject to this mode. Phase-space and Coulomb corrections give the lifetime a strong dependence on T 11, the total energy liberated in a decay. This dependence gives an average lifetime, ~ near: 0, ~~~1023yr(1 MeV/T11)

J. Rich et al., Experimental particle physics without accelerators

267

for nuclei with T0 between 0.5 and 4.0 MeV. For a given T0, the predicted lifetime varies by about an order of magnitude owing to well-understood Z-dependent Coulomb corrections and poorly-understood nuclear matrix elements. The latter factor gives an uncertainty to the predicted lifetime that is typically of order 5. The predicted lifetimes for the 2v 13~I~~ are in the range of 1026 to 1031 yr and are, thus, more difficult to study. The greater lifetimes predicted are due to the Coulomb suppression of 13~emission and to the lower values of T0 available in the candidate nuclei. The Ov decay proceeds through diagrams like that of fig. 2.9, in which the neutrino from the beta decay of one neutron scatters off a second neutron to produce a charged lepton. (There is one diagram for each massive neutrino.) It is clear from this that the decay cannot proceed unless neutrinos are Majorana particles, since neutrons emit antineutrinos but scatter from neutrinos. Additional suppression of this decay comes from the fact that, even if the neutrino emitted by the neutron is a Majorana neutrino, it has the wrong helicity to scatter from the neutron with the full (V— A) amplitude. In order for the decay to proceed, must (V then either massive neutrino yieldingfor a adecay 2 or anweexplicit + A) part have of the alepton current. Calculations varietyrate of proportional to (mv/me) nuclei give lifetimes, rot, in the range: ‘rOy

-~

10 15±2yr{(myIm~)2 +

}

2 ?~

where ~ is the ratio of the V + A and V— A currents. The rates are subject to the same uncertainty in nuclear matrix elements as in the case of the 2v mode. However, the ratio between the Ov and 2v nuclear matrix elements is thought to be calculable with somewhat greater precision (see, however, [Vogeland Zirnbauer 1986]). Since current experiments are sensitive to lifetimes of over 1022 yr, limits on (mv/me) or ~j have reached the i05 level. It has been recently shown that, if the weak interactions are governed by a gauge theory, the Ov mode is possible only if the neutrino is a massive Majorana particle (see, e.g. [Takasugi 1986; Kayser 19871.) This simplifies the interpretation of double-beta experiments in terms of neutrino masses. A complication is that the diagrams like that of fig. 2.9 for each neutrino may interfere destructively, leading to a further suppression of the rate [Picciotto and Kopac 19851. In this case, Ov-double-beta experiments are really neutrino-oscillation experiments with the neutrino source and target in the same nucleus.

Fig. 2.9. A diagram for neutrinoless double-beta decay.

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J. Rich ci al.. Experimental particle physics without accelerator.s

2.4.2. Double-beta-decay experiments Double-beta-decay experiments have used a wide variety of techniques. Calorimetric techniques with the parent nuclei integrated into the active element are sensitive primarily to the Ov mode, since the sum of the two electron energies yields a monochromatic line at T0. Track-chamber techniques are sensitive to both modes, though the Ov modes may have less background. Geochemical methods measure the accumulation, over geological time scales, of the daughter nucleus in minerals containing the parent nucleus. Hence, this method can only determine total double-beta-decay rates and is useful primarily in cases where the daughter nucleus is a noble gas, since the concentration of these nuclei from other sources is expected to be small. In addition, the40K retention of heavy gases canthat be 40Ar from decay and certainnoble isotopes of Xe verified by theofmeasurement of the concentration of are products uranium fission. Another related technique, the radiochemical technique, measures the build-up of the daughter nucleus in a large amount of material containing the parent nucleus, this time under laboratory conditions. This technique is interesting in the case where the daughter nucleus is short lived, preventing its identification in geochemical experiments, but facilitating its identification in radiochemical experiments. The best limits on neutrino masses come from experiments using the decays ‘28Te—~‘28Xe, 130 Te—* 131) Xe, 82 Se—~82 Kr and 76 Ge—~76 Se. The Te decays were investigated geochemically by several groups with the most impressive results being obtained by Kirsten et al. [1983,1986]. In this experiment, Xe was extracted from 4.5 g of native Te and analyzed for isotopic content with a mass spectrometer. Table 2.2 shows the isotopic composition of the extracted Xe and that of atmospheric Xe, . . both relative to 132 Xe. For the most part, the composition of the Xe .in the Te is. consistent with the atmospheric composition except for a factor of 30 increase in the tellurium for ‘3°Xeand slight increases for 129Xe and ‘3tXe. The excess for isotopes 129 and 131 can be explained by resonant capture of thermal neutrons, whereas that for ‘30Xe can be explained by double-beta decay of 30Te with a lifetime of 2.6 x 102t yr. 3°Xeand ‘28Xe. The concentration limitis on m,, can be placed by comparing the concentrations ‘ of the decay rates of ‘28Te and of A t2RXe consistent with the atmospheric concentration, and theofratio ‘30Te is measured to be less than 3 x l0~ (95% CL.). If only the 2v decay is present, the ratio is expected to be 1.8 x l0~,consistent with the measurement. For the Ov decay, the ratio should be larger because the weaker T 1128Te dependence to decay that of(Tfour-body phase space decay (Tof two-body phase space compared t30Te enhances the low-Q t 1 = 0.869 MeV) relative to the 11 = 2.533 MeV). This allowed the authors to place a limit of 5 eV on the mass of the neutrino (assuming only one diagram of .

Table 2.2 Xenon extracted from 4.494 g native tellurium [Kirsten et al. 1983]. All isotopes are measured relative to Isotope 24Xe

Sample 0.3556 ±0.0280 (1.3208 ±0.0208 7.152 ±11.036 146.9 ±I).6 424.86±0.69 113.36 ±0.48 100 39.11 ±1)48 33.39 ±1)46

Atmosphere 0.3537 0.3301) 7.136 98.32 15.136 78.9 100 38.79 32.94

J. Rich ci al.. Experimental particle physics without accelerators

269

the type shown in fig. 2.9). As discussed previously, this limit is relatively insensitive to the nuclear matrix elements since the ratio between the 128Te and 130Te elements should be reliably calculable. The limit is also insensitive to possible systematic errors associated with gas retention and mineral age, which would cancel in the decay-rate ratio. The decay of 82Se to 82K has been studied using both geochemical and counter techniques. Geochemical measurements give an average lifetime of 1.5 x 1020 yr with an uncertainty of about 10% [Kirsten 1969, 1984]. A recent lower limit of 1 x 1020 yr for the 2v mode from an experiment using a time-projection chamber to observe the electron tracks [Elliott et al. 1986] removes a long-standing contradiction between counter and geochemical results in favor of the geochemical experiments. Elliott et al. set a lower limit for the Ov lifetime of 3.1 X 1021 yr. A limit on the neutrino mass can be made by assigning the entire geochemical rate to the 2v mode in order to determine the nuclear matrix element. The limit on the Ov lifetime then leads to an upper limit of —-‘20eV for m~. The strongest limits on Ov-double-beta decay come from experiments using the decay 76Ge—~76Se. Natural germanium contains 7.7% 76Ge and a normal germanium semiconductor detector would record a line at 2045 keV corresponding to the Ov mode (if it exists). A 1-kg detector of natural germanium would have 6 counts per year at this energy, if the lifetime for the Ov mode is 1023 yr. Of primary importance in these experiments is the elimination of background due to the ambient radioactivity. This is done by using shielding and low-radioactivity materials in the construction of the apparatus. Counting rates near i0~ counts/keV~s have been achieved in detectors consisting of —1 kg of germanium. Several groups are working in this field, and the most recent publication gives a limit of 2.5 x 1023 yr for the Ov lifetime [Caldwell 1986; see also Avignone et al. 1985; Bellotti et a!. 1984a, 1986]. Combined with calculations of the nuclear matrix elements, this gives an upper limit of 3 eV for the neutrino mass. Experiments in progress may lower the limit on the lifetime by, perhaps, another order of magnitude. The background levels may soon be low enough to permit the direct observation of the 2v mode [Avignone et al. 1985; Caldwell et al. 1986]. This would allow an independent determination of the nuclear matrix element and make any mass limits more reliable. Further progress for 76Ge may depend on the development of more massive detectors using new, cryogenic, calorimetry techniques [Fiorini and Ninikoski 1984]. Time-projection chambers will improve the limits on t2Se and permit the study of i34Xe and t3ôXe [Bellotti et al. 1984b; Forster et al. 1984; Thomas 1987]. Counter techniques for studying the decays of t00Mo and isoNd were discussed by Ejiri et al. [1986]. Radiochemical experiments may give results of 238U [Haxton and Stephenson 1984]. Finally, the development of isotope identification with lasers may increase the sensitivity for some decays, especially those involving daughters that are noble gases [Hurst et a!. 1985]. 3. Neutrons

3.1. Introduction The development of intense thermal and sub-thermal neutron sources at nuclear reactors has made a great number of fundamental physics experiments possible. Interest continues to be strong in highprecision measurements of the basic properties of the neutron: its mass, charge, spin, magnetic dipole moment, and decay parameters. Experimental limits on the neutron electric dipole moment provide important constraints for models of CP violation. Baryon-number violation is being sought in experiments on neutron oscillations. Finally, neutron diffraction experiments have permitted the

270

J. Rich ci a!., Experimental particle physics without accelerators

observation of gravitational effects on neutrons and several striking illustrations of basic effects in quantum mechanics [Greenberger 1983; Rauch 1986]. The role of neutrons in fundamental physics was reviewed by Byrne [1984].Here, we concentrate on two topics that have received much attention recently: the neutron electric dipole moment and neutron—antineutron oscillations.

3.2. T violation and the neutron electric dipole moment* The study of CP violation (see the reviews of Wolfenstein [1985,1986]) has been handicapped by the fact that it has been observed only in the neutral-kaon system. Other places where CP violation might manifest itself are in the decays of B mesons [Bigi and Sanda 1985] and, implicitly via the CPT theorem, in T-violating electric dipole moments (EDM’s) of elementary particles [Ramsey 1982a, b]. CP/ T-violating interactions generate EDM’s through radiative corrections to the electromagnetic interaction vertex, in ways similar to the way that CP/T-conserving interactions generate anomalous magnetic dipole moments. In the classical limit, these corrections give a Hamiltonian of the form: H=eDuE,

(3.1)

where u is the spin of the fermion, E is the electric field, and D is a length giving the strength of the EDM. This Hamiltonian is manifestly P and T non-invariant, and would lead, for example, to the precession of a particle’s spin vector about the direction of an electric field. The present limit [Altarev et al. 1981, Lobashev et al. 1984, Pendlebury et al. 1984] on the neutron EDM, D~<6 x 10_25 cm, is some eleven orders of magnitude smaller than the neutron’s Compton wavelength, which characterizes the strength of the magnetic dipole moment. Theories invented to explain CP violation in the neutral-kaon system have traditionally been tested by comparing predicted EDM’s with experimental upper limits. Most attention has been drawn by the neutron because its lack of an electric monopole moment (charge) allows the isolation of small effects due to a dipole moment. In addition, most theories predict larger EDM’s for the neutron than, say, for the electron, where comparable precision has been obtained via the study of high-Z atoms [Vold et a!. 1984; Fortson and Lewis 1984]. Of course, electrons do have measureable EDM’s in some theories [Zee 1985; Nieves et al. 1986], and measurements in atomic systems remain important as tests of CP/T violation in the leptonic sector. Possibilities have been discussed recently by Bialek et al. [1966], by Avishai and de la Ripelle [1986], and by Raab [1987]. Following the development of modern gauge theories, much theoretical interest has been centered on two possible sources of CP violation: the Higgs sector and the Kobayashi—Maskawa mass matrix (see the review of Bigi and Sanda [1985]).The simplest theories of the first type predict a neutron EDM of the order of the present experimental upper limit [Anselm et al. 1985], and may soon be ruled out. The second type generate a neutron EDM via diagrams like those in fig. 3.1. The values predicted are at least five orders of magnitude below the present limit [Ecg 1985; Hamzaoui and Barrosos 1985]. Two groups have published limits on the neutron EDM near 1025 cm [Altarev et al. 1981, Lobashev et al. 1984, Pendlebury et al. 1984]. The method common to both experiments is a measurement of the spin-precession frequency of neutrons in parallel magnetic and electric fields. An EDM would cause the frequency to change when the direction of the electric field is reversed. We note that for D~= 1025 cm, the EDM induces a change in precessional frequency of ~ rad!s in an electric field of 100 kV/cm. *See also Note added in proof.

J. Rich et al., Experimental particle physics without accelerators

___

T~

‘U

i

271

Fig. 3.1. Some diquark diagrams contributing to the neutron EDM in the Kobayashi—Maskawa model (from [Hamzaouiand Barroso 19851).

Both experiments make use of the peculiar behavior of very slow neutrons in their interaction with matter. The passage of such neutrons through matter can be described in terms of an index of refraction, n, given by [Fermi et al. 1950]: n2 = 1

—

A2NaCOhIrr

±

1a~BIT,

(3.2)

3, aCOh is the where A isforward-scattering the de Broglie wavelength neutron,p~is N is the the neutron number of nuclei per cm coherent length of of thetheneutron, magnetic moment, B is the magnetic induction, and T is the neutron kinetic energy. The + I is for neutron spins parallel! antiparallel to the magnetic field. As in standard optics, total reflection occurs for glancing angles less than cos_i n. Since aCOh is positive for some materials and negative for others, both total internal and total external reflection are possible. For neutrons with velocities near 80 m/s (cold neutrons), critical angles are typically about 5°,permitting the production of low-divergence beams in beam tubes. For neutrons with velocities below 6 m /s (ultra-cold neutrons), they may be totally reflected at all angles of incidence, permitting the construction of neutron bottles. Since the index of refraction depends on the orientation of the neutron spin, a judicious choice of material can result in neutrons of one polarization being reflected at a surface while those of the other polarization are~transmitted. This simplifies the production of the polarized beams necessary for EDM measurements. The experiment of the Leningrad group was described by Altarev et a!. [1981] and Lobashev et al. [1984].Here we describe the experiment of the ILL(Grenoble) group [Pendlebury et a!. 1984]. The apparatus is shown in fig. 3.2. Ultra-cold neutrons pass through a guide pipe and a polarizing foil to fill up a 5-liter storage volume consisting of two 25-cm-diameter beryllium plates separated by 10 cm of beryllia insulator. After a filling time of about 12 s, roughly 5000 neutrons are contained in the —

FIVE LAYER MUMETAL SHIELD GUtDE CHANGE-OVER SYSTEM GUIDE FROM UCN S RCE

GLASS VACUUM ENVELO

HIGH VOLTAGE LEAD

POLARISING MAGNET

POLARISING FOIL

SPIN FLIP COIL

NEUTRON UCN DETECTOR’ B FEL AND SHIELD

COIL

STORAGE V~J.R1E

im

Fig. 3.2. Apparatus used by Pendlebury et al. [1984]to measure the neutron EDM.

272

J. Rich ci a!., Experimental particle physics without accelerators

bottle, where they can be retained by closing the neutron valve. Storage times are typically 1 minute and are limited by various absorption processes in the walls. The storage volume sits in a static magnetic field of 10 mG, corresponding to a precession frequency of 30 Hz. An electric field of 10 kV/cm can be applied parallel or antiparallel to the magnetic field, and it is this field that would modify the precession frequency, if the neutron were to have an EDM. The spins of the neutrons are initially aligned with the static magnetic field in the storage bottle. After the filling of the bottle and the closing of the valve, the neutron spins are turned 90°into the plane perpendicular to the static magnetic field. This is done by the application of an oscillatory (—30 Hz) magnetic field perpendicular to the static field. This oscillatory field is applied for a time, 2 s. The neutrons are then allowed to precess about the static field for a time t2 40 s. After this a —

second oscillatory field pulse, phase coherent with the first, is applied for the same time, t1. The second pulse leaves the neutrons in a spin state that depends on the extent to which the spin precession and the oscillating field get out of phase during the time between the two pulses. The neutron valve is then opened, and the neutrons spill out. The polarizing foil now acts as a spin analyzer, and neutrons in the correct spin state pass through it into a neutron counter. Figure 3.3 shows the number of counts as a function of the frequency of the oscillating field. The curve has a form that is typical of separated oscillatory-field experiments [Ramsey 1980], with its center at the average precession frequency in the storage volume. The The difference is in agreement the of theoretical t slope,between dN/dp, successive has a valuemaxima between maxima and with minima order t value of (t2 +4t1/7r)

—tv.

2.

The EDM is measured by selecting a frequency that gives a maximum slope of the curve in fig. 3.3. Runs are then taken with the electric field parallel and antiparallel to the magnetic field. This shifts the entire resonance curve by an amount: h ~v = 2eD~E.

(3.3)

The EDM, D~,is then determined by the difference in counts, ~N, with the field parallel and antiparallel: eD5

=

h ~N/2ES,

(3.4)

200

OSCILLATING MA13NET~ FEW 0 29,5

I 29,6

I 29,7

FREQUENCY (Hzl— .

I 29,8

Fig. 3.3. A neutron magnetic resonance curve obtained by Pendlebury et al. [i964]. The solid line is a theoretical curve fitted using Ramsey theory.

J. Rich et a!., Experimental particle physics without accelerators

273

where S is the slope, dN/dv, of the resonance curve at the working point. The statistical uncertainty in this number is: 2eEt2 VW 10kV/cm is

-20

—5

X 10

cm

E

1

—

(3.5)

where N is the number of counts. We have approximated S by t2. The dependence on the storage time, t2, is one of the reasons for the improved limits given by experiments using storage bottles compared with those given by previous experiments using neutron beams. The limit on D~given by Pendlebury et al. is consistent with a purely statistical limitation, as given by eq. (3.5), in about 106 total counts. Progress is still being made by increasing the running time and neutron densities. Particular attention must be paid to systematic effects that could induce a counting bias for one orientation of the field over the other. Of special importance is the control of time variations in the magnetic field, and particularly variations correlated with the electric-field direction, due, for instance, to leakage currents. Experiments planned at both ILL and Leningrad [Golub 1984, Lobashev et al. 1984] should have sufficient statistics and a sufficient understanding of systematic effects to reduce the present limits by about an order of magnitude. 3.3. Neutron oscillations Interest in neutron oscillations (see the review of Baldo-Ceolin [1986])has been stimulated in recent years by gauge theories that predict the violation of baryon-number conservation. In general, such theories permit transitions between neutrons and antineutrons in the same way that interactions which change strangeness can change K°’sinto K°’s.Elementary quantum mechanics predicts that a beam of pure neutrons will, after a time t, develop an antineutron component whose amplitude squared is: 2{(~m2+ ~E2)~2t}, =

~m~~E2

(3.6)

sin

where ~m is the off-diagonal element of the neutron—antineutron mass matrix due to baryon-number violation, and ~E is the difference in the diagonal elements due to the fact that the neutrons and antineutrons are in a non-CPT-invariant environment (e.g., the presence of a magnetic field gives a neutron energy shift that is opposite that given to an antineutron of the same spin). In the above formula, we have neglected absorption (the imaginary parts of the mass matrix). Absorption provides a method of detecting the generated ,~‘sthrough their annihilation with ordinary matter. Apart from ~E, the development of the antineutron component depends on one theory-dependent parameter, ~m (or its inverse, ~ In Grand Unified Theories that conserve the difference between baryon number and lepton number (SU 5, for example), i~B= 2, E~L= 0 transitions are forbidden. This gives ~m = 0 and no oscillation. Partial unifications based 7ons, left—right symmetry [Mohapatra and which is within the reach of planned Marshak 1980] allow oscillations and give a ~ as low as i0 experiments (see also [Lazarides et al. 1986]). Two methods have been used to search for neutron oscillations. The first uses neutrons bound in nuclei. When a neutron is transformed into an antineutron, it annihilates with another nucleon in the

274

J. Rich et a!.. Experimental particle physics without accelerators

nucleus, leading to the production of pions as in proton decay. The problem with this method is that, owing to the presence of the nucleon potential, SE is quite large (of order 100MeV), and neutron oscillations are strongly suppressed. Roughly speaking, a nucleon in a nucleus develops an antineutron component that is equal to the time averaged value of n(t)~2 Sm2/25E2. The rate for the “decay” of the nucleus via n—n annihilation is then proportional to the product of this factor and the annihilation rate of an antineutron inside the nucleus, itself of order 1/SE. Hence, the nuclear lifetime, TN, is of order: —-‘

r~SE/A.

(3.7)

Complications neglected in this simple picture have been discussed by Kabir [1983]. Nuclear decay via fl—n annihilation would be characterized by the emission of about five pions, as is typical of low-energy baryon—antibaryon annihilation. Several proton-decay experiments have searched for such decays. The best limits come from the experiments using water Cherenkov counters [Jones et al. 1984; Takita et al. 1986]. These exeriments give TN >5 x 10~’yr for oxygen. This corresponds to a free-neutron oscillation time of about 108 s. The second method consists in using reactor neutrons propagating in a vacuum. In this case, SE is dominated by the Earth’s magnetic field, but a SE of ~~~l023eV can be obtained if the Earth’s field is sufficiently shielded. Figure 3.4 shows the apparatus used by Fidecaro et al. [1985].The neutron beam, which was brought to the experiment in guide tubes, had an intensity of 1.5 x ~ neutron/s over an area of 60cm2 with an average neutron velocity of 160 m/s. The neutrons passed through a magnetically shielded oscillation region 2.7 m long. At the end of the oscillation region was a 125-p.m thick carbon target, in which any antineutrons produced in the oscillation region would have annihilated. The target was surrounded by flash tubes and scintillators to identify the annihilation products and to veto cosmic-ray interactions, the primary source of background. The efficiency in identifying annihilations was estimated to be 0.3. A coil inside the shield could produce a magnetic field in the drift region. and was used to make background measurements by suppressing any potential oscillations. The number of antineutrons expected is determined by Sm and SE through eq. (3.6). Since the product of SE and the average time to travel across the oscillation region (t 06~ 0.025 s) was much less than unity in this experiment, eq. (3.6) reduces to the quasi-free form: —-—

=2(tOhS/tOSC)2.

(3.8)

i~(t06~)~ S Target

* ~

____________

~H~-+-T

l~

_

Streamer tubes

‘

p—metal shield

~J

Beam

Neutron guide

Fig. 3.4. Apparatus used by Fidecaro et al. [1985]to search for neutron oscillations. The figure shows the neutron guide (4.5 m long) and free flight vacuum vessel (2.7 m long) to the neutron beam dump and ñ detection system.

J. Rich et a!., Experimental particle physics without accelerators

Since no significant signal was observed, a lower limit could be set on t~>

N~rt~/N~ = 1.3

275

lose:

X 106 ~

(39)

where N~is the number of neutrons passing through the oscillation space (2.7 x 1016), r is the annihilation-detection efficiency (0.3), and Nb is the upper limit on the number of antineutrons observed (4). Experiments to improve this limit by at least two orders of magnitude are planned. One experiment under construction at ILL [Baldo-Ceolin 1984] should reach 108 s by increasing tobs (by lengthening the oscillation region) and by increasing the neutron flux (without significantly increasing the average neutron velocity). Other proposals are discussed in [ICOMAN 1983]. Experiments at meson factories [Iljinov et al. 1983] could, in principle, impose a lower limit of 1010 s on t~.

4. Proton decay 4.1. Introduction Modern interest in the stability, or otherwise, of the proton was stimulated by the advent (circa 1973) of Grand Unification Theories (GUT’s) and, in particular, by the natural way in which they incorporate proton decay. The GUT approach to unifying the Quantum Chromodynamics of strong interactions with the Weinberg—Salam—Glashow model of electroweak interactions, while, at the same time, removing some of the arbitrariness of both models, was extremely promising. The unification was to occur, however, on an enormous energy scale, and GUT’s portended a gloomy future for experimental particle phyics: the “desert” no new phenomena between the energy scale of electroweak unification (m~ 100 GeV) and that of grand unification (m~ iOH GeV). Possibly the only experimentally accessible consequence of GUT’s, and, thus, the only key to validating the theory, would be the predicted decay of protons and bound neutrons. The experimental task of searching for proton decay was and remains, a challenging one. Only the direct and unambiguous observation of several instances of the effect would constitute the incontestable evidence required, yet the proton lifetime in the simplest unification scheme was predicted to be in the region of 1029 to i03°yr. The amount of matter under observation had, therefore, to be correspondingly large (1030 protons weight 1.7 t), active throughout, and as free as possible of competing backgrounds. Two classes of detectors satisfied the demands of size and sensitivity at reasonable cost large water Cherenkov counters and large tracking calorimeters. Since the major source of background derives from cosmic rays, the detectors had to be adequately well shielded, and the simplest way of achieving this was to locate them underground. Seven proton-decay experiments have now been in operation for a number of years. The state of the science has been reviewed by Perkins [1984],LoSecco [1985], and, recently, by Meyer [1986].Although all experiments have observed candidate proton-decay events, either the events are consistent with background estimates, or their interpretation as proton decays is statistically incompatible with the results of other experiments. No convincing evidence of proton decay has been found. In addition, the minimal SU(5) GUT is in trouble: the lower bounds set on the proton lifetime in the decay channels favored by the theory appears to exclude the predicted value. In this chapter, we shall outline the current status. We begin by mentioning some of the theoretical —

—-‘

—

276

J. Rich ci al., Experimental particle physics without accelerators

expectations that have been derived in the framework of GUT’s. We then turn to the experimental method, the individual experiments, and their results to date. Finally, we speculate on what the future may hold. Those of our readers who wish to delve deeper into the subject are directed to the reviews of (mostly theoretical) Ross [i981], Langacker [1981],Lucha [1985,1986], Perkins [1984],LoSecco [1985] and Meyer [1986] (mostly experimental), and to the proceedings of the Workshops on Grand Unification [Ann Arbor 1981; Chapel Hill 1982; Philadelphia 1983; Providence 1984; Minneapolis 1985; Toyama City 1986]. 4.2. Proton decay in Grand Unified Theories

The Standard Model of elementary particles and their interactions has been remarkably successful in explaining a vast body of experimental data in a framework that is free of inconsistencies. It does, of course, have its shortcomings, a major one of which is the fact that the strong, weak, and electromagnetic interactions remain relatively independent of one another, leading to the large degree of arbitrariness illustrated by the multiplicity of free parameters in the model. The principal aim of GUT’s is to eliminate much of this arbitrariness, while retaining the attractive features of the Standard Model. The specific way in which this is achieved in GUT’s is by embedding the SU(3) X SU(2) X U(1) of the Standard Model in a larger group with a single coupling constant. The new group, if not trivial, embodies new symmetries relating the color of SU(3) to the flavor of SU(2) x U(1), and mixes quarks, antiquarks, leptons and antileptons together in the irreducible representations of the group. The vector bosons generated by the new symmetries then carry flavor as well as color, and have the character of leptoquarks, which change quarks into leptons, or of diquarks, which change quarks into antiquarks. The new symmetries must be very badly broken: at currently accessible energies, quarks resemble leptons as little as the strong, weak, and electromagnetic interactions resemble each other. The symmetry-breaking energy scale, typified by the masses acquired by the new bosons, must, therefore, be correspondingly large. The feeble decay of the proton is, thus, a natural consequence of GUT’s. 4.2.1. Proton lifetime in GUT’s The simplest proton-decay schemes in GUT’s (fig. 4.1) involve the exchange of a leptoquark boson of mass mx. This results in a lifetime dependence of m~a -2 from the vector-boson propagator (a is the GUT fine-structure constant). On dimensional grounds, we then expect a lifetime given by: —-

(m~Ia2m~)C where mp is the proton mass and C is a dimensionless factor taking account of the fact that the quarks are bound in a hadron. It can be calculated in a variety of models (e.g., the bag model) and would normally be expected to be of order unity. The GUT parameters, a and mx, can be estimated by extrapolating the U(1), SU(2) and SU(3) coupling constants to their point of intersection at high energy (s = m~).The extrapolation takes on its simplest form if one assumes that no new particle thresholds are encountered between the region of electroweak unification and Grand Unification. In this case, the value of the Weinberg angle is predicted (to 1%), and the extrapolation yields [Lucha 1986]: a—1/41 m~= (2.4 ± 1.4) x

1014

GeV/c2,

J. Rich ci a!., Experimental particle physics without accelerators

d

e~

____ U

u

277

e

d>k>Uc U

U

U

U>U

~

: :4~>::

Fig. 4.1. 5U(5) diagrams for p—+e~üuor e*dd via the exchange of massive bosons X (q = —4/3) and Y (q = 1/3) (m~— mr). The final-state quark—antiquark pair can combine to form non-strange mesons. The first three diagrams also contribute to the decay of bound neutrons if the spectator u quark is replaced by a d quark.

resulting in a predicted proton lifetime of: T~-—

5

X 1029±1yr

where the error in the exponent takes into account reasonable estimates of the uncertainty in the hadronic factor, C, as well as the uncertainty in the unification mass. The lifetime can be increased, obviously, by increasing mx, and this can occur, for example, if there are more than three fermion families, or by incorporating technicolor into the GUT. Adding extra Higgs particles to the scheme has the opposite effect. Proton decay could also be mediated by a Higgs exchange. In the basic SU(5) GUT, this is expected to be less important than gauge—boson exchange because of the weakness of the coupling of the Higgs to light fermions, but it could become competitive in GUT’s with mH ~ mx. In supersymmetric GUT’s, the proton lifetimes depend on a host of mixing angles and small mass ratios, resulting in no definite predictions. To summarize, the GUT framework permits the lifetime quoted above to be adjusted in many ways even nucleon stability could be postdicted. —

4.2.2. Proton-decay modes Decay modes open to the proton are restricted by energy-momentum conservation, which limit the masses and the multiplicity of the decay products, and by symmetry considerations, which limit their flavor. In the former context, two-body modes and light-decay products are expected to dominate. In the latter context, Weinberg [1979] has derived two general selection rules for baryon- or leptonnumber-violating processes mediated by the exchange of a single superheavy scalar or vector: z~LIzXB= 1 and t~SIz~B = 0 or —1. The first rule requires one of the decay products to be an antilepton (either e~,p.~~ ii.~,or the second requires another of the decay products to be a non-strange meson (either ‘ir, ‘q, p, or w) or a meson of positive strangeness (K~or K°or the corresponding first excited states K* (892)). The expected decay channels are, therefore, quite circumscribed. Further symmetry considerations lead to simple relations between specific decay amplitudes, and ~T);

278

J. Rich ci al., Experimental particle physics without accelerators Table 4.1 Expected proton branching ratios for SU(5) [Lucha 1986] Decay mode

Branching ratio

p—sesr

31—46

p—seg p—~e p

1)—S

(%)

2—IS

15—29 11-17 p—~p ~ p—s~K

1—7 1—20 0—I

corrections have to be made for phase-space and hadronic effects. Finally, one obtains a list of nucleon branching ratios like that of table 4.1 [Lucha 1986] for the SU(5) decay modes of the proton. The dominant SU(5) modes are expected to be p e m°for the proton and n —~e m for the neutron, where m = ‘n, p or w. Supersymmetric GUT’s, on the other hand, incorporate symmetries that favor quark transitions from the lightest GUT generation to the heaviest, and, therefore, prefer p—* i~TK~ and n—+ i~TK°.Such variability has a considerable impact on experimental design. —~

+

-

4.3. Proton-decay experiments 4.3.1. Detectors The two classes of proton-decay detectors are distinguished principally by size and sensitivity. In the tracking calorimeters, iron plates provide the sample of protons under observation; planes of gas tubes of one sort or another provide the sensitive medium. Notwithstanding the low cost at which these components can now be manufactured, the Cherenkov detectors, whose proton sample and sensitive medium are combined in the water, are cheaper and can be made typically an order of magnitude larger. The Cherenkov detectors, however, are only sensitive to charged particles whose velocity is above the Cherenkov threshold, f3 > 1/n = 0.75. They are also limited in the resolution of their imaging capability. Nevertheless, they are fully sensitive to the proton-decay mode that is expected to dominate in SU(5) theories, p—~’Tr°e~. Three Cherenkov detectors, 1MB, Kamiokande and HPW, as well as the upgrades 1MB III and Kamiokande II, are described in table 4.2. Basically, they consist of large tanks of purified water viewed by —1000 photomultipliers distributed in a grid on the surfaces of the tanks or, in the case of HPW, throughout the water volume. A charged particle above threshold emits Cherenkov light in a cone of opening angle U = arc cos(1/n) = 41°,and its trajectory, including the direction, is reconstructed from the geometric pattern and the relative timing of PM’s illuminated. In the detectors with surface-mounted PM’s, a stopping track lights a ring of PM’s; an exiting track lights a filled circle. The decay of stopping muons can be inferred from a delayed light pulse. The total pulse height registered by the PM’s gives the energy deposited by the particle the total energy for electrons, photons and neutral pions, the total energy less than 250 MeV for muons because of the muon rest mass and the energy deposited below threshold. The Cherenkov detectors have an additional advantage in that a fifth of their mass is in the form of free protons. This is important for two reasons: one is the absence of final-state meson interactions in the nucleus, the second is the absence of Fermi momentum. The net result is that free-proton decay has —

J. Rich et a!., Experimental particle physics without accelerators

279

Table 4.2 Characteristics of existing and future proton-decay detectors Experiment

Type

Starting date

Fiducial mass (kton)

1MB 1 1MB III HPW

Water

Aug. 82 June 86 March 83 (stopped) July 83 Jan. 86 proposed Oct. 80 Dec. 85 July 82 March 84 1987 project

3.3

Water

Kamiokande I Kamiokande II Super Kamiokande Kolar I Kolar II NUSEX Fréjus Soudan II ICARUS

Water Water Iron Iron Iron Iron Liquid argon

I I

0.42 0.88 0.80 22 0.065 0.12 0.12 0.56 —0.7 4

I

I I

50

Sup erk am iok ande~,/

20

—;

now

i:

IMBI

-: 2-

/ 1—

/

/

/

/

/

,

/

/

2-

-

I

/ /

,/

/ .,_-_/-_ I ,,,,i I,,, Kolar I ,.~‘,‘ / /I’ / ,,v , ,.‘ ~ / ,1 I I

1983

‘,

~_/

/

/i/

,/

/

,‘.~‘I
I

5

—

/

/

‘i

/

II I

I

/ i

1985

—

II

1987

I I I I

/~

//

I

Soudan II

I

1989

1991

[year] Fig. 4.2. Integrated luminosity vs. time for existing and proposed proton-decay detectors.

280

J. Rich et a!.. Experimental particle physics without accelerators

a higher detection efficiency and that the kinematics of the decay are better defined, both being effects which contribute to the fight against background. Four sampling calorimeter detectors KGF, NUSEX, Fréjus and Soudan II are described in table 4.2. They are clearly superior to the Cherenkov detectors in terms of their multi-track efficiency and their imaging resolution. A disadvantage is their lack of free protons. This results in a reduced efficiency for hadronic decay modes because final-state hadrons have a large probability for absorption (—30%) or for a large-angle scatter or for charge exchange (—30%) in the iron nucleus containing the decaying proton. (These probabilities are somewhat less for the oxygen nuclei in water detectors.) Their compactness and modularity, on the other hand, are bonuses. The modularity of the calorimeters allows them to be taken to accelerator beams for the study of their response to neutrinos, an important means of understanding the principal background to proton decay. This was done by the NUSEX collaboration. Figure 4.2 shows the integrated luminosity vs. time of existing and proposed proton-decay detectors. At present, three detectors, 1MB, Kamiokande and Fréjus are the most sensitive, not only in terms of integrated luminosity but also in event-reconstruction capability. —

—

4.3.2. Backgrounds (See Perkins [1984] for a thorough discussion of this topic.) The critical factor restricting the sensitivity of any proton-decay experiment is, ultimately, the background due to the interactions of 0.5—2 GeV neutrinos from the decays of cosmic-ray muons, pions, and kaons in the Earth’s atmosphere. Such interactions are calculated [Gaisser et al. 1983] and observed [Haines et al. 1986] to occur at a rate of about 130/kton yr. It is only those neutrino interactions whose topology is consistent with the kinematics of proton decay that constitute the irreducible background which is the ultimate limitation to sensitivity. In principle, proton-decay events are distinguishable through momentum and energy conservation: .

p~=0, and ~ ~

+

m~= mp.

where the sum is over all final-state particles. In practice, cuts derived from these relations are inefficient, to some degree, in rejecting background because of (a) detector resolution; (b) the presence of invisible particles (e.g., neutrinos) in the decay channel sought; (c) the Fermi motion of the decaying nucleon if it is bound in a nucleus; and (d) the final-state interactions of hadronic decay products, again in the case of bound nucleons. The efficiency of the cuts imposed on the data is calculated by performing a Monte Carlo simulation of the experiment. Such simulations are considerably more reliable if the response of the detector to neutrinos is well understood. To this end, the NUSEX and Fréjus collaborations used experimental data to buttress their calculations: the NUSEX group exposed part of their detector to a CERN neutrino beam; the Fréjus detector was sufficiently similar to the Aachen—Padova neutrino detector that the data of the latter experiment could be adopted by the Fréjus group. The differences between cosmic-ray and accelerator neutrinos in terms of energy distribution, flavor, and angle of incidence have still to be contended with, however.

281

J. Rich et al., Experimental particle physics without accelerators

Depending on the decay mode studied, the probability for a neutrino event to simulate a proton decay is of order 1% for present detectors. This gives a neutrino-induced “proton-decay” rate of about 1/kt~yr, and limits the sensitivity of the detectors to lifetimes shorter than -~-i0~ yr. Another potential background is caused by neutrons produced by cosmic-ray muon interactions in the rock surrounding the detector. Calculations have shown that the muon-induced neutron background is negligible compared with the neutrino background, as long as the muon flux is attenuated by an overburden of 1600 mwe of rock or more, and, a fortiori, fiducial-volume cuts are effective against this background because of the short interaction length of the neutron. 4.3.3. Results All experiments have observed proton-decay candidates, i.e., contained events with a total energy and a momentum balance consistent with proton decay, but only the KGF collaboration [Krishnaswamy et at. 1981, 1982] claim to have in fact observed proton decay. The six KGF events are consistent with the decays: p—~e~’rr°, p- ii~rr4~,and n~_~etri(fully contained); n—p e~ir,p—~e~p°, and p—* e~w° (partially contained). The expected number of neutrinobackground events is given as <0.05 for four of the listed modes. The nucleon lifetime corresponding to the (partially) contained events is estimated to be 7.5(6) x i03°yr. This is very difficult to reconcile with the limits set by the other experiments. The best published limits come from the 1MB and Kamiokande experiments. (The Fréjus collaboration [Bareyre et al. 1986] have yet to announce their results.) Figures 4.3 and 4.4 [Meyer 1986] show i/B Limits (90 % C.L.) I

I

p —-e~it0 +

.•~

I

I

I

I

P

.‘ ~i’

peri p —e~

p

—~

e~p0

p e~K0 p —e~K~ p p

___________

—

p

—

p

—

n

—

fl

—

n

iui~~

— ~—--.

p —p~K0

n

_______

— —

~,

)‘

_..~

p~p0 e~it e~p

_-~ —

-

~

~

______________

I

I

I

_________

11111

1031 •Kamiakande 1.47 kTy

1032 1MB 3.8 kly

yr

Fig. 4.3. Lifetime limits of 1MB and Kamiokande for decay modes with charged leptons (from the review of Meyer at the Sendai Conf.).

282

J. Rich et al., Experimental particle physics without accelerators

%

i/B LimIts (90 I

111111

P

—

P

—

p

—

vK

p

—

vK~

n

—

vn~

57t

CL.) I

N

~

_,,.‘~

fl-~vq —

vu

—

vp

—

vK0

—

vK~0

0

n

_J_LJJJJI I

I

IIILII

1031 •Kamlokande 1.47 kTy

1032 ii

yr

1MB 3.8 kly

Fig. 4.4. Lifetime limits of 1MB and Kamiokande for decay modes with neutrinos (from the review of Meyer at the Sendai Cont.).

their limits (as reported at the Sendai Conference, July 1986) on rn/BR for a variety of modes of branching ratio, BR. They are derived from the formula: rn/BR < 6

X

1032 yr LEXIN

where L is the integrated luminosity in kt yr, s is the mode-dependent detection efficiency, X is the fraction of protons or neutrons in the target, and N is the 90% CL. upper limit on the number of candidates for the studied mode. The limits in figs. 4.3 and 4.4 use protons and neutrons bound in oxygen nuclei and depend, therefore, on calculations of nuclear reabsorption and scattering. The 1MB collaboration has also published limits using only free protons [Blewitt et al. 19851. The upper limits for the two experiments are in general comparable, in spite of the higher luminosity of 1MB, because this experiment is background limited for most of the modes. In the low-background mode p~_~etn.°, the combined limit is near 4 X 1032 yr, about one order of magnitude above the upper limit for the SU(5) prediction. For the two-body decay favored by supersymmetric GUT’s (p—~vK~), Kamiokande has set a limit of 5 x i03’ yr, a factor of four better than 1MB, because their better light collection results in better background rejection. The situation looks grim for the SU(5) GUT; other GUT’s are, for the present, saved by their lack of firm quantitative predictions. .

4.4. The future of proton-decay experiments In the next decade, limits on proton decay should be lowered by, perhaps, another order of magnitude. Kamiokande and 1MB should reach the level of i0~yr for the favored SU(5) proton mode, at which point the rate will become dominated by single-pion production by cosmic-ray v~.The Fréjus and Soudan II experiments should be able to lower the limits on some multiparticle modes, to which the water detectors are insensitive. The planned liquid-argon time-projection detector ICARUS [Rubbia et

J. Rich et al., Experimental particle physics without accelerators

283

al. 1985] should also be able to study multiparticle modes as well as the supersymmetric mode p K~v. The modest mass (4000t) will, however, prevent great progress from being made. Progress beyond the level of i033 yr will require both much larger detectors and a reduction of the neutrino background either through substantial improvements in energy resolution or through the direct reduction in the neutrino flux by, for example, locating a future experiment in a tunnel on the Moon [Pati, Salam and Sreekantan 1986]. Such ambitious experiments will not, however, benefit from the strong theoretical motivation that has driven the current generation of experiments. (It should be noted that while existing detectors have, so far, failed to detect proton decays, their physics potential has not been limited to this field. A variety of other results, concerning neutron oscillations, neutrino oscillations, monopoles, dark matter, and cosmic rays, are discussed in other chapters of this review.) —*

5. Atomic parity-violation experiments 5.1. Introduction Studies of simple atomic systems such as hydrogen, muonium, positronium and geonium have long played a central role in the development and verification of QED, which, partly as a result, is the best tested and most accurate theory in physics (see the review of Brown and Gabrielse [1986]). While progress continues to be made in the pure-QED sector, the past decade has witnessed an increasing change of emphasis in favor of investigations of parity violation in atomic systems with a view to testing the Weinberg—Salam—Glashow theory of electroweak interactions. Parity violation in atomic systems provides a unique opportunity to investigate the WSG model. Since parity-violating effects in atomic systems result from the interference between weak and electromagnetic amplitudes, they can convey information about the relative phase of amplitudes, information which is unavailable in, for example, neutrino—nucleus scattering. In addition, atomic experiments explore a momentum-transfer region totally different to that explored at high energies, so they complement such high-energy studies as, for example, the SLAC experiments of polarized electron—deuteron scattering [Prescott et al. 1978, 1979]. An as yet unrealized possibility is the observation of effects due to the radiative corrections responsible for the energy dependence of the effective coupling constants. It would require a substantial increase in the sensitivity of future experiments, but is nevertheless an enticing possibility since the demonstration and elucidation of such effects constitute an essential test of gauge theories. In this chapter, we will present some of the basic physics underlying experiments in atomic parity violation and illustrate the techniques used and the results obtained. More complete treatments of this very complex subject can be found in the reviews of Bouchiat and Pottier [1984,1986], Fortson and Lewis [1984], and Commins and Bucksbaum [1980]. 5.2. Phenomenology Parity-violating effects in high-energy electron—nucleon scattering are relatively straightforward to calculate. The interference between the y- and the Z°-exchangediagrams (fig. 5.1) gives a pseudoscalar contribution to the scattering cross section which is proportional to the electron’s longitudinal

284

J. Rich et a!.. Experimental particle physics without accelerators

y ~

N~N

N_N

(a)

Fig. 5.1. Diagrams for electron—quark scattering. The interference of diagram (a) with diagram (b) gives pseudoscalar terms in the cross section.

(b) e_____________

Fig “Diagrams” for the absorption of a photon by an atom. The interference of diagram (a) with diagrams (b) and (c) gives pseudoscatar terms in the absorption cross section.

polarization, ~ Pe This pseudoscalar term is the manifestation of parity violation, since the mirrorreflected experiment would measure a different cross section. Parity-violating effects in atomic systems are much more difficult to calculate. Experimentally, what is observed are the effects of photon-induced transitions between atomic states. Very schematically, such transitions proceed through the three diagrams shown in fig. 5.2. The exchange of photons and Z°’sbetween the electron and the nucleus is meant to symbolize the fact that the electron is bound in the nucleus’s Coulomb and Z°field. The interference of diagram 2a with diagrams 2b and 2c generates pseudoscalar terms in the transition rate that violate parity. Since the atomic electrons are bound to the nucleus, the calculation of parity-violating effects in atomic systems is a four-step process: 1) An effective potential for the atomic electrons moving in the Z°field of the nucleus is determined from the weak Lagrangian. 2) The effect of this potential on the atomic wave function is determined using standard stationarystate perturbation theory and a knowledge of the unperturbed wave function. The important effect, at this stage, is the mixing of states of different parity. 3) The matrix elements for photon-induced transitions between the perturbed atomic states are calculated using the ordinary electron—photon interaction Hamiltonian. The existence of the oppositeparity admixtures results in pseudoscalar terms in the transition rate, which results, for instance, in different rates for transitions induced by positive- and negative-helicity photons. 4) The calculated transition matrix elements are used to calculate observable parity-violating effects. e.g., optical rotation. An experimental result is significant in the context of particle physics proper if, given the results of a particular measurement, it is possible to retrace the steps enumerated above to gain information about

J. Rich et al., Experimental particle physics without accelerators

285

the original weak-interaction Lagrangian. We now describe in more detail the techniques used in the first three steps, and then illustrate the last step with optical-rotation experiments and Stark experiments in forbidden transitions. 5.2.1. The parity-violating potential The weak neutral-current Lagrangian for the electron—nucleus system is the product of the electron current and the nuclear current: (5.1)

where the sum extends over the different protons and neutrons in the nucleus. Each current is the sum of vector and axial-vector components, and it is only the terms in the Lagrangian that couple a vector and an axial-vector current that violate parity. The parity-violating Lagrangian is then given in terms of the electron, proton and neutron fields by: LPV

=

(G/V~)~ ~

+ C~~i~y~n) + (G/\I~)~ ë~e(Capj5y~ysp + Canfl~y~y 5n). (5.2)

The first term couples the electron axial current with the nucleon vector current, and the second couples the electron vector current with the nucleon axial current. C~,,C~, Cap and Can are parameters that, in the WSG model, are determined by the weak mixing angle, O~,and by the axial coupling constant in neutron 13 decay, g~(—.1.25): 2Ow) (5.3a) C~1,=~(1—4sin C~=—~

(5.3b)

Cap= ~g~(1—4sin2~)

(5.3c)

Can =

—~g~(1 —4sin2 Ow).

Experimentally, sin2

Ow

=

(5.3d)

0.226 ±0.004 so C

5~is the largest of the four coupling constants. We note, 2 Ow however, radiativeabout corrections to the graphs in high-energy figs. 5.1 and experiments 5.2 make theineffective value of sinvalue in atomic that experiments 5% lower than in the which the quoted was measured [Marciano and Sirlin 1983, 1984; Lynn 1984]. The above Lagrangian is given in terms of quantized field operators, but, in order to do perturbation calculations with the atomic wavefunctions, we require an effective electron—nucleus potential, V, that is a function of the relative position of the electron and nucleus and of their spins. One way of obtaining this potential (see, e.g., [Sakurai 1967]) is to calculate the low-energy limit of the scattering matrix, ~ extracted from the Lagrangian using the Feynman rules, and to equate this matrix with the standard expression of potential-scattering theory: M

3r,

1~= Jv exp{—i(p’ —p) r} d .

(5.4)

)

286

J. Rich et a!.. Experimental particle physics without accelerator,c

where p and p’ are the initial- and final-state center-of-mass momenta. Reversing the above formula, one sees that the potential is simply proportional to the Fourier transform of the scattering matrix. Using eqs. (5.2) and (5.3) to compute ~ and replacing the nucleon Dirac spinors with their low-energy limits, one finds: (5.5) for the potential due to the nucleon vector currents. Here, u, p(= —ihV) and r denote the electron’s spin, momentum and position. Parity violation is manifest in the appearance of the pseudoscalar helicity operator (o- p), and the short range of the weak interactions is reflected in the delta function. Q~is proportional to the sum of the vector couplings (C5~and C~~) of theN.nucleons the for nucleus and, 0.25, for a 2 Ow)Z It is seeninthat, sin2 Ow nucleus of Z protons and N neutrons, is equal to (1 4 sin the electrons couple primarily to the neutrons. The factor N in Q~ enhances parity-violating effects in heavy nuclei. The other parity-violating part of the effective potential, coming from the coupling of the electron vector current with the nuclear axial-vector current, is suppressed by a factor (1—4 sin2 Ow). In addition, since the coupling is proportional to the nucleon spin, the total coupling is proportional to the nuclear spin, so there is no large enhancement of parity violation in heavy nuclei. —

—

—

5.2.2. Modifications of atomic wave functions due to the parity-violating potential We now consider the effect of the potential of eq. (5.5) on the atomic wave function. In the absence of parity violation, the atomic states, H, n), are labeled by their parity, .11 ±1, and by any other quantum numbers (represented here by n). Since the perturbing potential, V, is a pseudoscalar, it connects states of opposite H, but of the same total angular momenta. Standard stationary-state perturbation theory can be used to calculate the eigenstates of the complete Ham” fan: (H), n)

=

H, n)

+

~ ~

m),

(5.6)

with the opposite-parity admixture coefficients given by (—H,m~V~H,n EmnE(Hn)_E(_Hm) —

(

The H in the perturbed state is placed in parentheses since it is now only a nominal parity. The matrix elements in eq. (5.7) can be estimated in the independent-particle model of the atom [Bouchiat and Bouchiat 1974]. They are non-zero only between s-wave and p-wave states because the delta function in the effective potential requires a non-zero value at the origin for the wave function or its gradient. In this case, the matrix elements are typically of order 10~9Z3K(e2/a 0),where a0 is the Bohr radius. One factor of Z comes from Q~(—N-— Z), and the other two come from the value and the gradient of the atomic wave functions at the origin. K is a relativistic correction factor21a important for high-Z atoms (K-—2.8 for cesium and —9 for lead). For 17Z3K. typical level spacings of shows 0.05e the 0, enormous eq. (5.7) The factor Z3K then gives admixtures of opposite-parity states of order 10 advantage of using heavy atoms.

J. Rich et al., Experimental particle physics without accelerators

287

5.2.3. Rates for photon-induced atomic transitions The effects of the parity admixtures are best seen in photon-induced transitions between atomic states of the same nominal parity, where full-strength (electric-dipole) transitions are forbidden. The transition rate is governed by the electron—photon Hamiltonian (see, e.g., [Sakurai 1967]): H.in ~ —f mc pA(x,t)—~ 2mc u.(VxA(x,t)),

(5.8)

where m, p, x and o refer to the electron, and A(x, t) is the quantized photon field. Let us consider the matrix element of Hint between the final atomic state (H), n’) and the state consisting of the initial atomic state and a photon of momentum k and helicity h, (H), n, k, h). From eq. (5.6), this matrix element is the weighted sum of the matrix elements between the unperturbed states and the matrix elements between the unperturbed and admixed states: ((H), fl’~Hini~(H), n,

k, h) = A~ + A_

(5.9)

A+=(H,n’~Hjnt~H,n,k,h) A

= ~ ~mn(H,

(5.10)

n’~H~~j—H, m, k, h)

+ Enm(~1, ~

n, k, h~.

(5.11)

We can associate A + with the diagram in fig. 5.2a, and the two terms in A with the diagrams in figs. 5.2b and 5.2c. The total transition probability is now given by: -

Wc~A+~2+2Re(A+A*)+A.~j2.

(5.12)

Because of the small magnitude of the opposite-parity admixtures, we can normally neglect A 2 A + and A are functions of the variables defining the initial and final states, and their exact form and magnitude depend on the details of H 1~1.We can, however, make one important conclusion about A + and A using only the fact that Hint is a parity-conserving operator ~ the matrix P] = 0).elements By multiplying 1P in eqs. (5.10) and (5.11), we quickly see that for the Hint on each side by P parity-transformed states are given by: -

-

-

((H), ~

n, —k, —h) = A.÷ A —

,

(5.13)

i.e., the two amplitudes acquire a relative minus sign. Because of this, the interference~term in eq. (5.12) is a pseudoscalar function of the kinematical variables. The available pseudoscalars are the scalar products of the photon momentum, k, and the various angular momenta: the photon spin (k. = h) and the initial and final atomic polarizations. The exact combination of these pseudoscalars that appears in the interference terms can be determined only by a complete calculation. The existence of the pseudoscalar term in the transition rate means that reactions involving configurations related by mirror reflections have different rates. The size of these parity-violating asymmetries is determined by the ratio, between the first and second terms in eq. (5.12). To estimate z.l we must consider the details of Hjnt~Because the unperturbed states have the same parity, A + is determined by the Ml (magnetic-dipole) matrix element, M, between these states. This element is ~,

288

J. Rich et a!., Experimental particle physics without accelerators

normally of order ea0/137. By convention it is real. A~in eq. (5.11) is determined by the El (electric-dipole) matrix elements between the unperturbed atomic states and the opposite-parity admixtures. These elements are normally of order ea0. The sum of these elements with the weighting in eq. (5,11) is called the parity-violating electric-dipole amplitude, E~.If there is no violation of time-reversal invariance (in V(r, u)), E~is pure imaginary with respect to M. Taking the estimates for the magnetic- and electric-dipole matrix elements and the estimates of the mixing coefficients, ~ is of order: 4Z3K. (5.14) ~=Im(E~)/M~10~ This gives, for example, the relative difference between the cross sections for absorption of left and right circularly polarized photons. 5.2.4. Extraction of physics from atomic experiments Before discussing some experimental applications of these ideas we will make some comments on the particle physics that can be learned from these asymmetries. The asymmetry, ~i, is a product of Q~, (through eqs. (5.5) and (5.7)) and the atomic matrix elements. Apart from verifying the existence of parity violation in atoms, a measurement of ~iis interesting to particle physicists only to the extent that the atomic matrix elements can be calculated. This suggests using atomic hydrogen, where the wave functions are very precisely known. Unfortunately, due to the lack of the Z3K enhancement, experiments have not yet reached the precision necessary to observe such effects in hydrogen. Parity violation effects have been observed in Bi, Pb, TI and Cs. The cesium measurements are especially interesting because atomic matrix elements are most reliably calculable in atoms with only one electron outside a completely closed shell. Hence, these experiments now yield the most reliable values of Q~. The experiments on the other, higher-Z, atoms remain interesting because the verification of the rise of ~i with Z verifies the short-range nature of the force leading to the parity mixing of atomic states. Factoring out the atomic matrix elements, the atomic experiments yield a value of Q~that can be c~

sin2 ~

//~

0.4

~-/

/( / /~~/o

I

-1

~

~~,J’

/(SLAC~/’ Li,

‘/

c~ 0.8

‘~

~

sin2 e =

Cesium

-1

90% conf. regions

Fig. 5.3. Determination of the couplings of electron-axial current with the vector currents of the u quark (Ca) and the d quark (Cd). The experimental hands are determined by the SLAC electron—deuteron experiment [Prescottet a). 1978, 1979] and by the atomic-cesium experiments of Bouchiat et a). [1982,1984, 1985, 1986] and Gilbert et a). [1985,1986]. The graduated segment gives the WSG prediction as a function of sin2 O,~. The plot is from the review of Bouchiat and Pottier [1986].

J. Rich et al., Experimental particle physics without accelerators

289

compared with the WSG value of (1 4 sin2 Ow)Z N. In a more general theoretical framework, the experiments measure the coherent sum of the weak couplings of the electron axial—vector current to the neutron and proton vector currents. Assuming CVC (conserved vector current hypothesis) these couplings are directly proportional to the electron couplings to the u and d quarks. For cesium (188 u quarks and 211 d quarks) Q~ 188(C~+ l.l2Cd), where C~and Cd are the strength of couplings of the electron axial current to the vector currents of the u and d quarks. For comparison, in high-energy electron—deuteron experiments the electrons scatter from each quark incoherently. Hence, this experiment is sensitive to the weak quark couplings weighted by the quark charges, C~ ~Cd. This combination of C~and Cd is almost exactly orthogonal to the combination appearing in ~ so atomic-parity-violation experiments yield information that is complementary to that given by the high-energy experiments. To illustrate this, fig. 5.3 [Bouchiat and Pottier 1986] shows the constraints on C~and Cd based on the SLAC experiment and the cesium experiments of Bouchiat et al. [1982, 1984, 1985, 1986] and Gilbert et a!. [1985, 1986]. —

—

~

—

5.3. Optical-rotation experiments Optical rotation refers to the rotation of the plane of polarization of a linearly polarized light beam. In a medium in which no handedness is defined by magnetic fields or molecular structure, such a rotation indicates parity violation, since the sense of rotation is opposite to the sense in a mirror image of the experiment. Plane-polarized light is a superposition of two circular polarization states, and a rotation of the polarization plane will result from a difference, ~n, in the index of refraction associated with the two states. For a beam of photons of angular frequency, w, the rotation angle after a length I is given by: =

(wic) iXn 1.

(5.15)

The index of refraction is related to the real part of the forward-scattering amplitude, f(w), through: n

=

1

+

2ir (clw)2 NRe(f(w)),

(5.16)

where N is the density of scatterers in the medium. This relation makes it clear that optical rotation results from a difference in the scattering cross section for the two helicity states. If the frequency of the beam is near that needed to excite a higher atomic state, the forwardscattering amplitude is determined by the absorption matrix elements, M and E~,discussed in the previous section. It is given by the standard Breit—Wigner formula: 2 =

c2

M~2±2Im(EM*) (i~E)2+ (F12)2 (z~E i112), —

(5.17)

where i~.Eis the difference between the photon energy and the energy of the excited state, and [‘is the width of the state. The ± refers to the two photon helicities. Equation (5.17) then shows how a difference in the photo-absorption probability leads to a difference in the forward-scattering amplitude. Equation (5.16) then gives the difference in refractive index for the two helicities: =

8ITN Im(E~M*)(~E)2+(F/2)2

(5.18)

290

1. Rich ci a!., Experimental particle physics without accelerators

It has a dispersive shape, going through zero at the center of the resonance (~E= 0) and extrema at z~E=±f/2. An experimentally interesting number is the rotation angle for a path length equal to one absorption length. The total cross section and the absorption length are determined by the imaginary part of f(w) (optical theorem). Using eqs. (5.15) and (5.18) we find a rotation angle of Im(E~)/Mafter one absorption length for L~E= ±[‘/2. Using the estimates of E~and M given in the previous section, this gives angles of i07—i05 radians for high-Z atoms. The measurement of such small rotation angles presents a considerable experimental challenge. All experiments measure the transmission of a laser beam through an atomic vapor sandwiched between two crossed (linear) polarizers. Figure 5.4 is a schematic of the apparatus of Emmons et a!. [1983].In such an arrangement, the transmitted intensity is: I

=

I~sin2(~~ + 0~ ~PNC

+

1PNC is the rotation angle due to parity violation; ~ is a controlled where I~ is the incident intensity; ‘ rotation effected either by purposely misaligning the polarizers or by inducing a Faraday rotation; and ~r is any residual rotation due to imperfections in the apparatus. If ct~is modulated (for instance at a frequency w), the transmitted intensity will have a component I~CQfl(IpNc+ ~1ir)sin wt. The isolation of this component (with lock-in techniques) determines the sum, c~PNC+ cJ3 ‘1~pNc can be separated from the much larger I~by using the dispersive shape of the dependence of ~PNC on the photon wavelength. Sweeping through the resonance then isolates ‘pNC~ as shown, for example, by fig. 5.5 [Emmons et a!. 1983]. Of course, Pr is not completely independent of the photon wavelength, and the fact introduces systematic errors that must be understood. Table 5.1 (from the review of Bouchiat and Pottier [1986])gives the results of various measurements of optical-rotation effects in bismuth and lead. The results are presented as the ratio between E 0. the parity-violating electric-dipole amplitude, and M, the magnetic-dipole amplitude. The experimental precision in all experiments is limited by the systematics of the measurement of rotation angles. Also

LASER DIODE POLARIZER

FARADAY CEL~

VAPOR CELL

SOLENOID -

~

-

--~~OVEN

SIGNAL DETECTOR

Fig. 5.4. Schematic of the apparatus used by Emmons et a!. to measure parity-nonconserving optical rotation in atomic lead.

J. Rich et al., Experimental particle physics without accelerators

0.4

~

291

~00~

I09 frequency

(0Hz)

Fig. 5.5. Data from the atomic lead experiment of Emmons et a). Theoretical curves (lines) are fitted to the experimental data (points) for (a) absorption, (b) Faraday rotation at 30mG, and (c) ~ The relative optical depths are 1, 1 and 8.5 respectively. No data are shown on resonance for PPNC because of yearly total absorption of the light there. The two absorption peaks on each side of the central resonance are due to the hyperfine components of the lead isotope of spin ~.

Table 5.1 Results from optical-rotation experiments. Initial results with bismuth subsequently rejected or improved are not listed [Lewiset a). 1977; Baird et a). 1977; Bogdanov et at. 1980]. Theoretical values refer to the 2 O.~—0.22 transition, not to the specific experiment and are calculated for sin lO8xE/M Experiment ~‘ Theory Transition

reference

Experiment

Theory

reference

Bi, 648nm

—20.2±2.7

—13

Sanders 1980

Bi, 876mm

Barkov and Zolotorev 1978, 1979, 1980 Taylor 1984 Birich et a). 1984 Hollister et al. 1981

—9.3±1.15 —7.8 ±1.8 —10.4±1.7

Pb, 1.28 sm

Emmons et al. 1983

—9.9

—17 —10.5 —11 —13 —8 —11 —14

Novikov eta). 1977 Martennson et at. 1981 Sandars 1980 Novikov et a). 1977 Martennson et a). 1981 Novikov et a). 1977 Emmons et al. 1983

±2.5

292

J. Rich

Ct

al., Experimental particle physics without accelerators

shown in table 5.1 are the results of various calculations of the atomic matrix elements. The large spread in the theoretical results is due to the rather complicated electronic structure of these atoms. While a general agreement with the WSG model is seen, some experimental and theoretical work remains to be done. 5.4. Stark experiments in forbidden transitions The second place where parity violation has been observed in atomic systems is in forbidden Ml transitions in thallium (62Pl/2—~72Pt/2){Bucksbaum et al. 1981a,b; Drell and Commins 1984, 1985] 2S 2S and in cesium (6 112—*7 112) [Bouchiat et al. 1982, 1984, 1985, 1986a,b; Gilbert et al. 1985, 1986]. In these transitions, the Ml matrix elements are suppressed because it is only the principal quantum number that changes. Hence, the asymmetry Li (eq. (5.14)) is expected to be quite large (10~—10~). In fact, the smallness of the Ml matrix element makes the interference term in eq. (5.12) too small to be, as yet, observable. This problem has been solved by the application of a DC electric field. As with a parity-violating atomic potential, this mixes states of opposite parity (Stark effect). The mixing terms are given by eq. (5.7) with V replaced by —eEr, and result in a third term, AE, in the transition amplitude (eq. (5.9)): AE

=

~ amn(H, n’~H1~j—H, m, k, h~+ an,m(—TI, m~H1~jH, n, k, h~

(—H, m~r~H, n) ~mnE(Hn)E(H,m)

(5.19)

(5.20)

.

Since the Stark Hamiltonian conserves parity, AE can play the role of A ÷, and it is the pseudoscalar interference between AE and A (eq. (5.9)) that is observed. This presents considerable experimental advantages, since the signal is now proportional to a controllable parameter, the electric field. Its value can be chosen to optimize the signal-to-noise ratio and its reversal permits the subtraction of background. The interference term contains a term proportional to h(k x E) J, where J is the final-state atomic polarization. This term generates a small final-state polarization perpendicular to the laser beam and to the electric field. The polarization changes sign when the helicity of the initial-state photon or the electric field is reversed. In the cesium experiment, this polarization is measured by measuring the circular polarization of the decay fluorescence. it is measured by selectively 2P In the thallium experiment, 2S exciting the hyperfine components of the 7 112 state to the 8 11, state with a second laser. The dependence on the circular polarization of the second2Plaser of the intensity of the decay fluorescence of 2St/ the 8 2 state determines the polarization of the 7 112 state. The parity-violating asymmetry, Li, is extracted by comparing signals under mirror-reflected experimental arrangements, i.e., by reversing the electric field and the photon helicities. Figure 5.6 shows a schematic of the apparatus of Bouchiat et al. The polarizations of the incident and detected photons are varied continuously, so that the parity violating signals can be isolated with lock-in techniques in combination with some discrete parameter reversals (e.g., of the electric field). Care must be taken to eliminate false asymmetries due to imperfect reflections of the experiment. In the experiment of Bouchiat et al., the systematic errors associated with such imperfections were reduced to a level (——5%) where they were smaller than the statistical errors (—-15%) after several weeks of running. -

.

J. Rich et a!., Experimental particle physics without accelerators

293

~

/

~

U

0’

~-/vI’\ s~~)//7(~)

/ /

/

M

1

L

Fig. 5.6. Schematic of the apparatus of Bouchiat et a). The main elements of the apparatus are: L, a resonant continuous-wave laser beam; A, polarization analyzer; FL, filter and lenses; D, detector of the de-excitation fluorescence. Mirrors M~and M2 inside the cesium cell allow approximately 60 forward—backward passages of the beam through the atomic vapor.

In addition to experiments that use electric fields only, experiments have also been performed in crossed electric and magnetic fields with thallium [Drell and Commins 1984, 1985] and with cesium [Gilbert 1985]. The existence of a static magnetic field allows one to construct other pseudoscalars. For a photon polarization, j3, possible pseudoscalars include (j~ k)k. (E x B) and (JJ B)~.(E x B). Experiments in zero field are also planned [Herrmann et al. 1986]. Table 5.2 (from the review of Bouchiat and Pottier [1986])summarizes the experimental results and theoretical calculations for thallium and cesium. Results are presented as ratios of E~,the parityviolating electric-dipole amplitude, to /3, the factor of proportionality between the Stark amplitude and the electric field. The agreement of the WSG predictions with the results of the cesium experiments is at the level of 10%. These results lead to limits on the weak coupling like those in fig. 5.3. .

Table 5.2 Results from Stark experiments on forbidden transitions. Theoretical values refer to the transition, not to the specific experiment and are calculated assuming Q~= —112, /3 = 205a0 for tha)li~mand Q~ = —70.0, /3 = 27a~for cesium E 1/3 (mv/cm) Experiment I’ Theory Transition reference Experiment Theory reference TI 6P112—7P11,

Cs 6S112—7S1,,

Bucksbaum et al. 1981a,b

—1.8 ±0.6

Dre)) and Commins 1985

—1.73

±0.33

M. Bouchiat et a). 1982, 1984, 1985, 1986a,b

—1.52

±0.18

Gilbert et al. 1985, 1986

—1.65

±0.13

—1.31 —2.17 —1.88 —1.80 —1.50

Neuffer and Commins 1977 Martensson 1986 Sushkov 1986 Das 1986 Dzuba et a). 1985

—1.52

Martensson, 1985 Johnson et a). 1986 C. Bouchiat et a). 1983, 1986 Martensson 1986

—1.59 —1.53

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J. Rich ci al., Experimental particle physics without accelerators

5.5. Atomic-hydrogen experiments The general phenomenology discussed above applies as much to atomic hydrogen as to the heavier atoms. An advantage of hydrogen is that the interpretation of experimental results is not hampered by uncertainties in atomic wave functions. A disadvantage is that the asymmetries are small because of the lack of Z3K enhancement. All current atomic-hydrogen experiments study transitions between the nearly degenerate 2S 1/., and 2P1/2 levels. In zero field, these levels are separated by the Lamb shift (1058 MHz). The parity-violating mixing between these states is, thus, enhanced by the small energy difference in the denominator of eq. (5.7). The denominator can be further reduced with a static magnetic field (Zeeman effect). At a level crossing of a pair of hyperfine components of the 2S~72and 2P1/2 states, the effective denominator is the width of the 2P11. state (100MHz). Under these conditions, the parity-violating potential induces mixing coefficients of order 10 Attempts to observe parity-violating effects in this system have been hampered by a variety of experimental problems including the system’s sensitivity to stray electric fields which induce 2S12—2P1~2 mixing. Experimental progress has been discussed in the review of Fortson and Lewis [1984]. 5.6. The future Progress in experimental atomic physics will lead not only to more precise measurements of parity violation but also to the observation of qualitatively different parity-violating effects, e.g., the effects of the coupling of the electron vector current with the nuclear axial-vector current. Of course, the long-term goal is to reach a precision where one can see the effect of WSG radiative corrections. This will require either a factor of —l0~improvement in the experimental precision in hydrogen or a factor of —10 improvement in the experimental and theoretical precision in cesium. Recent progress in theoretical calculations for cesium have been discussed by C. Bouchiat et al. [1983,1986], MartenssonPendrill [1986], Sushkov [19861and Das [1986].

6. Time variation of the fundamental constants 6.1. Introduction The Standard Model of particle physics contains at least 17 free parameters, comprising particle masses, coupling constants, and mixing angles. Since the origin of these “constants” is not understood, the question of their constancy with time is open. The issue was first raised by Dirac some 50 years ago in the pre-Standard-Model era. He noted that 2lGmemp, the ratio of the electromagnetic forces between an e2Im~c3.Dirac electron and a speculated proton, e that this was roughly equal to the age of and the gravitational Universe measured in units of equality was not coincidental to the human epoch, but that the equality must always be true. This would require at least one of the fundamental constants to vary with time. Dirac personally preferred a variation of the gravitational constant, G, but other possibilities have been proposed. Inspired by these speculative ideas, the experimental study of possible time variations of physical constants has developed into a fascinating, if somewhat marginal, branch of physics. Reviews of the field have been made by Dyson [1972,1978], Bekenstein [1982], Irvine [1983], Norman [1986], and Irvine and Humphreys [1986].

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Recent theoretical ideas based on extra dimensions (Kaluza—Klein and Superstring theories) may increase the relevance of limits on the time variation of the constants. In these theories the value of coupling constants are related to the radii of compactified dimensions. As pointed out by Marciano [1984],these radii should not be strictly constant. While most of the time variation could be expected to have occurred in the very early stages of the Universe, it is possible that observable monotonic or oscillatory effects may persist to the present. The time variation of coupling constants due to changes in these radii were discussed by Marciano and by Kolb et al. [1986], Weiss [1986], and Wu and Wang [1986]. Measurements of the time variation of the constants can be placed into one of two categories. One consists of laboratory or astronomical experiments designed to observe a current variation. The other consists of geophysical or astronomical observations that compare the present value of a constant with either its value at a particular time in the past or with its average value in the past. Unless time variations obey a simple power law in time, each type of measurement gives complementary information. 6.2. Current variations We now discuss two experiments that measure the current variation of the constants. Since variations of the constants implies changes in the characteristics of measuring apparatuses and in the environment, care must be taken to establish what it is that is actually being measured. In the first experiment, Turneaure and Stein [1976](see also [Turneaure et al. 1983]) measured the relative drift of two clocks: one a standard cesium atomic clock, and the other a superconducting cavity oscillator. The frequency of the first, z.~,is determined by the hyperfine splitting of the ground state of cesium: hii~~ ~ Here, me is the mass of the electron, and g~and ~ are the g factor and the mass of the cesium nucleus. The resonant frequency of a superconducting cavity of length 1 is of order: t’cav

‘—

c/I

This nominally classical frequency depends on h, me and a, since I is proportional to the interatomic spacing in the cavity, which is of the order the Bohr radius:

I—NhI(am~c), where N is the number of lattice sites along the length of the cavity. Combining all this, the ratio between ii~~ and ~~‘cav is given by: R~g~5(m~Im~5)a3. The clocks remain synchronized if R remains constant. Based on data taken over a 12-day period, Turneaure and Stein placed a limit on the present variation of R: <1.2 x lOtt yr’.

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We can make three comments on this limit. Firstly, while the authors reported only a limit on the first derivative of R, the experiment is sensitive to more complicated oscillatory time variations of R. Secondly, while ~ is not generally considered to be a fundamental constant, it is presumably determined by some more fundamental constants. We might, for instance, be tempted to replace me/mcs by meIAQcD. Thirdly, since in a measurement we always compare two quantities of the same dimension (in this case the frequency of the two clocks), we can only directly measure the time variation of dimensionless combinations of the fundamental constants. These include dimensionless coupling constants and mass ratios. Measurements of the time variation of constants with a dimension (Ii, c and m) are more delicate: they involve comparing the properties of “old” and “new” particles at a given time. Possibilities and limits were discussed by Baum and Florentin-Nielsen [19761,Solheim et al. [1976], Mansfield and Malin [1976],and Barnet et al. [1985]. In the second experiment, an atomic clock was compared with a “planetary” clock. In order to understand the significance of such comparisons, we consider the simple case of a planet consisting of N~hydrogen atoms revolving around a sun consisting of N~hydrogen atoms. For a circular orbit, Kepler gives the orbital frequency, r~,to be: =

G2m~N~N~/21TL3,

where G is the Newton constant, mh is the mass of the hydrogen atom, and L is the angular momentum of the orbit. L is equal to nh where n is the principle quantum number of the orbit. If the physical constants vary adiabatically, n will not change. Taking the ratio between the atomic-clock frequency and the planetary frequency we find: (Gm~/hc) 4

=

-.3

(N~N~n .)

-

g~~a (meImcs)(me/mh) By repeatedly measuring a planet’s period with an atomic clock, we can place limits on the variation of the dimensionless combination of fundamental constants in the above expression (assuming that N~,N~

Table 6.1 Limits on the time variation of some constants. Limits for quantities given with an asterisk are derived assuming only the given constant varies in time. The Hobble constant is lOOh km s’ Mpc~()
Method

Hellings et al. 1983 Turneaure and Stein 1976 Shlyakter

Planetary tracking Clock comparison Prehistoric neutron capture Fine structure in radio galaxies Re lifetime Hyperfine structure in QSO’s Primordial nucleosynthesis

1976 Bahcal) and Schmidt 1967 Lindner et at.

1986 Tubbs and Wolfe 1980 Ko)b et a).

1986

Quantity. measured

Q,

d~nQ)Idt (yr ~1

Time base (yr)

(0.2±0.4)x 10

H

6

g~,(m/M)a3

<1.2 x 10

0.003

0*


2x io~

a

<1.3h

a~

<2 X 10~

4.5 x l0~

g~(m/M)a2

<2h

10’~

5 X tO°Ih

0*

<1.5h

10

6.6 X 109/h

X

X

X

l0~~

~

2 x lOd/h

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and n are constant). If, from other experiments we know that the denominator does not vary with time, this experiment can place a limit on the time variation of the dimensionless gravitational constant, 2 GmhIhc. A more general theoretical analysis of the information that can be obtained by tracking planets was made by Adams et al. [1983].The best experimental limits come from the laser tracking of Mars using mirrors placed on this planet by the Viking landers. Using measurements taken during a six-year period, Hellings et al. [1983]report G’ dGldt = (0.2 ±0.4) x 10~yr1 (assuming all other constants to be truly constant). This result rules out the time variation of G predicted by Dirac’s original theory. The experimental uncertainty is in the range of the time variation of G predicted, under certain circumstances, by Superstring theories [Wu and Wang 1986]. 6.3. Past variations* We now turn to the second class of experiments, those that compare the present values of constants with their values in the past. Dyson [1967]noted that strong limits can be set by comparisons of the “laboratory” lifetimes of certain radioactive isotopes with their “geological” lifetimes, i.e., those deduced from the isotope’s abundance in geological or astronomical samples of known age. Because, the age of such samples is generally determined by radioactive dating (e.g. potassium—argon dating), what is actually measured is the ratio between the lifetime of the studied isotope and the lifetime of the isotope used to date the sample averaged over the time that has elapsed since the sample’s formation. (Since this is a dimensionless quantity, comparison with the laboratory ratio leads to limits on dimensionless quantities.) The long-lived nucleus with the lifetime that is most sensitive to the fine-structure constant is 187Re, which decays to 187Os by 1~emission with a lifetime of 4 X 10t0 yr and a Q value of 2.5 keV. The strong dependence of the lifetime on a arises because of this small value of Q, since a small change in the relative electrostatic binding energy of Re or Os gives a largetofractional Q. Estimates 18000. Compared this verychange strong independence on [Dyson a, the 1972] give a Re lifetime proportional to a lifetimes of other nuclei can be considered independent of a and can be used to give the age of the sample. Comparison of the laboratory lifetime [Lindner et a!. 1986] with that deduced from Re and Os isotopic abundances in meteorites [Luck and Allegre 1983] gives an upper limit on at daldtl of 2 x ~ 15 yr~(assuming everything else constant). A considerable improvement on this limit was made by Shyakhter [1976]. He observed that the positions of thermal—neutron capture resonances are very sensitive to the values of the interaction coupling constants. An example of such a resonance occurs in 150Sm, causing a large cross section for neutron capture on n + t49Sm_* lSOSm*~~÷ 150Sm + -y. The resonance corresponds to a neutron kinetic energy, T~,of 0.098 eV and has a width of 0.063 eV. T~is determined by energy conservation: = E Li, —

where Li is the binding energy per nucleon (m 149 + m~ The m150 position 8MeV), is the excitation energy 150Sm that forms the resonance. of and the E resonance in the thermal of the excited state of region is due, then, to the equality of Li and E to one part in 108. —

*See also Note added in proof.

—

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J. Rich et al., Experimental particle physics without accelerators

Both Li and E are functions of the strengths of the strong, electromagnetic, and weak interactions. A change in one of their coupling constants would upset the balance of E and Li and move the resonance out of the thermal region. We can express the dependence of E and Li on a given coupling constant, g, through the relations: dLiILi=/3~dg/g, and: dE/E=/3~dg/g. f3~and f3E can be calculated in the framework of the nuclear shell model. The dependence of T~on g is then given by:

Hence, unless 13E /3~,a change in g is amplified by a factor of order i08 to give a much larger change in T~. A very strong limit on the time variation of the coupling constants can be made by considering the isotopic abundance of Sm in a uranium deposit in 0kb, Gabon, This deposit formed a natural fission reactor —2 X i09 yr ago, as is indicated by the fact that it is heavily depleted in 235U and rich in the fission products of 235U [Maurette 19761. The deposit was also found to be heavily depleted in 149Sm. This is, of course, explained by the existence of the thermal-neutron capture resonance, which was apparently still in the thermal region 2 x i09 yr ago. Detailed considerations indicate that the relative change of T~from its current value must be less than 10%. Shyakhter estimated that the limit on the change in the position of the resonance implies a limit on the rate of relative change of the coupling constants for the strong, electromagnetic and weak interactions of 5 X 10i9 yr’. l0’~yr~ and 2 x 1012 yr~,respectively. An interpretation of the time variation of the “strong-interaction coupling constant” in terms of more fundamental constants must await a better understanding of nonperturbative QCD. The observation of spectral lines from distant galaxies gives information on fundamental constants at early times and great distances. The measured shift of only one spectral line cannot be distinguished 2 or from a Doppler shift,time but oftheemission. relative shift of two or hyperfine-structure lines measures a a2(m~/m~)g at the Bahcall and fineSchmidt [1967] used the fine-structure splitting observed in radio galaxies to place a limit of 1.3 x 1 on a’(da/dt)I. Observations of 10t2 been yr used to set the limit on the relative hyperfine splittings in QSO’s [Tubbs and Wolfe 19801 have time variation of Igpa2(me/mp)~at 2 x 1014 yr’. Finally, cosmological deuterium and helium abundances have been used to measure certain constants at the time of cosmological nucleosynthesis. Kolb et al. [1986] (see also [Khare 1986]) set a limit of 1.5 x l0~~ yr’ on a<(da!dt)~(assuming everything else constant), as well as limits on the rates of change of the weak-interaction and gravitational constants. These limits, though not as restrictive as the other limits, are important because they come from an earlier time. They are, thus, important for theories where the constants are expected to vary only at very early times.

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6.4. Future varitions The future of the study of the time variation of the constants is not entirely clear. Technological progress will certainly allow us to place tighter limits on the present variation of the constants. Studies of past variations depend on better understanding of the physical history of the Universe, and, perhaps, on the lucky discovery of effects that depend strongly on the constants, as in the case of thermalneutron capture. Whether these limits will ever make a real contribution to the development of a more complete theory of particle interactions depends on our gaining a better understanding of the origin of these constants.

7. Cosmic-ray physics 7.1. Introduction

With a history spanning seven decades, cosmic-ray physics is one of the most enduring fields of experimental physics. Discovered by Hess in 1912, cosmic rays have remained an enigma to the present day. While much is now known about the properties of the primary flux, there are still significant gaps in our knowledge. Very little can be stated with certainty concerning the source of cosmic rays or of the acceleration mechanism that imparts such enormous energies to single protons or nuclei (the highest detected energies correspond to the kinetic energy of a tennis ball traveling at 50 km/hr!). There is growing evidence, however, that certain types of stellar systems may be responsible for a substantial portion of the flux. Once a major experimental resource of particle physics, cosmic rays declined in importance following the invention of particle accelerators. Their role in particle physics is nevertheless far from defunct. There exists now an interplay between accelerator-based and cosmic-ray-based particle physics whereby each in its own way informs the other. In this chapter, we summarize the current status of the field. After describing, first, what is known about the primary flux and, second, the detection techniques appropriate to different regions of the cosmic-ray energy spectrum, we attempt a brief overview of the contributions to particle physics that cosmic-ray physics has made in the past and can be expected to make in the future. We conclude with a relatively detailed exposition of an issue which has caused the accelerator-based community to sit up and take notice in no uncertain terms: the underground observations of muons apparently related to the X-ray binary, Cygnus X-3. 7.2. The primary cosmic-ray spectrum The particles that impinge on the top of the Earth’s atmosphere have an energy spectrum that extends to at least —100 EeV (1 EeV= i03 PeV= 106 TeV). The all-particle spectrum (fig. 7.1 [Jones 1985]) has, over most of its range, the form of a power law dNIdE 1 IE~ with a “knee” at —1 FeY, where the spectral index changes from y 2.7 to y 3.1, and a possible “ankle” at —10 EeV. The precise form of the spectrum in the region of the knee and, particularly, at the highest energies has still to be established, and is the subject of active research. The particles that make up the CR flux are predominantly light nuclei, although all stable nuclei, —

-—

—

300

J. Rich et a!., Experimental particle physics without accelerators N-N CM. ENERGY ~ 1.0

0.1

(1ev)

10

100

102 -

1012 1010

.

8—

\\

\

<108 ~1010

10~

-~

~ id~12~

~._

iO14~

~

I~_

~)

10

10121013 1014 1015

1016 1017 1018 1019 1020

ENERGY (eV) Fig. 7.1. The integral spectrum of the primary cosmic-ray flux vs. energy per particle (bottom scale) and vs. the equivalent energy in the CM of a nucleon—nucleon system.

many long-lived radioisotopes, electrons, and antiprotons have also been detected. In the low-energy region of the spectrum, protons and then a-particles are the dominant components, followed by the CNO, the medium-heavy (Z = 10—20), and the Fe (Z = 21—30) groups of nuclei in that order. The composition of CR above —100 TeV/particbe has not been firmly established, and is again an area of active research. The relative abundance of the Fe group is known to be increasing in the 10 GeV to 10 TeV region, but in the absence of incontestable data opinions differ as to what the behavior is at higher energies. One point of view is that the increase continues until heavy nuclei become the predominant component of the all-particle spectrum in the region of the knee and beyond; the other point of view is that the increase is a transitory phenomenon, associated with the knee, and that proton dominance is re-established by 100 PeV. The question of the relative abundance of iron is a very important one, since the interpretation of very-high-energy CR data rests on an understanding of —

—

primary composition.

Anisotropies in the arrival directions of CR have long been sought in the hope that they might provide clues to the origin of the flux, particularly at the highest energies. Years of painstaking work have indeed revealed departures from isotropy, but the effects are generally small, and it is not far from the truth to picture the local flux as isotropic. An exciting recent development (and an exception to the above generalization) has been the possible observation of point sources of y’s with energies in TeV and PeV ranges. (Some of the evidence, which is compelling but not yet incontrovertible, will be described in connection with Cyg X-3 in a later subsection.) The sources appear to be either X-ray binaries (like Cyg X-3) or pulsars (like that in the Crab), and the hunch is that, at such high energies, the y’s are produced hadronically. Thus, for the first

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time in the history of cosmic rays, it may be possible to identify specific CR sources with some degree of confidence. Finally, although they have yet to be detected, it is virtually certain that ultrahigh-energy neutrinos must be present in CR. Their detection with sufficient efficiency would constitute an invaluable means of addressing the problems of the origin and acceleration of CR, topics which, though fascinating, are beyond the scope of this review. 7.3. Experimental techniques Cosmic-ray experiments may be broadly divided into two classes depending on the energy and, therefore, the flux of that part of the CR spectrum that is investigated: a) those in which the primary particle and its interaction are observed in the detector; and b) those in which the primary is not observed directly, and what is sampled is the so-called extensive air shower (EAS), the cascade of secondaries resulting from the primary interaction in the atmosphere. The line of demarcation between the two classes lies somewhere in the region of 1 particle/m2 hr in terms of flux, which corresponds to 100 TeV/particle in terms of incident energy. The techniques used in the two cases are summarized in fig. 7.2 [Gaisser and Yodh 1980] and have been described in the reviews of McCusker [1975],Gaisser et a!. [1978], and Gaisser and Yodh [1980].

~ SINGLE INTERACTIONS ATMOSPHERIC CASCADES balloon—borne

,

ground based

(satellite) small I large ~extensive (small)air shower (large) arrays— calorimeter 1~~r imeterl

I

emulsion (small)

chambers (large)

F—Fly’s Eye———-~

.—emulsion stock typical area solid typical angle exposure

Energy

tsr 5m’sr SOm2sr lO4m2sr l—lOOkmtsr .lm’sr .5m day day months yr yr yr —lOyrs

eV per 1012 nucleus) in GeV) 102

Integral flux(per sr) i top of atmosphere’ lm2s’

l

lQ’~ t

,

IQ’

lO~

__________

Im2hr’

i

___________

10”

1020 10’

__________________________

3m2yr~ lkmtday’ .O3km2yr’

All particles

Fig. 7.2. The experimental techniques appropriate to different energy ranges, and thus different fluxes, of the incident cosmic-ray spectrum [Gaisser and Yodh 1980].

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7.3.1. Extensive air showers The core of an EAS consists of a cascade of energetic, forward-going hadrons produced in and initiating successive interactions with atmospheric nuclei. It is narrow, usually not exceeding a few meters in width throughout its length, and is the source of the (mostly) pions that give rise to the other components of the EAS. Neutral pions produced in the core give rise to electron—photon cascades, which envelope the core. This component reaches a maximum density at a depth in the atmosphere which depends on the primary energy, and has a lateral spread typically of the order of a few hundred meters. The electrons in the electron—photon cascade also produce a significant flux of Cherenkov radiation, beamed in a cone (<100) around the core. Charged pions migrate away from the core. The more energetic usually interact, while the lower-energy ones decay, giving rise to a muon and neutrino flux that extends out beyond the electron—proton cascade. 7.3.2. Traditional EAS detection The traditional technique of investigating the ultrahigh-energy CR flux through the detection of EAS was originated by Rossi, and consists in sampling the EAS at sea-level with a number of small detectors distributed over a large area. The wide-area density distribution is used both to estimate the size of the EAS and to locate the core; fast timing is used to reconstruct the shower front, and, thus, the arrival direction of the EAS. The major arrays currently in operation are the British array at Haverah Park, the Soviet array at Yakutsk, and the Japanese array at Akeno. The Haverah Park array is based on a few large water Cherenkov counters; the Yakutsk and Akeno arrays are based on a larger number of small plastic scintillators. In many cases, the basic detectors are supplemented with a number of more specialized detectors, such as magnetic spectrometers, lead-scintillator calorimetric sandwiches, and so on. A complementary technique [Khristiansen 19791 is based on the detection of the Cherenkov light emitted by the electron—photon cascade in its passage through the atmosphere. In this case, the basic detector is a mirror with a photomultiplier at its focus. Such “air-Cherenkov” installations can, of course, only be operated on clear moonless nights, and must be located far from sources of ambient light. The determination of primary energy from sea-level measurements of the EAS is one of the major difficulties of EAS experiments. Despite the large number of interactions that contribute to the generation of an EAS and the large number of particles that are produced, EAS are subject to large fluctuations, primarily due to fluctuations in the primary interaction and those immediately thereafter. Standard estimators of primary energy including various “size” parameters (total number of electrons or muons in the shower), the “age” parameter (describing the stage of shower evolution at sea level), the inferred depth of maximum of the electron—photon cascade are reliable only to a limited degree for several reasons: shower fluctuations coupled with the rapidly falling primary energy spectrum; uncertainties in primary composition; and energy calibration, which has to rely on sophisticated mathematical and computer modeling of shower developments in the atmosphere and is, therefore, subject to uncertainties in and lack of knowledge of information about nuclear collisions at very high energies. —

—

7.3.3. The Fly’s Eye observatory The Fly’s Eye detector [Cassiday 19851 observes EAS directly and calorimetrically in a very large volume through the fluorescence of molecular nitrogen in the atmosphere. Although fluorescence is a

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very weak effect, it has the advantages of being isotropic, so that EAS can be observed from the side, and of being a measure of shower density at the point of emission. The technique is, thus, an improvement on the traditional EAS array and on the air-Cherenkov technique (the Fly’s Eye installation can also be operated in air-Cherenkov mode, of course) in terms of acceptance, shower imaging, and calibration. The detection unit is a large-diameter, spherical-section mirror viewed by photomultipliers located in the mirror’s focal plane. The 67 units at the main site of the observatory contain a total of 880 PMs, which collectively image the entire night sky, the projection of the PM acceptances onto the celestial sphere resembling the compound eye of an insect hence, the name. A further 8 units, located at a second site, 3.3 km distant, view an azimuthal quadrant of the night sky. The pulse integral and timing of each PM is recorded when an EAS “flashes” across the night sky. The hit pattern and timings of the PMS are used to reconstruct the trajectory of the EAS, and the pulse integrals, suitably corrected for light attenuation and Cherenkov-light contamination, are used to reconstruct its longitudinal profile and its energy. The detector is sensitive to EAS with energies above 0.1 EeV, and can “see” a sufficiently energetic EAS at a distance of more than 20 km. The site, Dugway, Utah, was chosen for the clarity of its atmosphere and the absence of ambient light. Observing periods are limited to clear, moonless nights, corresponding on average to the rather low duty factor of 6.3%. Starlight, diffuse galactic radiation, photochemical processes in the ionosphere and scattered sunlight all induce a DC background in the PMs. Fluctuations in this DC signal and wandering sources, such as planets, aircraft and certain stars, constitute the noise that limits sensitivity. The experimental questions addressed by the installation are: measurement of the proton—proton total cross section; investigation of the primary CR flux (energy spectrum, chemical composition, isotropy) at the highest energies; searches for anomalously penetrating EAS; and searches for -y-ray sources. —

7.3.4. DUMAND

The j~eepI~~nderwater Muon ~nd Neutrino i~etector[Grieder 1986] is another unconventional project. The ultimate aim of the project is to instrument 0.25 X 0.25 X 0.5 km3 of the Pacific Ocean with a 3-dimensional array of photomultipliers, and to use this volume of sea water (30 million tons) as an active detector for very-high-energy muons and as both a target and detector for very-high-energy neutrinos. The final detector will consist of a 6 x 6 matrix of vertical detector strings anchored to the ocean bed at a depth of 4.8 km, 30 km off the coast of Hawaii. Each 500-m string will support 21 specially designed, wide-solid-angle photomultipliers, and 3 sophisticated control modules to monitor and operate the photomultipliers and to transmit data to the on-shore computer. All components will have to function reliably in an inaccessible and very inhospitable environment, and a prototype string is currently undergoing tests. The experimental goals of the project are fourfold. Firstly, in the field of astrophysics and astronomy, DUMAND will search for an extraterrestrial muon neutrino flux. Such a flux could identify likely sources of CR. Secondly, through a study of muons with energies greater than 3 TeV, DUMAND will be able to investigate the primary CR flux between 10 TeV and 1 EeV, and derive the energy spectrum and the chemical composition, as well as search for anisotropies. Thirdly, the experiment will be able to investigate the physics of muon and neutrino interactions at energies that will remain beyond the scope of accelerator experiments for the foreseeable future. Finally, it will be able to search for new

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penetrating particles (e.g., photinos) produced in the atmosphere or in stellar objects [Robinett 1986; Midorikawa and Yoshimoto 19861. 7.4. Particle phyics in cosmic-ray experiments It is not exaggeration to say that particle physics was born in the cloud chambers of early CR experiments. Many of the “stable” particles in the Particle Data Booklet the i-r’s, the K’s, the A, etc. were discovered in such experiments during the heydays of the 1930’s and 1940’s. (The last such discovery was that of the ~ in 1953.) During the 1950’s, the two fields started to diverge, and by the 1960’s accelerators had established their ascendancy over CR as the major resource of experimental particle physics. Though results continued to emerge from CR experiments, the superiority of accelerator experiments in terms of control, reproducibility, and statistics led to a growing tendency on the part of accelerator-based physicists to regard CR data skeptically or, even, to ignore it completely! A significant number of accelerator-based discoveries were, nevertheless, first glimpsed in CR experiments. A partial list of such examples might be: the rise in total proton—proton cross section; the behavior of mean multiplicity as a function of energy; the rise in the central rapidity plateau; the increase in mean momentum with energy; the observation of scaling in the forward region; the behavior of mean multiplicity as a function of atomic number; the observation of charmed particles; and the observation of jets. There is every reason to suppose that CR physics will continue to play a role in giving accelerator-based physicists a foretaste of what the future holds in store for them. In the remainder of this chapter, we discuss some of the measurements and observations of current interest. We cannot hope to do justice to the large and varied amount of work being done in the field, and apologize in advance to our CR colleagues. —

—

—

— — — —

— — —

7.4.1. Total cross sections The rise in the pp total cross section later confirmed at the Intersecting Storage Rings in 1973 was predicted by Yodh et al. [1972] on the basis of CR data, and it is clear that the determination the pp cross section at ultrahigh energies will remain the province of CR EAS experiments. The principal causes of uncertainties in CR total-cross-section measurements are incomplete knowledge of the primary composition, EAS fluctuations, and the extraction of o-10~(pp) from unei(p-Air). These systematic effects have continued to become better understood [Yodh et a!. 1983], making possible results of the precision of the Fly’s Eye measurement [Baltrusaitis et a!. 1984] o~0~(pp) = 120 ±15 mb at ~ 1 EeV which is compatible with the continued (In ~)2 evolution of the cross section up to =30 TeV. —

—

7.4.2. Ultrarelativistic heavy-ion collisions Lattice-gauge calculations have suggested that, at sufficiently high energy densities, nuclear matter may undergo a deconfinement phase transition leading to the formation a quark—gluon The 3, a of density that could plasma. be achieved critical energy density is thought to be in the region of a few GeV/fm

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through the interaction of a CR nucleus in an emulsion chamber at a detectable rate. The Japanese— American emulsion-chamber team (JACEE) have, in fact, observed six high-multiplicity nucleus— nucleus interactions with estimated energy densities in the region of 2—5 GeV/fm3 [Wosiek 1985]. The events are unusual in that the average transverse momentum of secondaries is abnormally high and the event-by-event rapidity distributions of secondaries appear to contain fluctuations of a non-statistical character. While it is possible that the events represent a first observation of the quark—gluon plasma, it is far too premature to claim them as such, and more data are clearly required. 7.4.3. Searches for exotic particles Some CR experiments are sensitive to certain types of hypothesized new particles. A long-lived particle of very large mass (>1 TeV) produced in an air shower would encounter a ground-based detector delayed with respect to the shower front by a significant interval. It does not matter if the delayed signal were caused by the massive particle itself, or by its decay products, or by secondaries produced through its interaction in the atmosphere, when searching for such a signal. The EAS-imaging detectors and the underground calorimeters could also observe a highly penetrating component of the primary or secondary CR by requiring that its interaction vertex be located deep inside the atmosphere or by detecting anomalous tracks deep underground. Searches of this type could signal the existence of heavy leptons, heavy quark matter, supersymmetric particles, magnetic monopoles, or other weakly interacting components of the CR flux. The results are, for the present, mostly negative [e.g., Battistoni et a!. 1983; Baltrusaitis et a!. 1985; Mincer et a!. 1985]. Yock [1986], however, has recorded four anomalous events, which could be explained by the existence of a long-lived particle with a mass of —4.5 GeVIc~. The Kolar Gold Field underground experiment [Krishnaswamy et al. 1976, 1977] has reported several curious events that they have interpreted as new particle production. They are characterized as multitrack, large-opening-angle events, some with a vertex in air. The new proton-decay experiments should be capable of clarifying the nature of these events. 7.4.4. Centauro events The original Centauro event was found in the two-storey emulsion chamber of the Brazil—Japan collaboration on Mt. Chacaltaya [Lattes et a!. 1973]. The lower chamber, a 6-cm Pb-emulsion sandwich, contained —200 TeV of visible energy, the upper chamber, a 7.8-mm Pb-emulsion sandwich contained only —30 TeV of visible energy, and the tracks measured in the chambers extrapolated back to an interaction point about 50 m above the detector. (The two chambers were separated by a 23-cm layer of pitch, corresponding to about 0.3A 0 and 0.4X0, and a 1.5-m air gap.) Analysis of the event led the authors to conclude that 74 hadrons had been produced in the primary interaction, but that none of these were neutral pions. (The name “Centauro” arose because of the ostensible incompatibility of the information furnished by the upper and lower chambers.) Five more similar, but somewhat less spectacular, events have been observed. All the events cluster around an estimated incident energy of about 1700 TeV and constitute about 5% of all observed interactions with visible energy >100 TeV, and are further characterized by large secondary transverse momenta. Searches at the highest available accelerator energies have not, however, shown any indication of such an effect, though this may be due to a threshold. If the events are proton-induced, they should be seen at the SSC. No convincing interpretation of these events as a background from known processes or as a true signal due to a plausible new particle or interaction has, as yet, been put forward, and, given the

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J. Rich et a!., Experimental particle physics without accelerators

amount of time that has elapsed since their discovery, it satisfactory explanation.

is

possible that the events may never find a

7.5. Cygnus X-3 7.5.1. Astronomical observations Cygnus X-3 is a remarkable astrophysical object. It was first identified 20 years ago as a powerful point source of X-rays. It lies, as its designation implies, in the direction of the constellation Cygnus, which places it in the plane of the galaxy roughly at right angles to the direction in which we view the center of the galaxy. Its exact coordinates are right ascension a = 20.53 hr, declination 8 = 40.91°. Astronomical distance is always hard to estimate, and the case of Cyg X-3 is no exception. Fortunately, a gigantic burst of radio activity persisting for a few days in October 1982 provided the necessary means [Dickey 1983]. The galaxy is pervaded by clouds of hydrogen, whose velocity distribution within the observable part of the galaxy is quite well known owing to the radiation of the 21-cm hyperfine line. The Doppler shift of the 21-cm line in the absorption spectrum of Cyg X-3 recorded in October 1982 could thus be used to limit the distance of the object. Cyg X-3 is thus found to be on or beyond the periphery of the galactic disk. An extragalactic location can, however, be ruled out on the grounds that it would require an impossibly high luminosity for the object. We, therefore, locate Cyg X-3 in an exterior galactic spiral at —10 kpc from us, roughly the same distance from us as we are from the galactic center.

The X-ray, infrared, and radio emissions of Cyg X-3 are clear and unambiguous. The average luminosity in these wavebands is 5 X 10’~,iO’7 and 10’s GW respectively, compared with a total solar output of 4 X ~ Not only is Cyg X-3 very bright, however, it is also very variable. The X-ray and IR emissions are modulated with a very precise period (fig. 7.3) described by the ephemeris of van der Klis and Bonnet-Bidaud (the figures quoted are an unpublished update on earlier work [1981]): T=JD 2440949.8965 (10) p

0.i9968338 (18) days 0= dPI dt= 1.02 (7) x

PHASE Fig. 7.3. The Cygnus X-3 light curve at X-ray wavelengths. The counting rate (s ‘)ts plotted vs. the Cygnus X-3 phase.

J. Rich et al., Experimental particle physics without accelerators

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where T0 is an instant in the past of minimum emission measured in Julian days (the origin of the scale is around 4710 B.C.; 0:00 U.T. on 1st January, 1987 is JD 2446796.5000); P0 is the period of Cyg X-3 at t = T~ and dPldt measures the lengthening of the period (the figures in parentheses express the uncertainties in the last digits). The near equality of the period and a geophysical harmonic is a coincidence that plagues the interpretation of observations to be discussed below. The peak amplitude of the IR emission is constant to within 10—20%, but the X-ray amplitude can vary by an order of magnitude or more on a time scale of weeks or months. The radio emission does not have any regular periodicity; instead, it occasionally flares up by two or three orders of magnitude for a period of days. Such outbursts occurred in September 1982, October 1983, and October 1985. The latter outburst was accompanied by an upsurge in the X-ray emission as well. It has not been possible to identify an optical source with Cyg X-3. This is held to be due to absorption of the optical portion of its spectrum, either in the clouds of the intervening galactic arm or in a hypothesized gaseous cocoon that envelopes the system. There are also indications that Cyg X-3 is a broadband source of gamma-rays and, by extension, of cosmic rays, since very energetic photons are more likely hadronic (1T°—~.-y-y)rather than electromagnetic in origin. The evidence in favor of such emission is, however, more contentious than that of an the other emissions, and will be discussed later. 7.5.2. Structure The model of the Cyg X-3 system that has evolved from its observed spectral features is that of an asymmetrical eclipsing binary: a neutron star possibly a pulsar in close orbit around a more conventional, main-sequence star. The gravitational field of the neutron star deforms its companion, drawing its outer atmosphere out into a spatially extended disk of matter that encircles and spirals in on the neutron star in the plane of the orbit. Close to the neutron star, the accretion disk is heated and ultimately ionizes. The plasma so formed accretes under the influence of the neutron star’s magnetic field at its magnetic poles, creating very hot regions. In this picture, the radio emission is associated with extended accretion disks, and the IR and X-ray emissions with the hot regions close to the neutron star. The modulation of the latter emissions arises because of the occultation of the source by the companion star. The size of the X-ray-emitting region can be estimated on the basic of Stefan’s law of blackbody radiation (relating the power radiated, the surface area, and the temperature): the size thus obtained, —10km, corresponds well with the dimensions expected of neutron stars. The orbital radius can also be estimated, by invoking Kepler’s third law. Making the not unreasonable assumption that both stars have roughly the same mass as our Sun (the orbital radius is, in any case, a function of the cube root of the sum of the masses), one obtains a radius of .~~106 km, roughly double the Sun’s radius or one-hundredth the size of the Earth’s orbit. —

—

7.5.3. Gamma-ray astronomy A dozen or more groups have searched for evidence of a -y-ray flux emanating from Cyg X-3. While the majority report positive results (see the review of Watson [1985]), the statistical significance of the signals reported by individual experiments is marginal, the observations of different groups in similar spectral regions often do not accord with each other, and some aspects of the events claimed as signal are bizarre. (Gamma-ray signals from nine other stellar objects have also been reported, but Cyg X-3 is the strongest candidate.) The low-energy end of the -y-ray spectrum (30 MeV to 5 GeV) has been investigated using balloonand satellite-borne detectors; at intermediate energies (100 GeV to 100 TeV), the results come from

308

J. Rich et a!., Experimental particle physics without accelerators

air-Cherenkov installations; and, at high energies (100 TeV to 10 PeV), from EAS arrays. The difficulty besetting all experiments is the extraction of a signal from the background. Clear excesses of events pointing back at Cyg X-3 have been obtained by only two groups, whose results are, for other reasons, problematical. All experiments necessarily support their claims by showing that the distribution of the arrival times of events is modulated with the characteristic period of Cyg X-3. The unfortunate near equality of the period and the fifth harmonic of the Earth’s rotation period means that the detectors view the source at the same time of day on successive days, and are thus susceptible to unexpected systematic effects. Furthermore, in order to maximize their signal-to-noise ratio, many groups have adjusted the binning of or the cuts placed on their data, and it is then hard to assess the true significance of the peaks that emerge. The two satellite experiments, a 13-day exposure aboard SAS II in 1973 [Lamb et al. 1977] and a 300-day exposure aboard COS-B during 1975—82 [Hermsen et al. 19851, are in direct contradiction. The SAS II collaboration found enhancements in the phase diagram and an excess of events pointing back -10

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J. Rich et a!., Experimental particle physics without accelerators

309

to Cyg X-3; the COS-B collaboration found neither, and could set a 2o- upper limit on the flux at a value an order of magnitude less than the flux claimed by SAS II. The results of the ground-based experiments are summarized in figs. 7.4 and 7.5 [Watson 1985]. Taken at face value, the data, and particularly the air-Cherenkov data, appear to establish an effect, despite the considerable disagreement amongst the EAS measurements of the flux. The spectrum is consistent with a differential spectral index y 2.1 (compared with 2.7 for the cosmic-ray flux), and would correspond to a luminosity at source of 1022 GW, assuming isotropic emission. Hillas [1985]has calculated that, if the ~y-rayflux originates from the interaction of protons accelerated in the Cyg X-3 system, then the power output of Cyg X-3 should be in the region of 1023 GW (the equivalent of more than a million suns), easily sufficient to power the CR flux of the entire galaxy in a limited energy region. The Kiel group [Samorski and Stamm 1983] is the only EAS group to observe a peak in the distribution of arrival directions consistent with the location of Cyg X-3. Their array was equipped with muon detectors, and they found that the showers constituting the signal were not muon poor: the muon density found was 80% of that of proton-induced showers, compared with the 10% expected. This would imply either that there is an anomalous behavior of the high-energy photonuclear cross section [Ochs and Stodilsky 1986] or that the particle responsible for the showers is of a new type. A more conservative interpretation is that the Kiel signal is a statistical fluctuation of normal nucleus-induced showers. The large variation in the measured flux is difficult to interpret. Bhat et al. [1986]have suggested that S 6

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1985].)

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J. Rich et a!., Experimental particle physics without accelerators

the scatter of the EAS points is genuine, and that the -y-ray luminosity of Cyg X-3 is decreasing exponentially with a lifetime of about 2.5 yr. Chardin and Gerbier [1985] and Chardin [1987]take a different view: the more recent points, which indicate lower fluxes, correspond to observations of higher precision as would be expected if the signals reported were merely statistical fluctuations. These authors have criticized some of the analysis techniques used by the experimentalists involved, and, on the basis of their own simulated analysis, suggest that the true significance of the data is substantially less than that claimed. What should one conclude? The relatively good agreement in the position of the phase peaks of the different experiments (fig. 7.5) is quite compelling, and the concensus amongst the CR community is that Cyg X-3 is indeed a source of high-energy -y-rays, albeit probably a very variable one. Improved data would certainly be welcome, especially in the PeV region, and will doubtlessly be forthcoming. The observatories at Haverah Park, La Palma, and Dugway are to be upgraded in terms of their angular and temporal resolution and their acceptance; and plans are afoot to re-equip the hectare of steerable mirrors of a disused solar-energy installation in the French Pyrenees as an air-Cherenkov [Fontaine 1987]. Halzen, Hikasa and Stanev [1986]have described a variety of particle-physics experiments that could exploit point sources of high-energy photons. —

7.5.4. The underground-muon enigma While the Kiel results hinted that Cyg X-3 may be emitting new particles, the interest of the particle physics community was primarily stimulated by reports from underground detectors of penetrating muons coming from its direction. Two groups have published positive results: Soudan I and NUSEX. The Soudan I experiment (mostly) The first indication of a possible underground muon anisotropy [Bartelt et a!. 1985] came from the 31-ton Argonne—Minnesota (Soudan I) calorimeter located under 1800 hglcm2 of rock. This rock overburden corresponded to an energy threshold of 600 GeV for muons produced in the atmosphere. In a rather contrived analysis of multimuon events (events containing multiple, parallel, time-coincident muons), they found an excess of bursts of events (multiple events within a 200-mm interval) directed from a region of the celestial sphere (45°< 6 <75°,280°< a <310°)in the vicinity of Cyg X-3 (6 = 41°, a = 308°)but not actually containing it. There was, at this stage, no evidence of Cyg X-3’s characteristic period in the data. According to Marshak’s chronicle of events [Marshak 1985], this original Soudan result spurred the Irvine—Michigan—Brookhaven (1MB) collaboration to a search of their recorded data for an effect related to Cyg X-3 by temporal modulation as well as by direction of origin. Since the 1MB proton-decay detector (a water Cherenkov) did not have as high a multi-track efficiency as a calorimeter and because its trigger was biased against vertical muons, the 1MB data sample consisted of single muons at large zenith angles. The analysis initially seems to have borne fruit: the phase plot the distribution of muon arrival times (suitably corrected for source ephemeris) plotted modulo the period—exhibited a peak in the phase interval [0.2,0.3], a result published in the New York Times. The collaboration must, on further consideration, have had serious reservations about the authenticity of this initial finding for it never appeared in the scientific literature. (They later reported a null result [Bionta et a!. 1986].) News of the 1MB analysis did, however, prompt the Soudan group to re-examine their data. In their second analysis [Marshak et al. 1985a], the Soudan group concentrated on their single-muon —

J. Rich et al., Experimental particle physics without accelerators

311

data (784 456 events collected during a 0.96-yr lifetime between September 1981 and November 1983). Selecting events whose arrival directions lay within 3° (twice the angular resolution of the detector) of an adjustable point on the celestial sphere in the vicinity of Cyg X-3, they sought the maximum phase-plot signal by maximizing the x2 of a null hypothesis that the contents of each bin in the phase plot be consistent with the mean with respect to the location of the window. The result is the histogram in fig. 7.6 (the points in the figure represent the estimated off-source background). The maximum x2 (49.5 for 19 degrees of freedom) occurred with the angular cut centered on 6 = 43.5°, a = 306.7°,and the enhancement in the [0.65, 0.90] phase interval consists of 84 ±20 events above background, equivalent to a flux of 7 X 10_li cm~2~ Figures 7.7(a—c) show the variation of the x2 maximized with the two celestial coordinates and with the period used to compile the phase plot (the arrows indicate nominal Cyg X-3 values). The phase plot for events centered on the Cyg X-3 direction was presented in an ensuing publication [Marshak et al. 1985b], and is shown here in fig. 7.8(a). The enhancement in this case is 25% smaller 60 ±17 events and, though the corresponding x2 is not quoted, figs. 7.7(a) and (b) suggest that it is in the region of 30, again for 19 degrees of freedom. In the later publication, the Soudan collaboration adduce two further observations in support of their contention. The first is the phase plot for pairs of events occurring within 30 mm of each other, which is shown in fig. 7.8(b) (the phase plotted is the average for the two events). Off-source plots (figs. 7.8(c) and (d)) were used to estimate the background level. The event-pair signal in the [0.65, 0.90] phase interval 29 ±6 events above a background of 40 events is more pronounced than in the single-event case, a circumstance the authors attribute to the longer-term, episodic variability of Cyg X-3. The second piece of corroborative evidence concerns a 34.1-day periodicity claimed for Cyg X-3 by Molteni et al. [1980]on the basis of X-ray observations. In the Soudan data, it was found that on nine occasions either three or four muons had been observed in the 1.2-hr phase peak of a single (standard) Cyg X-3 cycle. The 34.1-day phase plot of these instances of “high activity” is shown in fig. 7.9 (the —

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events marked “A” and “R” are not Soudan events). The authors calculate that the probability that the clustering of events in the [—0.1,0.2] phase interval is a statistical fluctuation is 1%. The true significance of all these data is hard to assess, partly because of the nature of the analysis protocols developed by the collaboration. The choice of null hypothesis (uniform phase distribution) which defined the x2 subsequent maximized to elicit a signal is not as self-evident as might as first seem, since it presumed the absence of systematic bias. The background estimate plotted in fig. 7.6 was derived from an ensemble of manufactured events embodying ten times the statistics of the real data, yet this control sample deviates from the null hypothesis (x2 = 28 for 19 degrees of freedom) fully as much as in the case of the truly on-source phase distribution (fig. 7.8(a)). The coincidence of the Cyg X-3 period and the peak in the x2 distribution as a function of period (fig. 7.7) is misleading since this period was assumed when the angular window was chosen to maximize the signal. If this signal is a statistical fluctuation, then it is normal that it has a maximum at the nominal period. These are but two of the criticisms that have been leveled against the Soudan I results (see, for example, Chardin [1987]). We must conclude that their evidence is weak. The NUSEX experiment The most impressive evidence of an underground muon anomaly connected with Cyg X-3 came from a third proton-decay experiment: the so-called Ni,icleon stability Experiment (NUSEX). The detector, a 150-ton calorimeter located under 5000 hg/cm2 of rock, recorded 21700 single-muon events during a 2.4 yr lifetime between June 1982 and February 1985. The average rock overburden (6200 hg/cm2) corresponds to an energy threshold of about 5 TeV for muons produced in the atmosphere. In their analysis of these events, the NUSEX collaboration, like the Soudan collaboration, found it necessary to perform a maximization of the signal sought with respect to the angular window used to select events. In the Soudan case, this took the form of varying the location of a window of fixed size; in the NUSEX case, it took the form of varying the size of a window whose center was fixed on the nominal direction of Cyg X-3. The NUSEX group have, in fact, presented two analyses which differ in the shape of the window used: in the original publication [Battistoni et al. 1985], it was square 10°x 10°in 6 and a; in a later conference report [D’Ettore Piazzoli 1985], it was circular with a 9° diameter. The two presentations differ very little in their import, and we concentrated here on the latter solely because it was more fully documented. NUSEX’s on-source data sample consisted of 142 muon events whose arival directions lay within 4.5° of the direction of Cyg X-3. The off-source sample was selected from 27 similarly isometric zones in the same declination band as the on-source sample, thus ensuring that the muons in both samples had traversed the same rock overburden. The on-source phase plot is shown in fig. 7.10. It exhibits a peak in the [0.7, 0.8] phase interval comprising a total of 31 events including background. The off-source phase distribution was consistent with uniformity and corresponded well with the calculated background. A x2 test of the agreement of the on-source distribution with the off-source background (11.39 ±0.23 events per bin) yielded 30.5 for 10 degrees of freedom (P(>~2)= 3.6 x 10~~), while, when the same test was performed excluding the peak, the x2 found was 9.73 for 9 degrees of freedom. This 19-event signal, averaged over the Cyg X-3 period, corresponded to a flux of —5 x ~o 12 cm2 s The depth distributions of the background-subtracted in-phase events and of the 111 out-of-phase events are shown in fig. 7.11. The absence of events at larger depths indicated that the primary was not of a very penetrating nature, thus ruling out neutrinos. The collaboration also investigated the significance of the signal as a function of source ephemeris by varying the values of the period and its derivative. The results, expressed in terms of the x2 test for —

J. Rich et a!., Experimental particle physics without accelerators

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uniformity, indicated that departures from the nominal (van der Klis—Bonnet—Bidaud) ephemeris led to a deterioration of the signal. A perplexing feature of the NUSEX data is the angular dispersion of the muons that contribute to the phase-plot enhancement. The angular width of the signal corresponds to the full 9°diameter of the event-selection window, as demonstrated in fig. 7.12: when the size of the window was decreased, the significance of the signal diminished; when the size was increased beyond 9°,no increase in significance was found. This dispersion of the data (fig. 7.13) cannot be accounted for in terms of detector angular

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J. Rich et al., Experimental particle physics without accelerators

317

resolution, which was measured to be 1°or better, nor in terms of multiple scattering, which was expected to contribute a further 0.6°.No convincing explanation of the effect has been offered by the NUSEX collaboration, or, for that matter, by anyone else. The sheer improbability of such an angular spread having its origin in a physical process is the major factor weighing against the NUSEX result on self-consistency grounds. The problem of interpretation Suppose that the Soudan and NUSEX signals were to turn out to be genuine. The muons themselves must obviously be produced locally (in the atmosphere or in the rock above the detectors) through the interactions of a flux of, for the present, anonymous primaries. What do the experimental observations tell us about the nature of the primary particle, or cygnet, as it has been dubbed? Gaisser and Halzen [1986] and Berezinsky, Ellis and loffe [1986]have provided detailed replies to this question. A few simple considerations show that the cygnet could not be a known particle: — it must be neutral to retain its directionality in the galactic magnetic field; — its lifetime must be sufficient to cover the 10 kpc that separate the Earth and Cyg X-3; it must produce muons comparatively readily; and its interaction cross section must be in the semi-strong range, bounded from below by the fact that NUSEX sees no signals at zenith angles larger than that corresponding to 7000 hg/cm2 of rock cover. Of the known neutral particles, even the neutron is too short-lived to satisfy the lifetime requirement; the photon is ruled out because it couples too weakly to muons; and the neutrino is excluded by its weak interaction cross section. The time-of-flight limit on the cygnet lifetime is: -~

— —

>

10’~/y,

where y is the cygnet’s Lorentz factor. Thus, it would require a neutron of i09 GeV to make the —40 000-yr journey in one lifetime. The maintenance of phase coherence during transit of cygnets of different energies (velocities) implies a lower bound on the Lorentz factor: -y = EC/mC> iO. This can be transformed into an upper bound on the cygnet mass. If the NUSEX muons originate in the atmosphere (a circumstance that, for reasons mentioned later, seems untenable), their energy is >5 TeV. If we further assume that 10% of the cygnet’s energy is transferred to the muon, then we obtain the conservative limit: m~<5 GeV. The angular dispersion observed by NUSEX cannot be due to scattering in the interstal!ar medium without loss of phase coherence owing to the path-length dispersion entailed by such scattering. Moreover, kinematics dictates that muons sufficiently energetic to penetrate the NUSEX rock overburden cannot acquire an angular dispersion of much more than 1°in a cygnet—nucleon interaction, whether the muons are produced directly or in the subsequent decay of a secondary. The 5°dispersion observed implies E~<250 GeV, which, in turn, implies that muon production takes place within 1000 hg/cm2 of the detector, and which also permits us to revise the limit on the cygnet mass: m~<250 MeV with E~ 2.5 TeV. In order to penetrate sufficiently deeply (-—4000 hg/cm2), the cygnet—nucleon cross section cannot be -~

318

J. Rich et a!. - Experimental particle physics without accelerators

greater than —4 pb. On the other hand, since NUSEX did not observe a muon signal beyond a certain zenith angle, it cannot be less than ——2 rib: 2<

UCN <4

~b.

Berezmnsky et al. have stressed the similarity between NUSEX in relation to Cyg X-3 and the CERN neutrino experiments in relation to their ultimate source, the SPS (fig. 7.14). Is it conceivable that a particle with the properties that can be attributed to the hypothetical cygnet could have escaped detection in accelerator experiments? The null experiments (especially Fréjus) A total of nine experiments (table 7.1) have searched for muon signals connected with Cyg X-3. Their results are summarized in fig. 7.15. Aside from Soudan I and NUSEX, all experiments have reported a null result. The data of the Fréjus experiment [Berger et a!. 1986] are of particular significance. This experiment is comparable to the NUSEX detector in terms of rock overburden (profile as well as thickness), but superior in terms of sensitivity (the mass of the Fréjus calorimeter is 1 kton). The NUSEX collaboration have recently reported [D’Ettore Piazzoli 1986] that the most significant portion of their signal was recorded during 1984 (figs. 7.16(a)—(c)), a period during which the Fréjus detector, though on-line, observed no effect (fig. 7.16(d)). This suggests that the NUSEX result is a statistical fluctuation. Cygnet or ugly duckling? The Soudan I evidence is weak. The NUSEX evidence, though more robust, is contradicted by the observations of other experiments. It is particularly difficult to reconcile the NUSEX data with those of the Fréjus experiment. The effect, if assumed to be genuine, is impossible to interpret without the most radical consequences. We, therefore, believe that the NUSEX data represent a statistical fluctuation. A remaining hope for the cygnet is that it be observed by a second-generation experiment with much greater acceptance like the MACRO experiment [MACRO 1986].

Cygnus X-3

\

Detector .

.

Surf ace of each

J~o~gJc~2 Accelerator

Beam -dump

.

Detector

Fig. 7.14. A schematic comparison of the configurations of Cygnus X-3, the earth, and NUSEX with that of the SPS accelerator, the beam dump and shielding, and the CERN neutrino experiments.

J. Rich et a!., Experimental particle physics without accelerators

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J. Rich et a!., Experimental particle physics without accelerators

EXCESS MUON FLUX FROM CYGNUS X-3 DvtB ~

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2] ROCK THIOC~ESS[hg/cm Fig. 7.15. The excess muon flux (cm2 s~)and the 90% C.L. upper muon-flux limits measured by various detectors plotted as a function of detector depth (hg/cm2). The numbers in brackets refer to particular Cygnus X-3 phase intervals.

to

20.

5-

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0 0.

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Fig. 7.16. (a—c) The NUSEX phase plots corresponding to observation periods in 1982, 1983 and 1984 respectively [D’Ettore Piazzoli 1986]. (d) The Fréjus phase plot corresponding to its 1984 observation period [Berger et al. 1986].

J.

Rich et a!., Experimental particle physics without accelerators

321

8. Magnetic monopoles 8.1. Phenomenology of GUT monopoles Magnetic monopoles have been the subject of a great number of reviews [Groom 1986; Giacomelli 1986; Musset 1986; Preskill 1984; Giacomelli 1984; Carrigan and Trower 1983] and one book [Craigieet al. 1986]. Because of this our treatment will be brief. The modern study of monopoles began with Dirac, who showed that, in order to maintain the consistency of quantum mechanics, the existence of a magnetic monopole would imply the quantization of charge. Such “Dirac” monopoles would have a magnetic charge that is a multiple of the fundamental magnetic charge, q~: q~= (1/2a)e,

(8.1)

where a is the fine-structure constant, and e is the fundamental electric charge. Given the widespread confusion concerning electromagnetic units, it is, perhaps, worth emphasizing that eq. (8.1) means that, if the magnitude of the electrostatic force between two stationary electrons is equal to F, then the magnitude of the force between two stationary monopoles separated by the same distance is equal to 2F. At the same separation, the magnitude of the Lorentz force between a stationary monopole (13712) and an electron moving at a velocity v perpendicular to the separation vector is equal to (v /c)(137 /2)F. The mass of the monopole was not fixed by Dirac’s arguments, so monopole searches prior to 1975 concentrated on light (<10 GeV/ c2), relativistic monopoles produced at accelerators or in cosmic rays. A review of these searches was given by Craigie et al. [1986]. Polyakov [1974] and ‘t Hooft [1974] generated a revival of interest in magnetic monopoles by showing that their existence was a natural consequence of the basic ideas of Grand Unified Theories. These “GUT” monopoles are expected to have the Dirac magnetic charge, but to have masses near the unification mass. If one makes the famous “desert hypothesis”, i.e., that there is no intermediate energy scale between 100 GeV and the unification scale, then the unification mass is M~ 1014 GeV/c2, and the monopole should have a mass of Mm M~/a~1016 GeV/c2. Here, a~is the fine-structure constant renormalized at the unification mass, and is larger than 1 / 137. The production of GUT monopoles at accelerators is, thus, impossible, and any monopoles in existence must have been created during the Big Bang. Initial calculations of the present-day density of relic monopoles suggested that the number density might be comparable with that of baryons. This would lead to a cosmological mass density 14 orders of magnitude higher than that observed. Inflationary cosmological models avoid this problem by diluting the monopole concentration during a period of exponential expansion. As a result, it is entirely possible that the present monopole density is far too small to be observable (——1 in the visible universe), although this is not necessarily the case (see [Preskill 1984]). Super-heavy relic monopoles are expected to have a motion that would now be determined by galactic gravitational and magnetic fields. For masses greater than 1017 GeV/c2, gravitation would dominate, and monopoles would have velocities near the galactic virial velocity of about 200 km/s —103c. Below this mass, acceleration by galactic magnetic fields would give higher velocities (/3 103M~2where the monopole mass is in units of i017 GeV/c2). The large mass and low velocity expected of GUT monopoles determine present-day detection strategies. Whereas relativistic monopoles have a large specific ionization (facilitating their detection ——

-—

—

-—

322

J. Rich et a!., Experimental particle physics without accelerators

with scintillators), slow monopoles lose energy at a rate similar to that of minimum-ionizing particles, and generate signals spread out in time as the monopole passes slowly through the detector. Monopoles with masses near i01I~~ GeV/c2 and with /3 —— i03 have sufficient kinetic energy to pass through the Earth, so monopole detectors can be placed underground to minimize the background from normal cosmic rays. A final probable characteristic of GUT monopoles is that they catalyze proton decay [Rubakov 1981; Callan 1982] through reactions like: monopole

+

p

—~

monopole +

IT°’rr°e± -

The cross section for such a reaction is expected to be characteristic of the strong interactions (mb). There are a variety of astrophysical limits on the flux of low-velocity monopoles. They serve as an indication of the sensitivity required of monopole detectors. The existence of the galactic magnetic field has been used by Parker [1970,1983] to set the most model-independent limit. He noted that observed galactic electric fields are very small because they are “shorted out” as they accelerate electrically charged particles. On the other hand, the observed 2—3 pgauss magnetic field implies there are few magnetic monopoles, and Parker set a limit on the monopole flux of iü’~cm2 s~sr’ for monopoles of mass 10 GeV/c or less. The upper limit rises to 10 cm s sr for monopoles of 10 GeV/c. Above this mass, the flux limit again falls due to the requirement that the monopole mass density not exceed the total mass density of the galaxy. The Parker limit for a mass of 1016 GeV/c2 corresponds to an incident flux of one monopole per year in a detector of area 250 m2. Direct monopole searches are just now beginning to achieve this sensitivity. Stronger astrophysical limits come by assuming that monopoles catalyze proton decay with cross sections in the millibarn range. Monopoles trapped gravitationally in astronomical objects would then catalyze proton decay at a high rate, providing a new source of energy. Such a source of energy would be especially important in a neutron star, causing it to heat up and emit a substantial flux of ultraviolet and X-ray photons. Observational limits on the ultraviolet and X-ray luminosity of old pulsars have been used to set a bound on the flux of monopoles of about 10_2 cm~2s’ sr~[KoIb et a!. 1982; Dimopoulos et al. 1982; Freese et a!. 1983]. This is to be compared with a limit of 7.2 X 10_15 cm2 s’ sr’ set by proton-decay experiments that have looked for multiple proton decays induced by a passing monopole [Errede et a!. 1983]. 8.2. Heavy-monopole detectors Detectors of cosmic-ray monopoles fall into one of two categories: induction detectors, relying on the electromagnetic interaction between a monopole and a conducting loop; and detectors based on monopole interactions during their passage through matter. As we will see, the two types of experiments are complementary. The induction technique is the only technique that is based solely on a straightforward application of Maxwell’s equations modified by the presence of monopoles. The passage of a single monopole through an isolated, superconducting loop generates persistent currents in the loop that cause a change in the magnetic flux through the loop given by (cgs units): —

~41rq~.

(8.2)

J. Rich et a!., Experimental particle physics without accelerators

323

For a Dirac magnetic charge, this is twice the fundamental quantum of flux, cI~= hcl2e = 2.07 x i0~gauss cm2. As emphasized by the advocates of this technique, the signal is independent of the monopole mass, velocity, and electric charge, which is not the case for other types of monopole detector. The flux change is detected via a jump in the loop current, the size of which is determined by the loop’s self-inductance. For a circular loop of diameter D and wire thickness d, the inductance L is given by: L

=

O.41T (D/1 m)[ln(8D/d)

—

1.75] 1iH.

(8.3)

The logarithm is of order 10 for D = 1 m and d = 0.25 mm, so: -

137 1 ec

~t-—-~-

~

i~

-~

x 10’~amps

~

(8.4)

-

While signals of this size can be detected easily with SQUID’s, such a signal is much smaller than that caused by normal fluctuations in ambient magnetic fields. Great care must, therefore, be taken to shield or stabilize a!! external magnetic fields. On the other hand, eddy currents, induced by the monopole’s passage in such magnetic shielding, reduce the signal below that given by eq. (8.4) by an amount that depends on the monopole’s trajectory. Inductive coupling between shield and loop must, therefore, be minimized if a unique monopole signal is to be preserved (see [Caplin et al. 19861). There are two clear, but perhaps not fundamental, problems with the induction technique. The first is that false events can be generated by mechanical or thermal effects. Such effects could well be the origin of the candidate events reported by two experiments [Cabrera 1982, 1983; Caplin et al. 1986]. Present efforts are concentrated on controlling these effects by monitoring mechanical shocks, by using loop structures (gradiometers) insensitive to non-monopole fields, and by requiring coincidences between more than one loop. 2. The other problem is that the expense of large cryogenic systems has limited detector sizes to ~1 m At present, four groups [Incandela et al. 1984; Bermon et al. 1985; Caplin et al. 1986; Cromar et al. 1986] have published limits on the monopole flux near 5 X 1012 cm2 s~sr~(see table 8.1), giving a combined limit near 10_12 cm2 s~sr~,but still more than three orders of magnitude above the Parker limit. Experiments that are planned (see, e.g., Incandela et a!. [1986]and the review of Groom [1986]) may have sufficient sensitivity to reach the Parker limit, but only after several years of running time. A Table 8.1 Monopole flux limits from induction detectors Reference

Cabrera 1982 Cabrera et al. 1983 Incandela et al. 1984 Bermon et al. 1985 Caplin et al. 1985, 1986 Cromar et al. 1986

Number of candidates

Limit (90% CL) (1012 cm2 s~sr’)

1 0 0 0 1 0

610 37 6.7 5.5 6.0 5.0

324

J. Rich et a!., Experimenta! particle physics without acce!erators

discussion of the ultimate limitations of this technique has been given by Frisch [1983].The possibility of using non-superconducting loops has been discussed by Price [1983]. The second class of experiments use conventional particle detectors to search for slow, penetrating particles with energy losses consistent with those calculated for massive monopoles. While such detectors can be made much larger than existing inducton detectors, the interpretation of results depends on calculations of the detector’s response to monopoles. Taking into account only the effect of the monopole’s induced electric field on atomic electrons, we would expect a slow monopole to ionize like a particle of charge q~v~~1/c, Vrei is orbital the relative monopole-electron 3c, Vrei is essentiallywhere the atomic velocity (of order a ‘c). velocity. Using thisFor andmonopoles eq. (8.1), slower than 10 we expect, very roughly, that a slow monopole ionizes like a normal particle of the same velocity but with charge e/2. As is well known to high-energy physicists, specific ionization rises at low particle velocity like /3 2 It is perhaps less well known that it falls again below /3 102 reaching the level of a minimum-ionizing particle near /3 ~ The detection of monopoles below this velocity with standard techniques is then difficult. Detailed calculations (reviewed by Groom [1986]) give, for example, a cutoff on the production of scintillator light in the range (1—6) x 104c. (By a curious coincidence, this cutoff velocity is just below the galactic virial velocity.) Drell et al. [1983]identified another mechanism important at low monopole velocities. The passage of a monopole near an atom induces atomic-level crossings via the Zeeman effect, and may leave the atom in an excited state. In helium, the resulting energy loss is about ten times greater than that due to normal ionization. If a proportional counter were filled with helium and a quenching gas of low ionizing potential, ionization electrons would then be produced through collisions between the excited helium atoms and the quenching gas (the Penning effect). This mechanism forms the basis of recent monopole searches using proportional counters [Kajino et a!. 19841. A great number of experiments using scintillators and proportional chambers have published monopole flux limits (see fig. 8.1 and the reviews of Giacomelli [1986] and Groom [19861). The experiments differ in their calculated velocity thresholds ranging up from 104c. The lowest limits come from the Baksan experiment [Alexeyev et al. 1985], which reported a limit near the Parker limit (l0_15 cm2 s’ sr’) for velocities greater than 10~3c. The experiments with the lowest velocity thresholds use helium-methane proportional chambers [Kajino et a!. 1984; Masek et al. 1985], and have reported limits near 3 x 10_13 cm~2~ sr~ or velocities greater than —2 x 104c. Several large detectors that are now operating [Giacomelli 1986; Groom 1986] will improve these limits. Plastic track-etch detectors may be sensitive to monopoles with velocities somewhat lower than the cutoff velocities for scintillators and proportional chambers. Price [1984] set a limit of 10~3cm1sr~~ for monopoles with velocities near 10~4c.A 800m2 track-etch detector is now operating in Japan. Planned detectors were reviewed by Groom [19861and Giacomelli [1986].The largest, the MACRO experiment [MACRO 1986] planned for the Gran Sasso laboratory, uses scintillators, streamer chambers, and track-etch detectors to cover an area of more than 10000 m2. This will allow a search for monopoles at fluxes well below the Parker limit. Finally, we note one existing observational limit below the Parker limit. Price et a!. [1986]searched for fossil monopole tracks in 4.6 x 108 yr old mica. They calculated that visible tracks would be produced by the passage of a monopole bound to a heavy nucleus. The formation of such bound states is plausible owing to the strong monopole—dipole interaction, though such states would be short lived if monopoles catalyze proton decay. Assuming that they are stable, the authors used the non-observation —

J. Rich et al., Experimental particle physics without accelerators

10—11

I

I

325

I

TARLE

indurtion (all)

I 1012-

Tr.Etch

10-13

/

scint.

B~ELLI~~:Etrh

~

He

HARA

-

PRICE

-

E KRISN ASWAMY tas counter io—l’

-

-

DOKE Tr.Etch Scint. i0—~

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I

10—’

ALEXEYEV I

i~—~

I

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10_i

1

Monopole velocIty 13 Fig. 8.1. Some monopole flux limits for induction, scintillator, helium-proportional-counter, and track-etch detectors. The velocity range of the limits must be calculated for each detector.

of tracks to set limits between 5 X i0’9 and 5 X i0~’7cm2 s~’sr~for monopoles with velocities near 103c. Loopholes in the arguments by Price et al. have been discussed by Groom [1986]and Giacomelli [1986].

9. Fractionally charged particles 9.1. Introduction Fractionally charged particles (FCP’s) have been the subject of a multitude of searches ever since Gell-Mann [1964]and Zweig [1964]proposed that quarks of charge ~e and ~e were the fundamental constituents of hadrons. Although unsuccessful, these searches have been essential in that they led to the notion of confinement, a notion now central to QCD. Search for FCP’s will continue to be important, either as tests for the breakdown of confinement, or as searches for fractionally charged non-quark objects proposed by other theories (see for example [Ingelman and Wetterich 1986]). Quark searches may be fairly clearly placed into one of four categories: accelerator searches; cosmic-ray searches; searches for fractional charges residing in bulk matter; and searches for fractional—

326

1. Rich et a!., Experimental particle physics without accelerators

ly charged particles extracted by various means from bulk matter. Searches using all of these techniques were reviewed in detail by Jones [1977]. Marinelli and Morpurgo [1982] reviewed bulk-matter techniques emphasizing magnetic levitation, but also discussing some new techniques not discussed by Jones. Kim [1973] reviewed extraction and bulk-matter techniques emphasizing magnetic levitation. Lyons [1985] recently reviewed the entire field with the emphasis on accelerator and cosmic-ray searches. Here, we provide a short review of the non-accelerator searches, and give some prospects for the future. 9.2. Cosmic-ray searches

Fractionally charged particles have been sought in cosmic rays in a variety of configurations and conditions: at high altitude, at sea level and underground; at large and at small zenith angles; as isolated tracks and as tracks accompanied by or delayed with respect to a shower. The best upper limits on the flux (see the review of Lyons [1985])are generally near 10_b cm2 sr’ ~ (30m2 sr~y1), though a deep underground experiment designed to detect magnetic monopoles, reported limits near 10_12 cm2 sr’ s1 on penetrating FCP’s [Mashimo et a!. 1983; Kawagoe et a!. 1984]. The surface cosmic-ray flux is more than eight orders of magnitude larger than the limits on the surface FCP flux. To eliminate this background, all searches rely on the fact that fractionally charged particles ionize less than integrally charged particles of the same velocity, The ionization is generally measured by scintillator stacks, or by tracking chambers in the case of FCP’s accompanied by air showers. If non-relativistic particles are to be included in the search, the ability to measure the velocity is also essential, because of the rise of specific ionization at low velocity. Published flux limits can be interpreted either as limits on the primary cosmic-ray FCP flux or as limits on the FCP production rate by normal cosmic rays. Because the normal cosmic-ray flux falls rapidly with energy (see the chapter on cosmic rays), interpretation of flux limits in terms of a production cross section requires assumptions about the energy dependence of the cross section. Various possibilities and comparisons with accelerator searches were discussed by Jones [1977]. 9.3. Searches for fractional charges residing on bulk matter

The presence of an FCP can be unambiguously established by measuring a residual fractional charge on a sample of bulk matter. A “theoretical” limit on the concentration of FCP’s in matter can be derived by assuming that all terrestrial FCP’s come from cosmic rays and by then using the limit on the surface FCP flux. Taking a flux of 10” cm2 sr1 s~over the history of the Earth (3 x i09 yr) and assuming that the FCP’s are spread through the crust to a depth of 3 km (the geological mixing depth), we can expect at most 1 FCP per 200mg of material (10-23 FCP/nucleon). The most sensitive experiments, summarized in table 9.1, have not studied such a large amount of material, so one must hope that, because of chemical effects, FCP’s have become concentrated in certain materials or that there is a large primordial density of FCP’s on Earth. The chemistry of quarks was recently discussed by Lackner and Zweig [1983].The problems involved in calculating the cosmic relic density were discussed in Steigman [1979]. Two types of residual-charge experiments have studied milligram quantities of material. The first type is based on Millikan’s technique of observing the motion of charged drops under the influence of gravitational and electric fields in a viscous medium. The original Millikan experiment used drops of about lO~~ g in order that the effects of gravity would not completely dominate those of the electric

J. Rich et a!., Experimental particle physics without accelerators

327

Table 9.1 Results of searches for fractional charges residing on bulk matter

Mass Reference

Material

studied

FCP’s observed

Concentration (FCP/nucleon) (limits at 95% CL)

LaRue et al. 1981 Marinelli and Morpurgo 1984 Liebowitz et al. 1983 Smith et al. 1985 Joyce et a!. 1983 Savage et al. 1986

niobium iron iron niobium sea water mercury

1.1mg 3.7 0.72mg 4.7mg 0.05mg 2.0mg

5 0 0 0 0 0

2 X 10_20 <1.3 5< 10_2I <6.9 x 10~ <15<10_Al <1 X 10_In <5 x 10~

field. A modern, automated version of this experiment, used by the San Francisco group [Hodges et al. 1981], permits the use of heavier drops and shorter measurement times. This technique can be used to search for FCP’s in any liquid. The group has reported null results for searches for residual charges of + ~e or e (corresponding to a quark of charge ~e and an extra electron) in 0.05 1 mg of water [Joyce et a!. 1983] and in 2 mg of mercury [Savage et a!. 1986]. The group has also searched (without success) for FCP’s in mercury exposed to a heavy-ion beam [Lindgren et a!. 1983]. Magnetic levitation is the other technique that has been used to search for residual fractional charges. In these experiments, a diamagnetic or ferromagnetic object is placed at a position of equilibrium maintained by an inhomogeneous magnetic field and the Earth’s gravitational field. The residual charge on the object is then measured by its motion in response to an oscillating electric field. The details of this technique were discussed by Marinelli and Morpurgo [1982]. Three groups have reported null results using ferromagnetic levitation. Liebowitz et al. [1983] searched for FCP’s in 0.72mg of steel balls. Marinelli and Morpurgo [1984], in an experiment with a different field configuration, searched in 3.7mg of the same material. Smith et a!. [1985,1986a,b] used 4.7 mg of steel-coated niobium. None of their accepted measurements yielded a residual charge consistent with ±~e, though one measurement, rejected for technical reasons, did [Smith et al. 1968a]. LaRue et a!. [1981]used the almost perfect diamagnetism of superconductors to levitate niobium balls at liquid-helium temperatures. Of 40 measurements on 13 balls, each of -~-0.1mg mass, 14 measurements (5 balls) gave residual charges consistent with ± Their measured FCP concentration is in conflict with the upper limits of the other experiments. Of course, because of our lack of understanding of FCP chemistry, this discrepancy can always be explained by the different materials used or even by different pre-test handling. On the other hand, great care must be taken in this type of experiment to eliminate effects that could mimic a fractional residual charge. A discussion of these effects and a criticism of the result of LaRue et al. was given by Marinelli and Morpurgo [1982, 1984]. —

~.

9.4. FCP extraction experiments A final type of FCP search is based on the idea that, since a single FCP can never be neutralized in normal matter, it should be possible to extract them from matter with electric fields. Their charge can then be measured via standard ion-beam techniques involving, for example, their acceleration in a static electric field followed by a measurement of their kinetic energy in a silicon barrier or in an electron-multiplier device. In addition to earlier work discussed by Jones [1977],Kutschera et a!. [1984] and Milner et a!. [1985]employed this technique. Inspired by the result of LaRue et al., they searched for FCP’s in niobium and tungsten.

328

J. Rich et al., Experimental particle physics without accelerators

These techniques have been employed, in conjunction with various enrichment schemes, to search for FCP’s in large quantities of matter. For instance, Chupka et a!. [1966]attempted to extract FCP’s from 201 of sea water onto a filament then used as the pole in an ion-beam device. While such techniques are useful in that they might lead to the discovery of FCP’s, negative results are difficult to interpret, again because of our lack of knowledge of the behavior of FCP’s in bulk matter. In addition, as recently discussed by Lewin and Smith [1985], ion-beam techniques are limited to FCP’s whose masses are less than 100 GeV because of the dependence of the energy transfer on particle velocity in silicon or electron-multiplier detectors. 9.5. Future prospects The future of FCP searches seems unclear. With the advent of every new accelerator, a ritual quark will certainly be performed. Large underground detectors planned for monopole searches may lower the cosmic-ray limits somewhat, though surface searches will have trouble fighting the cosmic-ray muon background. A new technique of measuring residual charges on large amounts of material would certainly be welcome. The problems of simply scaling the magnetic levitation techniques to higher-mass samples was discussed by Morpurgo [1986] with rather pessimistic conclusions. Two proposed experiments have been discussed, but have yet to yield limits. The first [Hirsch et al. 1979] relies on recently developed techniques for producing droplets of equal mass and of equal initial velocity. Their movement in an electrostatic field determines their charge. It is hoped that a few grams of material will be measured per day. A second technique [Price 1985; Price et al. 1986] measures the charge on a sample by moving it periodically into and out of a Faraday cage and measuring synchronously the signal induced on a low-noise amplifier. 10. Heavy particles bound in nuclei 10.1. Introduction In this chapter, we discuss searches for stable particles that are distinguished from ordinary stable particles by abnormally large masses rather than by abnormal electric or magnetic charges. Heavy stable particles are postulated in a variety of theories going beyond the Standard Model, e.g., supersymmetry where the lightest supersymmetric particle is expected to be stable. Such particles would have been produced during the early stages of the Universe, and would be present today in concentrations determined by their mass and their low-energy annihilation cross section [Wolfram 1979]. The searches for such relics complement searches for new stable particles at accelerators or in cosmic rays [Isgur and Wolfram 1979]. Heavy stable particles can be neutral, positively charged, or negatively charged. Heavy neutral relics with only weak interactions would now form a gas of slowly moving particles, perhaps bound gravitationally to galaxies. We discuss searches for these particles in the chapter on galactic dark matter. Heavy charged particles would most likely have recombined with electrons or protons and would now be present on Earth in the form of anomalously heavy isotopes. This would also be the case with heavy neutral particles with new interactions binding them to protons or electrons. In this chapter, we shall concentrate on searches for heavy particles in the form of heavy isotopes. Wolfram [1979] and Dover Ct a!. [1979]calculated the present-day abundances of heavy charged or

J. Rich et al., Experimental particle physics without accelerators

329

strongly interacting particles within the framework of standard cosmology. Because annihilation cross sections for such particles fall with mass, the relic density is an increasing function of mass. Predicted abundances are generally greater than 10~12 relative to protons. The fact that this abundance is above the experimental upper limits discussed below is generally taken as an argument against the existence of such particles. This would imply that the lightest supersymmetric particle is weakly interacting (photino, higgsino, or sneutrino) and should be sought using the methods discussed in the chapter on galactic dark matter. There are, of course, a variety of ways to dilute heavy-particle concentrations: cosmological inflation, finite particle lifetimes, and geochemical effects. Searches for heavy isotopes remain, therefore, of interest. The geochemistry of heavy charged particles was discussed by Cahn and Glashow [1981]. Heavy positive particles, X~,would have become attached to electrons to form a heavy isotope of hydrogen. On Earth, they would, then, be present in sea water, unless they are so heavy (m > i0~GeV) that they would have sunk into the Earth’s crust. Negative particles, X~,would have become bound to nuclei. An X bound to a nucleus of (Z + 1) protons would form an atom having the chemistry of the element with atomic number Z. Cahn and Glashow suggested searches for heavy isotopes of elements that have small terrestrial abundances compared with those of the following (Z + 1) elements in the periodic table (see [Haxton 1986] for a proposed search in technetium). 10.2. Experimental searches * Searches for heavy isotopes use a wide variety of techniques: ion beams [Smith et al. 1982; Midd!eton et a!. 1979; Boyd et a!. 1978; Muller et al. 1977; Alvager and Naumann 1967; Klein et al. 1981; Nitz et a!. 1986], neutron activation [Turkevich et al. 1984], laser spectroscopy [Dick et a!. 1984, 1986], (n, ‘-y) reactions [Holt et a!. 1976], solar-neutrino astronomy [Sur and Boyd 1985], anomalousfission searches [Barbiellini et al. 1983] and geochemical experiments [Haxton 1986]. Different experiments are complementary, since they all suffer from uncertainties due to the cosmological, astrophysical, geological, and chemical histories of the heavy particles. Mass-dependent concentration limits are summarized in fig. 10.1. In the following we discuss four experiments giving some of the best limits. By far the lowest limit on the existence of abnormal isotopes is that for hydrogen. Smith et al. [1982] set a limit of 10_28 for the fraction of hydrogen in the form of isotopes with masses between 12 and 1200 amu. According to the phenomenology of the previous section, the experiment, then, sets a limit on the abundance of positively charged heavy stable particles. The experiment used 60001 of commercial heavy water that had been extracted from 1.2 x 108 1 of normal water. The 6000 1 was then subjected to electrolysis for three years yielding 0.21 ml of water enriched in any superheavy water. The authors estimated the enrichment factor to be 6 x 1011 for water molecules containing hydrogen isotopes heavier than deuterium. The 0.21 ml was then scanned for heavy isotopes using the ion beam shown in fig. 10.2. The water was vaporized, ionized, and then accelerated through 130 kV. A magnetic field was used to sweep away the D2O remaining in the beam, and a carbon foil was used to range out any high-Z impurities. The remaining particles then passed through a time-of-flight system consisting of three secondary-emission counters. The resulting velocity measurement served to identify heavy particles. None was found, hence, the above limit. The sensitivity of this experiment was limited to particles with masses less than 1200 amu by the *See also Note added in proof.

330

J. Rich et al., Experimental particle physics without accelerators

I

I

1111111

I

IIIIII 1

Hel6)

-

10~15

oJ

11111)11

I

I

(III1~]

_~!J~_~—’~” ~(81

10

.~

I

~

Li

~~6l

—

__________

—

—.-..---.-—-.-

—

•-... —S H

o

10~O I

100

I

I

I

101

3

111111111

I ~IIIIII

102

I

I

I

I I III10~

i0

Mass I amu Fig. 10.1. Limits on the abundances of heavy isotopes of various elements. The curves are labeled by the chemical element studied and the reference as follows: 1 [Boyd et al. 1978); 2 [Mulleret al. 1977]; 3 [Alvagerand Naumann 1967]; 4 [Smithet al. 1982]; 5 [Turkevichet al. i984]: 6 [Kleinet al. 1981]; 7 [Middleton et al. 19791; 8 [Dicket al. 1984]. The dashed lines are preliminary results from [Nitz et al. 1986].

Low Moss Beam Stop

EnrIched D 20 Sample

ThICk FoIl

Ion

Magnetic Mass Selection

Source

HIgh Z

Tou~er~IIs

TIme of Flight Detection

Filter Fig. 10.2. Apparatus used by Smith et al. [1982]to search for heavy isotopes of hydrogen.

response of the secondary-emission counters and by the beam optics. A proposal to search for higher masses (>1000 GeV) [Pichard et al. 1986] involves sea-water centrifugation followed by a heavyhydrogen search via UV laser excitation. The technique of Smith et a!. has recently been extended to a variety of other elements [Nitz et al. 1986]. Dick et al. [1984,1986] used laser spectroscopy to search for anomalous isotopes of sodium. Their method consisted in looking for isotopic mass shifts in atomic transitions. The positions of all spectral lines are proportional to the reduced mass of the electron: mr

=

memn/(me

+

m~) me(l + me/mn) —

J.

Rich et al., Experimental particle physics without accelerators

331

where me is the mass of the electron and m~is the mass of the nucleus. Since the isotope shift is inversely proportional to the nuclear mass, the experiment has no fundamental upper limit in mass sensitivity. The experiment crossed a beam of atomic sodium with the beam from a tunable dye laser. Two photomultiplier tubes were situated normal to the plane of the two beams to observe the photons from atomic de-excitations. An increase in the photomultiplier rate when the laser was appropriately tuned would have signalled the presence of an anomalous isotope. Normally, the Lorentz tails of transitions in normal isotopes would limit the sensitivity to heavy isotopes, but this was avoided by using the “photon-burst” method. Since the lifetime of the excited state is about 10_8 s, and the atomic beam takes about i0~s to traverse the laser beam, a given atom can be excited and de-excited several times. By requiring more than one count during the transit time, the background due to transitions in the tails is suppressed. 12the ratio of heavy particles to nucleons for heavy Their results set an upper limit of 5 x ~o~for particle masses between 102 and i05 GeV. Their sensitivity falls at higher masses for a variety of experimental reasons, including gravitational effects on the trajectory of the sodium atoms. As discussed by the authors, the technique is applicable only to light alkali metals where the effects of the heavy nucleus are calculable. The group plans to repeat the measurement with lithium. This measurement is especially interesting because lithium is expected to be partly of primordial origin. Turkevich et a!. [1984]searched for heavy negative particles attached to a nitrogen nucleus (14NX~). Such an object would have the chemistry of carbon. When subjected to a neutron flux, the nucleus would be expected to transform to 14CX~via a (n, p) reaction. This object would have the chemistry of boron, but, unlike boron, be 3 radioactive like 14C. Assuming that the imbedded X changes the electromagnetic energy of the nucleus, but not significantly its shell structure, the authors calculated a half-life of 15 years and a ~3-energyend point of 0.8 MeV for the 14CX nucleus. The authors irradiated 30 g of graphite with reactor neutrons and then used chemical means to extract any boron. The radioactivity of the boron was then measured with 13 counters. No excess radioactivity was observed. Assuming the calculated (n, p) cross sections and 13 lifetime and end point, the authors set a limit of <3 X 10_15 X/nucleon. They estimate that the experiment is sensitive to X~ masses below i0~amu based on possible mass effects during the extraction procedure. Finally, the gallium solar-neutrino experiment [Kirsten 1986] is, surprisingly, another proposed heavy-nucleus search. Sur and Boyd [1985]calculated that a small amount of X~attached to nuclei in the Sun could have a drastic effect on energy-producing reactions in the Sun by lowering the Coulomb barrier for proton capture and by stabilizing A = 5 nuclei. In particular, the following reaction sequence could become competitive with the normal proton—proton cycle for X~concentrations of 10~15 p+4HeX~—*5LiX~ +~y 5LiX

—*

5HeX~+ e~+ v

(Emax

1 MeV)

p+ 5HeX~—*6LiX~ +~ p + 6LiX~—* 7BeX~+ ~ 7BeX~—*7LiX~ +e~+v p+7LiX—*4HeX~+4He.

(Em~1MeV)

J. Rich et a!., Experimental particle physics without accelerators

332

The effect of this new source of —1 MeV neutrinos on a given solar-neutrino experiment is easy to understand because of the fact that the total solar-neutrino production rate, R~,is very nearly determined by the observed solar luminosity, L: R~ LI(4mH — mue)c2, —

where m 11 is the atomic mass of hydrogen and mHe is the atomic mass of helium. The existence of the above cycle can, then, only come at the expense of the other hydrogen-burning cycles. The previously performed chlorine solar-neutrino experiment [Rowley et8Ba!.13 decay. 1984] was sensitive the The primarily existence of the newtocycle high-energy (—10 MeV) neutrinos the cycleOninvolving would then lower the rate for this from experiment. the other hand, the gallium experiment has a lower threshold (233 keV) and is sensitive to the low-energy neutrinos from proton—proton fusion. It is also sensitive to neutrinos from the new cycle but with a higher cross section because of their higher energy with respect to the proton—proton neutrinos. The new cycle would then raise the rate for the gallium experiment. Boyd and Sur calculated that, in order to lower the chlorine rate by a factor of three from the Standard Solar Model [Bahca!! et a!. 1982] (in order to be in agreement with the result of the chlorine experiment), the rate for the gallium experiment would go up by roughly a factor of two from the solar-model prediction. We know of no solar model that lowers the chlorine rate while raising the gallium rate, so the measurement of such a rate could be considered evidence for the existence of abnormal nuclei in the Sun.

11. Medium-range forces 11.1. Introduction Medium-range forces (MRF’s) can result from the coupling of massive bosons to protons, neutrons or electrons. The range of such a force is equal to the Compton wavelength of the boson, and, since we are concerned here with forces of macroscopic range (>1 mm), we are interested in bosons whose mass is less than i0~4eV. Theoretical justifications for the existence of such light particles have been discussed by a variety of authors: Gibbons and Whiting [1981];Moody and Wi!czek [1984];Chang et a!. [1985];Fayet [1986];Bars and Visser [1986];Barr and Mohapatra [1986];Goldman, Hughes and Nieto [1986];and De Rujula [1986a]. In the simplest case, the MRF generates a simple Yukawa potential, whose form allows it to be added directly to the gravitational potential. For two isotopically pure masses, m, and m 1, each of dimension much less than the boson’s Compton wavelength, A, the sum of the gravitational and MRF potentials at separation, r, can be written as: GNm.m. V(r) = r’ ‘(1 + cr~e<~), (11.1) where GN is the “real” Newton constant (i.e., the constant that would be measured at infinite separation). The ratio between the MRF and gravitational couplings, a~,,is given by: =

G~’/3~/3J,

(l1.2a)

J.

Rich et al. Experimental particle physics without accelerators

333

with the MRF “charge”-to-mass ratio, f3~,given by: —

Zj(qp+qe)+(Aj—Zj)qn ( .2b)

M.

The MRF “charges” of the proton, electron and neutron are q~,q~and q,~.Z1, A1 and M, are the atomic number, mass number and atomic weight of substance i. Before discussing experimental limits on the parameters A and a11, we shall make five comments on eqs. (11.1) and (11.2). Firstly, we note that the Newton constant is normally measured in Cavandishtype experiments, using masses separated by distances of order 10 cm. If A is much greater than this, then what is normally quoted as GN is actually G0 GN(l + a11), where i and j refer to the masses used in the experiment. In this case, if A is smaller than planetary distances, the masses of stars calculated using G0 would be wrong by the above factor. Secondly, for most elements, A, Z and M are nearly proportional to one another, and it is justified to consider aq to be a universal constant, a. This is, of course, not true in experiments specifically designed to test the composition dependence of “gravitational” forces. In the currently interesting case of a boson coupled to baryon number or hypercharge [Fischbach et56Fe. al. 1986a], ~ for coupling an object For an MRF to consisting of hydrogen differs by 1% from f3~for an object consisting of lepton number, this difference would be of the order of 50%. Thirdly, a general result of quantum field theory is that an attractive force (a 11 0) results from the exchange of an even-spin boson between matter fermions, and a repulsive force (a11 ~ 0) results from the exchange of an odd-spin boson. Fourthly, as emphasized by Goldman, Hughes and Nieto [1986],in many quantum-gravity models, one has pairs of nearly degenerate vector and scalar bosons. The first leads to a repulsive force and the second to an attractive, so that a small effective a may result from a near cancellation of the two large forces. In this case, an important experiment would be to investigate the gravitational acceleration of antiparticles [Gabrielse et a!. 1986] since the two forces would combine with the same sign to make a large effect. Finally, as recently emphasized by Moody and Wi!czek [1984],the Yukawa potential in eq. (11.1) is not the most general potential generated by the exchange of a massive boson. As an illustrative case, they considered the exchange of a spin-0 particle coupling to matter fermions with both scalar and pseudoscalar couplings (e.g., the axion). The effective potential, in this case, is generated by the three Feynman diagrams shown in fig. 11.1. The first diagram, with a scalar coupling at each vertex, generates the Yukawa potential represented in eq. (11.1). The diagram with a pseudoscalar coupling at each

-

(a)

~

g~-----~y~g~ (hI

~ (C)

Fig. 11.1. Diagrams for the scattering of two fermions by the exchange of a spin-0 boson with scalar coupling constants g~and pseudoscalar coupling constants g,.

334

J. Rich et al. Experimental particle physics without accelerators

vertex generates a spin—spin interaction that resembles normal magnetic interactions: 1

—nA

V(r)

~

m1m2 {~ ~ f(r) — (u1 r) (~2 r) g(r)}, .

(11.3)

where 2

+

(4~rI3)83(r),

f(r) = lIrA + 1/r and g(r)

=

1/r2A2

+

3/r3A

+

3/r4,

and the o~are the spins of two particles of masses m 1 separated by r. Finally, the diagram with a sca!ar coupling at one vertex and a pseudoscalar coupling at the other vertex generates a P- and T-violating potential of the form: 1

—nA

V(r)cI-~——

_

2}+(1—~2)

(11.4)

~,.r{1/rA+1/r

Moody and Wilczek discussed the rather weak existing limits for these two spin-dependent interactions, and described some interesting experiments to improve the limits. For the rest of this chapter, however, we shall on!y consider the potential given by eq. (11.1). 11.2. Limits on a and A Experiments on MRF’s attempt to measure the parameters A and a which, for the moment, we shall take to be composition independent. In general, one measures the spatial variation of a gravitational field due to some source and compares the variation with that calculated assuming Newtonian gravity. Since the potential in eq. (11.1) reduces to a hr potential in the limits rIA—*0 and r/A—*cc, a given experiment will give limits on a only for a restricted range of A corresponding to the scale of the experiment. The experimental situation was recently reviewed by Newman [19831,De Rujula [1986a,b] and Stacey et a!. [1986].Figure 11.2 is an update of Newman’s figure showing limits and measurements of a and A for negative a and for A less than planetary distances. Figure 11.3 is De Rujula’s [1986b] figure showing limits for positive a on a larger scale for A. For A between 0.5cm and lOm, limits on a come from laboratory experiments measuring gravitational fields generated by homogeneous objects. The best results have come from experiments using static gravitational fields measured with torsion balances [Chen et al. 1984; Hoskins et a!. 1985; Panov and Frontov 1979], and from experiments using slowly oscillating gravitational fields measured either with gravitational-wave antennae [Kuroda and Hirakawa 1985] or with superconducting gravity gradiometers [Chan et a!. 1982]. The limits are strongest for 1 cm < A < 10cm, where experiments require —a
J.

Rich et al., Experimental particle physics without accelerators

335

0

F —1

D -J

3.

4r____________ 1cm

1mm

-3

imI

I

—1

—2

I

0

1

(m)

LOG X

2

I

I

3

4

5

Fig. 11.2. Limits on a and A for a negative. The bands labeled C and H are the preferred regions of Long [1976]and Holding et a!. [19861, respectively. Theother lines are upper limits on log(—a) as a function of A and refer to the following experiments: A [Hoskinseta!. 1985]; B [Chen et al. 1984]; D [Kurodaet al. 1985]; E [Panov and Frontov 1979]; F [Ogawaet al. 1982]; G [Chanet al. 1982]; and I [Gibbons and Whiting 1981].

0

—•i—~————————————i~——

I

I

I I

LUNAR SURFACE GRAVITY

—1 2-

I

I

I

I I

I

MERCURY FLYBY

VENUS FLYBY

PRECESSION OF BINARY 1913.16 PULSAR / / /

____

GEOLOGICAL CAVENOISH” -4

EARTH SURFACE/LAGEOS

-

/

PRECESSION OF ICARUS

/ / /

a -~

-.5

-

-6

-

/

• ••

••“•EOTVOS

0

PRECESSION/

‘

OF MARS,’ MOON/EARTH

-7

-

MOON/LAGEOS

‘-“/

SURFACE

—8

ICKE PRECESSION

-

PANOV

OF MERCURY RIEARTH)

-~

1cm —10

im

I

I

—2

—1

I

0

1km I

I

I

I

1

2

3

4

I

OIMOON)

‘~I

I

7

8

DISUNI I

~‘

I

I

5 6 lagio IA/mi

9

10

11

12

Fig. 11.3. Limits on a and A for a positive (see text). The limits labeled “Dickie” and “Panov” are good only for MRF’s coupling to baryon number.

336

J. Rich et al., Experimental particle physics without accelerators

For A> 10 m, one uses gravitational fields generated by geological or astronomical objects. For A between i03 and 106 m, a is constrained by a comparison of the acceleration due to gravity measured at the surface of the Earth with the acceleration of satellites orbiting the Earth. A satellite orbiting at a height much greater than A will be unaffected by the MRF, whereas the acceleration at the surface of the Earth will be the sum of the Newtonian surface acceleration, g~(O), and the MRF surface acceleration, gMRF(O). For A R (R = radius of the Earth), the surface acceleration due to the MRF is given by [Gibbons and Whiting 1981]: -~

gMRF(0)

=

3aA

~g~(0),

(11.5)

where Pm is the mean Earth density, and p~is the mean density near the surface (to depth A). The factors AIR and PS’Pm reflect the fact that only matter near the surface contributes to gMRF(0)~ One can now compare the surface acceleration with satellite acceleration extrapolated to the surface assuming Newtonian gravity (equivalent to comparing GNMEarth as measured at the surface and in space). This will place a limit on the product a A (through eq. (11.5)). Rapp [1974,1977] reported agreement between the measured and extrapolated accelerations to 2 ppm. This number has, however, been described as conservative; see [Gibbons and Whiting 1981]. Taking 1 p.p.m. as an upper limit and PS’Pm as 0.5 gives the limit a~A<8 m. This constraint on a and A, shown in figs. 11.2 and 11.3 (labeled “Earth surface/Lageos”), is applicable for A < 106 m, beyond which the MRF would start to affect satellite motion. A comparison of satellite and lunar motion [Smithet al. 11985] can extend this limit to higher A [De Ruju!a 1986b]. The limit, shown in fig. 11.3 as “Moon/Lageos”, requires a~<10_8 for i07 m < A < 108m. The best limits on a~come at planetary distances, A 1011 m. As is we!! known, the existence of closed, non-precessing, planetary orbits is a consequence of a 1/r potential. The observed precessions of planetary and lunar orbits are consistent with perturbations due to other planets and with general-relativistic corrections. Mikkelsen and Newman [1977] used this agreement to set the limits shown in fig. 11.3 (as drawn by De Rujula [1986b]). The best limits come from the precession of 9 10 Mercury giving a~<2X10 for A—3 X 10 m. For A greater than planetary distances, a cannot be severely constrained because of our lack of understanding of galactic mass distributions. The fact that measured values of galactic gravitational fields seem to be an order of magnitude higher than values calculated from the distribution of normal stellar matter has been interpreted as evidence for the existence of “dark matter”, perhaps in the form of some new elementary particles. This subject is discussed in the chapter on galactic dark matter. Returning to smaller distance scales, figs. 11.2 and 11.3 indicate that the limits come from underground measurements of the gradient of the acceleration due to gravity. These important measurements serve as a bridge relating laboratory values of the Newton constant with the values relevant at astronomical scales. The means whereby underground gravity-gradient experiments can impose limits on a and A can be qualitatively understood by approximating the Earth as a non-rotating sphere (radius R, surface density ~ surface acceleration of gravity g(0)). To first order in a, AIR and z/R, the acceleration at a depth z is then [Gibbons and Whiting 1981]: —

~

(11.6)

J.

Rich et a!., Experimental particle physics without accelerators

337

where the second (third) term gives the z dependence of Newtonian (MRF) gravity. For z ~ A the last term cancels that part of g(0) due to the MRF (eq. (11.5)), and the acceleration is given by the Newtonian result. If A is greater than 1 m, GN is equal to G01(1 + a), where G0 is the laboratory value of the Newton constant. We can then express the gradient of g(z) in terms of a, A, and the measured quantities G0, g(0), Ps and R: dgldz = —4~{G0p5 g(0)/2irR} —

—

4iraG0p5(h

—

~e~z~).

An experimental value of dgldz can be compared with its calculated value for a eq. (11.7)). This yields an experimental number, r(z), defined by:

{~

r(z) =

—~

a{1

~ e_z~} =

—

(a

=

0)}

=

—a ~

{1

—

(11.7) =

0 (the first term of

~ e~},

(11.8)

or: —

—e(z)g(0)I4irG0p5R.

(11.9)

(Note that g(0) /(4i~G0p~R) is of order unity.) Since {1 — ~e~} only varies between 0.5 (z ~ A) and 1 (z ~‘ A), a limit on e(z) gives a limit on a that is nearly independent of A for 1 m < A < 106 m. If a non-zero value of e is measured, A can be determined by making measurements near z = A. Other methods of analyzing gravity-gradient data have been discussed by Gibbons and Whiting [1981]. If we neglect the weak z dependence in eq. (11.9), the gradient behaves as though the effective Newton constant differed from that measured in the laboratory by a factor near (1 a). For this reason, experimental results have been traditionally reported as comparisons between laboratory and mine values of GN. The accuracy of this technique is limited by the corrections that must be applied to the simple theory described above. Effects due to elevation and to the non-sphericity of the Earth are well understood, but it is difficult to account for the possible existence of nearby geological structures of a density differing from that sampled by excavation. In addition, the in-situ density of rock may be systematically different from its measured value after excavation. This is of critical importance since p5 determines the value of the gradient for a = 0. Stacey et a!. [1981]used mine data reaching a depth of about 1 km to limit a to less than 0.04 for 10 cm < A < i0~m. Their most recent results [Holding et al. 1986] suggest 0.0035 < a <0.015 and 1 m < A < 1000 m, on the basis of which they propose new measurements [Stacey 1983; Stacey et a!. 1986]. Perhaps the most promising experiments are those that measure gravity gradients underwater, thus benefitting from a local density distribution which is better understood than that near mines. Another possibility is to measure the gravity gradient above ground where the exponential falloff of the MRF should be seen. Efforts to do this have been hampered by accelerations due to the swaying of the measurement platform in the wind. —

—

11.3. The composition dependence of MRF’s Further evidence for a MRF came from a re-analysis of the famous Eotvos experiment by Fischbach et a!. [1986a].A symmetric version of the experiment is shown in fig. 11.4. It consists of two masses, m1

J. Rich et a!., Experimental particle physics without accelerators

338

—

=

F = ~ Fig. 11.4. A simplified version of the Eotvos experiment. A torque. T. about the suspension wire is generated if the two verticals defined by

F 1

and

are not parallel. The torque is measured by comparing the equilibrium position of the apparatus as shown with the equilibrium position of the apparatus rotated by 180°about the vertical. F~

and m2, of differing compositions attached to the ends of a bar freely suspended from a fiber. Also shown in the figure are the vector sums of the three external forces acting on the two masses: the gravitational force, m~g;the centrifugal force due to the rotation of the Earth, m~a;and the hypothesized MRF, FrRF. The direction of the gravitational force is determined by the mass distribution of the Earth, and the centrifugal force is perpendicular to the Earth’s axis of rotation. (Following Eotvos, we allow for a difference in gravitational and inertia! masses.) The direction of the MRF is determined by the nearby mass distribution, if A is small, or by the mass distribution of the entire Earth, if A is comparable with or greater than the radius of the Earth. The lengths L1 and L2 are adjusted so that the two masses are balanced. The fiber itself hangs in the “vertical” direction, the vertical being defined by the direction of the vector sum of all forces on the apparatus. Eotvos attempted to measure a torque on the bar about the axis defined by the fiber. Such a torque is generated if the vertical for one of the two masses (defined by the three forces actingT/m’ on it) differs from the vertical for the other mass. A violation of the equivalence principle (i.e., m~ 1”~ m~Vm~) would, as Eotvos noted, produce such an effect, and he reported his results as a difference in gravitational acceleration, ~g/g, of pairs of objects. A torque could also be produced by a compositiondependent MRF (FrRF F~RF), but only if the direction of F~RF or F~RF fails to coincide with the resultants of the gravitational and centrifugal forces. If the latter condition does not obtain, the only effect of a composition-dependent MRF would be to change the equilibrium values of L1 and L2. Since the Earth is nearly in hydrostatic equilibrium, the vector sum of the gravitational and centrifugal forces is, on average, perpendicular to the surface of the Earth. For a featureless surface over a homogeneous substratum, an MRF will also be perpendicular to the surface if A is much less than the radius of the Earth. The Eotvos experiment is then not sensitive to a composition dependent MRF, as noted by Bizzeti [1986],Milgrom [1986]and Eckhardt [1986].The experiment can be made sensitive to such a MRF by performing it in an asymmetric environment, e.g., at the foot of a cliff. It is also sensitive to a composition-dependent MRF if A is comparable with or greater than the radius of the Earth, since the MRF should then be nearly aligned with the gravitational force.

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Fischbach et al. [1968a]re-examined the data of Eotvos, and noticed that the measured value of ~gIg was proportional to the difference between the mass-number/atomic-weight ratios of the two substances (see fig. 11.5). Such an effect could result from a MRF coupled to baryon number or hypercharge. (The existence of such a force has also been discussed in connection with possible effects on K mesons [Aronson et al. 1986a,b; Bouchiat and Iliopoulos 1986; Suzuki 1986].) Owing to our lack of knowledge of the mass distribution in the vicinity of Eotvos’s experiment, we cannot extract values of a and A for the MRF. Fischbach et a!. considered the unrealistic case of a spherical rotating Earth with a featureless surface in which case an MRF with small A is aligned with the gravitational field. We can then use eqs. (11.2) and (11.5) to calculate the difference in “gravitational” acceleration of the two bodies: ~gIg

—

(aAI2R)(p51p0)(131

—

(11.10)

132)’

where f3~and 1~2are the ratios between the mass numbers and the atomic weights of the two bodies, and a is an average value of a.1. Using eq. (11.10), they found that the Eotvos data support aA 24 m, assuming Ps’Pm = 1. (The sign of a is opposite that originally reported by Fischbach et a!. [1986a];see [Thodberg 1986].) An alternative possibility, discussed by De Rujula [1986b],is to take A much greater than the radius of the Earth. In this case we have: (11.11) and the Eotvos data support a = 5 X 10~.On the other hand, no effect was seen in the modified Eotvos experiments of Dicke [Roll et a!. 1967] and of Braginski and Panov [1972].These experiments searched for a component of the torque with a period of 24 hr due to the gravity of the Sun. Since no effect was seen, we must have A much less than the Earth—Sun distance, i.e., A <2 X 1010 m. The constraint on a 0.8 ~ O.6~

T

I

I

I I

I

I

mognalium-Pt

~z.

0.4 0.2

/

Cu-Pt

V

72 ~

-0.2

4g-Fe-SO~

,,,,/

CuSO4 (solutionl-Cu -1.0 10C —

-

1.2-1.8

~~L_

-1.5

______

~ -0.3 ~ -1.2 -0.9 -0.6 ~i

~

~

0

I 0.3 . 0.6

I - 1.2 0.9

(B/s)

Fig. 11.5. The correlations between ~K = AgIg and difference in mass-number!atomic-weight ratio observed in the Eotvos experiment [Fischbach et al. 1986a]. A slightly modified version of this figure can be found in [De Rujula 1986b].

340

J. Rich et al., Experimental particle physics without accelerators

and A (assuming that the MRF couples to baryon number) is shown in fig. 11.3 by the curves “Dicke” and “Panov” [De Rujula 1986b]. Examining all constraints in fig. 11.3 we see that the only room for a MRF with A greater than the Earth’s radius is near A —-4 X i09 m. As reported by De Rujula [1986b], this possibility may be ruled out by the experiments of Dicke and Panov because of their sensitivity to acceleration towards the Moon. The conclusions of Fischbach et a!. have been discussed and criticized by a number of authors, e.g., Thodberg [1986],Keyser et a!. [1986],De Rujula [1986a],Neufeld [1986],Nussinov [1986],Thieberger [1986],Kim [1986]and Fischbach et al. [1986b,c,d]. Especially interesting was the possibility, raised by Chu and Dicke [1986],that thermal gradients could account for the correlation observed in the Eotvos experiment. Nevertheless, the only sure conclusion of a!! this discussion is that new experiments under controlled conditions are necessary to resolve the question. 11.4. Recent developments The results of Stacey et al. and of Fischbach et a!. have inspired a great number of experiments to confirm or refute their claims. Eotvos-type experiments are planned in asymmetric environments using hills [e.g. Raab 1987] or laboratory objects [e.g. Newman 1987] as sources of a MRF. Galileo-type experiments measuring the differential acceleration of pairs of test bodies of differing composition will exploit modern interferometry techniques [Cavasinni et al. 1986; Kuroda 1987]. Experiments measuring the differential acceleration away from a cliff of a liquid and an object floating in it are being conducted by two groups [Thieberger 1987; Bizetti 1987]. Balance-beam experiments that compare two masses are also planned. In the experiment of Speake and Quinn [1986]two masses of differing composition are compared, first, at the surface of the Earth where both would be subject to a MRF, and, second, in a tunnel, where the MRF should be nearly zero. The existence of a composition-dependent MRF would change the mass ratio of the two objects under the two conditions. In the experiment of Stacey [1987],one of the masses is suspended from the balance beam in a vacuum tube submerged in water. The level of the water can be changed and the effect of the measured mass ratio due to a MRF can be observed. Finally, we note the continuing efforts of Chan et al. [1982]to measure directly the Laplacian of the gravitational field with a superconducting gradiometer. At the Moriond conference in January 1987, three of these groups presented preliminary results. Stacey’s experiment rules out the part of his band in fig. 11.2 below A —20 m. As for the composition dependence of MRF, one experiment [Thieberger 1987] supports the claims of Fischbach et al. while another [Raab 1987] is in strong disagreement with these claims. “The plot is thickening” [De Rujula 1987].

12. Ga!actic dark matter 12.1. Introduction It has been apparent for some time that most of the matter in the universe does not significantly emit or absorb electromagnetic radiation, but manifests itself only through its gravitational interaction with luminous matter (stars and interstellar gas) [Faber and Gallagher 1979]. Recent ideas in cosmology and theories of galaxy formation suggest that this “dark matter” may consist of massive neutral elementary

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particles. Independent of these arguments, many particle theories (e.g., supersymmetry) predict the existence of such particles. These ideas, combined with recent advances in detection techniques, makes the search for particle dark matter an important area of research. The subject has been reviewed by a variety of authors: Primack [1984],Wilczek [1984], Olive and Schramm [1985]and Pagels [1985].Here, we shall briefly review dark matter in general terms, and then discuss some of the hypothesized particle dark-matter candidates, emphasizing, in each case, proposed detection techniques (see also the review of Smith [1986a]). Currently discussed candidates include axions, massive neutrinos, stable supersymmetric particles (photinos, sneutrinos, or higgsinos), and quark nuggets. 12.2. The cosmography of dark matter Evidence that the universe is dominated by dark matter exists at scales above that of galactic cores. The first evidence came at the scale of clusters of galaxies where the cosmological density can be estimated by observing the motion of individual galaxies and then applying the viria! theorem. At this scale, cosmological densities are usually given in terms of ~ the “critical” density above which gravitational attraction will eventually reverse the expansion of the universe: =

3H2/8irG.

(12.1)

The Hubble constant, H, is known only to within a factor of two owing to uncertainties in the intergalactic distance scale: H=100hkms~Mpc’,

~
(12.2)

giving: =

2

x 1029h2 g cm3.

(12.3)

The motion of individual galaxies bound in clusters indicates that the average cosmological density 12 (in unit of p~)is: 0.1<12<0.3.

(12.4)

On the other hand, the “baryonic” density (that of protons, neutrons and electrons) can be estimated from galactic luminosities. These estimates give a baryonic density, 12b’ about an order of magnitude smaller than the mass density: 12b~0.02.

(12.5)

This discrepancy constituted the original evidence of the existence of dark matter. (For a review see [Sandage and Tammann 1983].) Of greater importance, in the context of Earth-bound dark-matter searches, was the discovery in the 1970’s, that at least some of this dark matter is concentrated in “haloes” surrounding and pervading spiral galaxies like our own. Evidence of this comes from the velocity distribution of objects orbiting far

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from the galactic center. Galactic luminosity falls exponentially with the distance from the galactic core, and, if the galactic mass were concentrated in the luminous core, objects orbiting at a distance r far from the core would have velocities proportional to r112, as in planetary systems. Instead, the observed velocities are nearly independent of r out to distances of several times the core radius. This would indicate the existence of a dark component with a mass density falling only as r~2. The total mass of the dark component of spiral galaxies is estimated to be at least ten times the mass of the luminous component. In the vicinity of the Earth, its density, Phato’ is estimated to be [Ca!dwe!l and Ostriker 1981]: —25

—3

Phato~7)<1O gem -—0.4GeV/c2 cm3,

(12.6)

but is uncertain by a factor of about 2. It must be emphasized that there is no direct experimental evidence that this halo consists of exotic elementary particles, and we cannot, at present, rule out the possibility that it consists of ordinary matter in a form that does not significantly radiate or absorb light. There are, however, at least two theoretical arguments that it is non-baryonic. The first argument is based on models of cosmological inflation and nucleosynthesis. While inflationary models prefer values of 12 very near unity, calculations of primordial helium and deuterium abundances [Yang et a!. 1984] agree with the observed abundances only if the total baryon density is in the range 0.01 < 12bh2 <0.025. While this is in the range estimated from galactic luminosities, it is clearly inconsistent with the inflationary hypothesis (and the measured value of 12) unless the universe is dominated by non-baryonic matter. The second argument is based on models of galaxy formation. Present theories do not predict the observed characteristics of galaxies unless a massive non-baryonic component is added to the universe. Recent theories use “cold dark matter” [Blumenthal et a!. 1984], i.e., matter consisting of particles that were non-relativistic at the time the universe became matter dominated. Assuming, then, that the halo consists of a gas of elementary particles, the required sensitivity of Earth-based dark-matter searches is determined by the halo particle’s mass (unknown), by the local halo density (given by eq. (12.6)), and by the velocity distribution of the halo particles. The latter is determined by the details of the gravitational collapse that led to the formation of our galaxy, but it is expected to be a roughly isothermal distribution with an average velocity near 250 km s~(the typical virial velocity of the galaxy). This gives a flux, ~, of dark matter incident on the Earth of about: —17

—2

—1

q’—-lO gem s ~ x 106 particles cm2 ~ (1 GeV/mh) ,

(12.7)

for halo particles of mass mi,. This flux is expected to be anisotropic because of the Solar System’s movement about the galaxy. The Earth’s movement about the Sun should, in addition, lead to a yearly modulation of the flux [Drukier et a!. 1986]. 12.3. Axions The lightest dark-matter candidate is the celebrated axion [Peccei and Quinn 1977; Weinberg 1978; Wilczek 1978]. This particle was originally proposed to prevent large CP-violating effects in the strong

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interactions. Its characteristics are largely determined by an energy scale, f, its mass being of order: ma —3 eV (10~GeVIf),

(12.8)

and its couplings to quarks, electrons and photons being proportional to f’. Originally, f was expected to be near the weak-interaction scale (—300 GeV), giving an axion mass near 100 keV. A variety of experiments quickly ruled out masses near this value (see the reviews of Zehnder [1983]and Bardeen [1986]), and new versions of the axion (see [Srednicki 1985] for a review) were soon invented to avoid the experimental constraints. These theories raised the value off resulting in smaller axion masses and weaker couplings to matter. Constraints on this “invisible” axion come from astrophysics and cosmology. At masses below 100 keV (f> 300 GeV), axions can be thermally produced in stars. Because their weak coupling results in a long mean free path in matter, they are very efficient at conducting heat from stellar cores. This would shorten stellar lifetimes, resulting in fewer observable stars. This effect diminishes at very large f, where axions are so weakly coupled that they are not produced in sufficient numbers in stars. Many authors have drawn conclusions from such effects, the most recent being Raffelt [1986a]who used the observed white-dwarf density of the galaxy and limits on white-dwarf cooling times to set the limit: f>1O9GeV,

(12.9)

corresponding to: ma <3

X

102eV.

(12.10)

Similar limits come from considerations of red giants [Raffelt 1986b ,c; Pantziris and Kang 1986]. A lower bound on the axion mass comes from cosmological arguments [Preskill et al. 1983; Abbott and Sikivie 1983; Dine and Fischler 1983; Degrand et a!. 1986]. Axions are expected to have been produced in the early universe via a non-thermal mechanism resulting in a present-day cosmological density, ha: ~a .—f/10’2 GeV.

The requirement that 12

(12.11) <

1 then gives:

ma > i0~eV.

(12.12)

The axion (present version) is thus constrained to have a mass in a narrow cosmologically important window determined by eqs. (12.10) and (12.12). (Variants of the axion allow masses up to —25 eV.) Since axions are bosons, they are expected to cluster easily, and, if f is in the upper half of the window, they might form the galactic halo [Ipser and Sikivie 1983; Stecker and Shafi 1983; Turner 1986a]. A variety of experiments have been proposed to detect axions in this mass range. Sikivie [1983,1984] proposed detecting halo axions through their conversion to photons in a microwave cavity tuned to the axion energy and placed in a magnetic field. The coupling of the axion to the electromagnetic field would result in the production of photons of energy h v in the narrow range: mac2 < hi.’ < mac2 + ~mav2,

(12.13)

344

J. Rich et a!. - Experimental particle physics without accelerators

where v is the escape velocity of the galaxy (—103c). The spectrum of photons would then serve to measure the mass, the density and the velocity distribution of galactic axions, The most recent calculations of this effect were made by Krauss et al. [1985] and Sikivie [1985]. A possible cavity experiment, capable of scanning in the range 1010 GeV
12.4. Light neutrinos The only dark-matter candidate that is known to exist is the neutrino. Its cosmological mass density and its clustering properties are determined by its (unknown) mass. In the standard cosmology [Seigman 1979; Dolgov and Zeldovich 1981], the number density of a given species of light neutrino, n~,is determined by the observed photon number density, n 7. Assuming n,, = n0: 3. (12.14) n0 = ~n7 —150 cm Neutrinos with masses greater than —-i0~eV would now be non-relativistic, and have a mass density per species given by: +

p~=2.7 x

3(m~/1eV) (12.15) gcm This density is greater than the critical density for neutrino masses greater than 75 eV. The clustering of very light fermions in galactic ha!oes is rather delicate. During the gravitational collapse leading to the formation of a galaxy, the phase-space density of particles cannot increase. The requirement that the phase-space density of neutrinos in the galactic core be less than the pre-galactic phase-space density sets a lower limit on the mass of any fermion that might dominate the mass of a galaxy of core radius r~[Tremaine and Gunn 1979; Primack 1984]: .

103t

J. Rich et a!., Experimental partic!e physics without accelerators

m~>120eV100km/s lkpc

345

(12.16)

where a- is the one-dimensional velocity dispersion. For our galaxy, this corresponds to 30 eV, which is just compatible with the cosmological upper limit. However, other galaxies observed to have haloes give a lower limit of 500 eV. Hence, it seems unlikely that light neutrinos can account for all galactic haloes. In this respect, it must be noted that light neutrinos were still relativistic when the universe became matter dominated (hot dark matter), and are thus no longer favored as dark-matter candidates with a role in galaxy formation. Though a variety of schemes for detecting relic neutrinos have been proposed, none seem particularly promising. Some excitement was generated by the possibility of observing the forces exerted by relic neutrinos on macroscopic objects due to reflection or refraction. Unfortunately, these forces hve been shown to be too small to be detectable with present techniques [Cabibbo and Maiani 1982; Langacker et al. 1983; Smith and Lewin 1985; Tupper et al. 1987]. Weiler [1982]considered the annihilation of high-energy, cosmic-ray neutrinos with low-energy, relic neutrinos. The cross section has a maximum at the Z°resonance, giving an absorption length of the order of the Hubb!e radius. If relic neutrinos have masses in the eV range, neutrinos emitted by distant, high-red-shift sources with energies of 1011 ±1 GeV would be preferentially absorbed resulting in a dip in the neutrino flux observed on Earth. It is far from clear, however, that the flux of such neutrinos is sufficient to make this effect observable. De Rujula and Glashow [1980]considered the astronomical implications of an unstable relic neutrino decaying into a lighter neutrino and a monochromatic photon. For neutrino masses in the electron-volt range, the photons would be in the UV range. Decays of neutrinos in our galactic halo, and in that of a nearby galaxy, would lead to a peak in the UV spectrum, while the integrated spectrum for distant galaxies or from unc!ustered neutrinos would lead, owing to the cosmological red-shift, to a step in the spectrum. They concluded, however, that it is unlikely that a neutrino in this mass range would have a lifetime sufficiently short to make this an observable effect. De Rujula and Glashow notwithstanding, Auriemma et a!. [1985]observed some structure in the UV spectrum that could be interpreted in terms of the decay of —15 eV neutrinos, and Maalampi et a!. [1986]discussed models in which the neutrino lifetime is sufficiently short to account for this structure. The effect on the UV spectrum due to the decay of a light photino was considered by Cabibbo et a!. [1981]. -

12.5. Heavy weakly interacting particles* Heavy (m> 1 GeV) weakly interacting particles have recently received a great deal of attention as possible cold-dark-matter candidates. Discussion has centered around new particles in supersymmetric theories, the lightest of which is expected to be stable. Candidates include photinos, higgsinos and scalar neutrinos. Cosmological densities of such particles can be calculated in the standard cosmology [Wolfram 1979; Steigman 1979]. Unlike light neutrinos, which fell out of equilibrium when they were still relativistic, these particles were non-relativistic at this point, so their number density relative to the cosmological photon density was suppressed by a Boltzmann factor. The decoupling time is determined by their *See also Note added in proof.

J. Rich et al., Experimental particle physics without accelerators

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low-energy annihilation cross section, which can be calculated in a given particle theory. There is some liberty to adjust parameters and it is not difficult to generate cosmological densities in the observed range [Silkand Srednicki 1984; Ellis et al. 1984; Hagelin et al. 1984; Ibanez 1984; Campbell et al. 1986; Kane and Kani 1986]. In this case, it is expected that the particles could make up the massive halo. Two types of experiments have been proposed to detect such particles. The first type are direct detection experiments based on the e!astic scattering of the halo particles on heavy nuclei. (This type of experiment is also interesting for particles with strong interactions; see [Goodman and Witten 1985; Goldberg and Hall 1986; Spiro 1987].) The second type attempt to detect the cosmic-ray products of their annihilation in interstellar space, in the Sun, or in the Earth. Interest in the first type of experiment was generated by Goodman and Witten [19851who noted that the primary energy-loss mechanism of slow, weakly interacting halo particles during their passage through matter is elastic scattering off nuclei. The energy deposition from such a scatter could be detected by a sensitive calorimeter. In the collision of a halo particle (mass m~,velocity vh) with a target nucleus (mass mi), the nucleus receives a recoil kinetic energy, T, given by: T=5keV

mh

10 GeV

(1—cosO) 4X 2 2 (1 + X)

{

Vh

300km/s

(12.17)

}2

where 0 is the center of mass scattering angle and X = m~/mh.For the optimal choice of target nucleus (X = 1), this gives recoil energies near 5 keV (mh/lO GeV). Since the scattering is roughly isotropic in the center of mass, the recoil spectrum is flat out to a cutoff determined by m1 and mh (for a given vh). 2 = (hIR)2 for a nucleus of The distribution however, be cutoff momentum transfers radius R. (Abovemay, this value the nucleus no for longer appears as a point above particleq and coherence is lost.) The cutoff corresponds roughly to a nuclear recoil energy near (3 x 105/A513) keV for nuclear mass number A so this effect is important for heavy nuclear targets. Averaged over the velocity distribution of the halo particles and over scattering angles, we expect a nuclear recoil spectrum like that in fig. 12.1. The spectrum was calculated assuming isotropic scattering

(11 .1—.

1’

—

—

—

—

—

> 0

1.S

—

C =

——

=

I-

1 0

— — — — —

- 05~

~2.l 0

2

3

4

5

T/T Fig. 12.1. The nuclear recoil spectrum for halo particles. The spectrum is calculated assuming a Boltzmann distribution with i~v~) = 250 km/s, and isotropic scattering. The recoil energies are normalized to T 0 GeV)4X/(1 + X)2, where X is the ratio between the target and halo particle masses. The dashed line shows the ratio between the 1, =April 5 keVand (mb/i October spectra.

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Rich et a!., Experimental particle physics without accelerators

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and a non-rotating halo with a Boltzmann velocity distribution ((vt,) = 250 km/s). Also shown is the ratio between the May and November spectra under these conditions. The May recoil spectrum is enhanced at high energy because the Earth’s motion about the Sun has during this month a component in the direction of the Sun’s motion about the galaxy. This increases the target velocity in the galactic frame. At these low energies, the recoiling nucleus loses most of its energy through the production of phonons which eventually thermalize, heating up the medium. In semiconductors, some of this energy goes into the creation of electron—hole pairs [Chasman et a!. 1965] (the yield is about a factor of three less than that for an electron depositing the same amount of energy in the 10 keV range). Existing silicon (m~---263 GeVIc2) and germanium (m~‘—67) semiconductor detectors are, therefore, sensitive to recoil energies greater than —2 keV [Ah!en et a!. 1986] corresponding to particles of masses greater than —10 GeV. Proposed cryogenic thermal detectors (see below) may be sensitive to recoil energies and, consequently, particle masses more than an order of magnitude smaller. Cross sections for the elastic scattering of a variety of halo candidates off nuclei have been calculated by Goodman and Witten [1985],Wasserman [1986]and Drukier et al. [1986].The cross sections depend critically on whether the particles have vector couplings or only axial-vector couplings. As in the case of electron—nucleus scattering (discussed in the chapter on atomic physics), the low-energy amplitudes for vector couplings are coherent and proportional to the number of nucleons (as long as the de Broglie wavelength of the particle is much less than the nuclear radius). The low-energy axial couplings are proportional to the nuclear spin, so axial amplitudes are roughly a factor of Z smaller than vector amplitudes. Event rates are then determined by the cross sections, the density given by eq. (12.6), and the velocity distribution. Typical rates are shown in table 12.1 from [Goodman and Witten 1985]. For particles with full-strength weak vector couplings (scalar neutrinos and heavy Dirac neutrinos), event rates range from 50 to ~ kgt day~.For particles with spin-dependent couplings (photinos, higgsinos, and massive Majorana neutrinos), they are typically 0.1 to 1 kg1 day- for nuclei with spin, while for spin-zero nuclei (like the primary isotopes of silicon and germanium) the event rate is zero. These event rates have to be compared with the background from the scattering of X-rays emitted by radioactive impurities in the detector. The lowest background rate has been achieved in germanium crystals used in double-~3-decayexperiments. The spectrum obtained by one experiment [Ahlen et a!. 1986] is shown in fig. 12.2. (Note that, due to a lower efficiency for creating electron—hole pairs, nuclear recoils produce a factor ——3 less signal than X-rays depositing the same energy.) The integrated rate between 10 and 100 keV is about 100 kg~day1. Ahien et a!. used this spectrum to set limits on halo particles with vector couplings: if the halo were to consist entirely of particles acting with full-strength weak vector interactions, then masses between 20 GeV and 5 TeV are ruled out (see also [Caldwell 1987]). Table 12.1 Typical rates for elastic scattering on nuclei for some dark matter candidates Interactions with nuclei

Candidate particles

Typical rates (kg~day~)

spin independent

sneutrino

50—1000

spin dependent

heavy Dirac v photino higgsino heavy Majorana v

100—10000 0.1—1

(for m 5 = 2 GeV) (for m,, = 100GeV)

J. Rich et a!., Experimental particle physics without accelerators

348

102

6~’ZnX.ray ~.

I

~PbLX-ray

/

2’°Pby ray ~ Sri

•lil Pd

> ~

101

K X-rays

~

1

PbKX-ray

C 0

0

2

20

40

60

80

100

keV Fig. 12.2. The energy spectrum obtained with the 0.7 kg germanium spectrometer of Ahlen et al. [1986](ten-week exposure).

Because of the need to be sensitive to lower recoil energies and to use non-zero-spin nuclei as targets, further progress will depend on the development of new calorimetric techniques, most likely cryogenic. Some of these techniques have already been mentioned in connection with solar-neutrino detection [Cabrera et a!. 1985; Drukier and Stodolsky 1984], neutrino-mass measurements [Coron et al. 19851, and searches for double-~3decay [Fiorini and Niinikoski 1984]. They all make use of the decrease in specific heat with falling temperature, which makes materials sensitive to small depositions of energy. In bolometers [Fiorini and Niinikoski 1984; Coron et a!. 1985, 1987; Cabrera et al. 1985; Keyes 1986; Sadoulet 1987; Smith 1987], phonons produced in a nuclear recoil are detected after some thermalization with a thermistor or directly with, for example, a superconducting tunnel junction. (See [Caplin 1987] for a discussion of the possibilities.) In superconducting-grain detectors [Drukier and Stodolsky 1984; LeGros et al. 1986; Pretz! 1987], small superconducting grains are suspended in a dielectric material in a magnetic field. When the heat generated by a nuclear recoil causes the grain to go normal, the magnetic field penetrates the grain, and the resulting magnetic flux change is sensed by a current

J.

Rich et a!., Experimental particle physics without accelerators

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loop connected to an amplifier. In superconducting-filament detectors [Smith 1986b], the passage to the normal state is sensed directly through the increased resistance of a filament. It is certain that the above examples do not exhaust the possibilities. It should be emphasized, however, that, apart from bolometers that have been used for many years in other areas of physics, these techniques are still in the development stage. Even the utility of bolometers for particle physics has not been established because of the difficult problem of scaling up the existing milligram bolometers to the kilogram-mass detectors needed for dark-matter searches. In addition, background-reduction techniques already developed for doub!e-~-decayexperiments [Ahlen et al. 1986] will have to be improved to make experiments sensitive to particles with spin-dependent interactions. Once suitable detectors exist, the identification of a signal as due to halo particles will not be easy, since the recoil spectrum (fig. 12.1) is not very distinctive. One must use the dependence of the average signal, (T), on the atomic mass number of the target nucleus to demonstrate that the signal is due to a non-relativistic particle with the galactic virial velocity (/3 10 3)~ In particular, the maximum in ~T) should occur for Amax mh/l GeV (determining mh) with (T)max Amax/32 GeV— Amax keV. If the halo particle is more massive than the target nuclei available, (T) should increase with A like (T~ /32A GeV. The —10% yearly modulation in the counting rate above a threshold (fig. 12.1) is due to the fact that the particle and the Sun move with /3 — i0~while the Earth moves about the Sun with /3 10g. Finally, in the case of particles with spin-dependent interactions, the event rate should have a characteristic dependence on the spin of the target nucleus. Detection strategies based on superconducting-grain detectors were discussed in some detail by Drukier et al. [1986]. We now turn to the possibility of detecting on Earth the products of halo particle—antiparticle annihilations in interstellar space. Such annihilations would give a spectrum of particles superimposed on that of ordinary primary cosmic rays. Silk and Srednicki [19841calculated the fluxes of several annihilation products of photinos of mass —3 GeV and found that they should generally be lower than those of ordinary primary cosmic rays, with the exception of antiprotons. They noted that the reported flux of antiprotons below the kinematic threshold for secondary production could be explained by this source. Calculations of antiproton fluxes have also been given by Stecker et al. [1985]and Hagelin and Kane [1986]. The possibility of observing monochromatic photons from halo particles annihilating into quarkonium plus a photon was discussed by Srednicki et a!. [1986],Rudaz [1986],Bergstrom and Sne!!man [1986],and Turner [1986b]. In a somewhat different context, Olive and Silk [1985]and Stecker [1986] discussed the possible effects of gravitino decay on the spectrum of diffuse gamma rays. Sperge! and Press [1985]pointed out that halo particles could be gravitationally trapped in the Sun if, while traversing the Sun, they lost sufficient energy through collisions. The trapping rate is determined by the elastic-scattering cross sections discussed previously, and the equilibrium concentration is determined by losses due to annihilation and evaporation (see also [Krauss et a!. 1986]). For halo particles with masses greater than —6 GeV, annihilation is expected to be the dominant process. As originally pointed out by Silk et a!. [1985],annihilations in the Sun produce neutrinos that could be detected on Earth in proton-decay detectors. Srednicki et a!. [1987],Campbell et a!. [1986],Hagelin et a!. [1986], and Gaisser et a!. [1986] have calculated neutrino fluxes due to the annihilation of a variety of halo candidates in the Sun. The particle giving the best signature is the scalar neutrino, which normally annihilates into two monochromatic neutrinos. The flux, in this case, is higher than that due to the decay of cosmic rays in the atmosphere, so scalar neutrinos with masses greater than 3 GeV are probably ruled out by existing measurements [Haines et a!. 1986; LoSecco 1987]. Heavy Dirac neutrinos also have a large annihilation cross section into two neutrinos. Other halo candidates -‘-

—

—

—

350

J. Rich et a!., Experimental particle physics without accelerators 10

I

I

I

/~‘\(~0.5/kTyr)

dN dInE

-

5

-

—-—.--.-—..

-

051986]. Fig. 12.3. masses of 3,The 8 and differential 12GeV [Gaisseret neutrino-induced al. event In each rate case, (for alltheneutrino parameter flavors) E~(GeV) determining from thetheannihilation annihilationofcross photinos section captured (the mass by the of the Sunscalar for photino quark) was adjusted so that the cosmological photino density is equal to the closure density. The dashed line shows the background due to atmospheric neutrinos within a cone of half-angle 37°.

(photinos, higgsinos, heavy Majorana neutrinos) yield soft neutrinos through the decay of heavy annihilation products (b, -r, c). The flux, in this case, can still be larger than the cosmic v flux. Figure 12.3 [Gaisser et al. 1986] shows the expected spectrum of neutrino events due to photino annihilation in the Sun. The rates are in the range of several per kton-year and are comparable with the cosmic-ray background. Preliminary results from the 1MB collaboration [LoSecco 1987] and the Fréjus collaboration [Kuznik 1987] rule out fluxes of the magnitude shown in fig. 12.3 for photinos of masses between 5 and 10GeV. Freese [1986]and Krauss et al. [1986]considered halo particles trapped in the Earth. Interestingly, only particles with vector couplings can be so trapped, because there are relatively few non-zero spin nuclei in the Earth off which particles with spin-dependent interactions could scatter. Again, scalar neutrinos and heavy Dirac neutrinos give the best signal. Freese concluded that existing data exclude 12—20 GeV scalar neutrinos and 9—20 GeV Dirac neutrinos as the dominant component of the halo. 12.6. Quark nuggets Witten [1984] suggested that large aggregates of up, down and strange quarks in roughly equal proportions might be stable against decay to ordinary baryons consisting of up and down quarks. In his scheme, the large mass of the strange quark is compensated by the fact that a single strange quark added to an ensemble of up and down quarks can, due to the absence of Pauli blocking, go into a lower-energy orbital than an additional up or down quark. This could lead to stable “quark nuggets” composed of an optimal proportion of the three quark types. The characteristics of such objects have been studied theoretically by Farhi and Jaffe [1984] and reviewed by Farhi [1986].While the theoretical stability of quark nuggets has not been established, it is plausible that they might exist with masses ranging from —100 GeV to planetary masses. They would presumably be surrounded by an electron cloud to make them electrically neutral. Witten [1984]suggested that nuggets might be left over from a QCD phase transition in the early universe, and that their present density could conceivably account for the dark matter in galaxies. Alcock and Farhi [1985] and Madsen, Heise!berg and Riisager [1986]studied evaporation from such nuggets and concluded that only rather large nuggets (A> 1046_1056) could have survived until the present. A spectrum of lighter nuggets might also have been produced in the latter stages of stellar evolution.

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De Rujula and G!ashow [1984] considered a variety of detection schemes for cosmic-ray quark nuggets. Recently, experimental limits from an experiment designed to detect monopoles have been reported [Namamura et a!. 1985]. These data, and an analysis [De Rujula and Glashow 1984] of an earlier search for particle tracks in ancient mica seem to rule out a quark-nugget-dominated halo for g. Lighter nuggets would stop in the Earth’s crust and nugget masses between —i0’3 g and ~~,10_1 could be sought in bulk matter [Farhi and Jaffe 1985]. Heavier cosmic-ray nuggets could produce a variety of effects, including epilinear earthquakes. Quark nuggets have also been discussed in connection with the Centauro cosmic-ray events [Bjorken and McLerran 1979; Halzen and Liu 1985] and with astronomical gamma-ray bursts [Alcock et a!. 1986].

References Chapter 2 Abela, R., et at., 1984, Phys. Lett. B146, 431. Afonin, Al., et at., 1985, Soy. J. Nucl. Phys. 42, 719. Aglietta, M., et at., 1986, Il Nuovo Cimento 9C, 185. Ahrens, L.A., et al., 1985, Phys. Rev. D31, 2732. Alberini, C., et al., 1986, Il Nuovo Cimento 9C, 237. Albrecht, H., et al., 1985, Phys. Lett. B163, 401. Alexeyev, EN., et at., 1986, in: [Sendai 1986]. Altzitzogtou, T., et al., 1985, Phys. Rev. Lett. 55, 799. Angelini, C., et al., 1986, Phys. Lett. B179, 307. Avignone, FT., et al., 1985, Phys. Rev. Lett. 54, 2309. Bahcall, iN., 1978, Rev. Mod. Phys. 50, 881. Bahcall, iN., 1986a, in: Weak and Electromagnetic Interactions in Nuclei, ed. H.V. Klapdor (Springer-Verlag, 1986). Bahcall, J.N., 1986b, submitted to Rev. Mod. Phys. Bahcall, iN., et al., 1982, Rev. Mod. Phys. 54, 767. Bahcall, iN., et al., 1985, Astrophys. J. 292, L79. Bahcall, iN., et al., 1986a, submitted to Phys. Lett. B. Bahcall, iN., et at., 1986b, submitted to Phys. Rev. D. Baker, N.J., et al., 1981, Phys. Rev. Lett. 47, 1576. Baldini, A. and G.F. Giudice, 1986, University of Pisa report IFUP-TH 29/86. Baldo-Ceolin, 1986, in: [Moriond 1986, 1987]. Baltz, A.i. and i. Weneser, 1986, Phys. Rev. D35, 528. Barabanov, I.R., et al., 1984, in: [Homestake 19841. Berger, V., et al., 1986, Phys. Rev. D34, 980. Barone, A., et al., 1985, Nuct. Inst. and Meth. in Phys. Res. A235, 254. Bellotti, E., et at., 1984a, Phys. Lett. B146, 450. Bellotti, E., et al., 19Mb, in: The Time Projection Chamber, ed. iA. Macdonald (AlP Conf. Proc. 108, New York, 1984). Bellotti, E., et at., 1986, II Nuovo Cimento 95A, 1. Bennet, CL., et al., 1981, Phys. Lett. B170, 19. Bennett, CL., et al., 1985, Phys. Rev. C31, 197. Bernardi, G., et at., 1986, Phys. Lett. B181, 173. Bergkvist, K.E., 1985a, Phys. Lett. B154, 224. Bergkvist, K.E., 1985b, Phys. Lett. B159, 408. Bergsma, F., et al., 1984, Phys. Lett. B142, 103. Bethe, H., 1986, Phys. Rev. Lett. 56, 1305. Boehm, F., 1984, Comments Nucl. Part. Phys. 13, 183. Boehm, F. and P. Vogel, 1984, Ann. Rev. Nuct. Part. Sci. 34, 125. Booth, N.E., et al., 1984, in: [Homestake 1984]. Boris, S., et at., 1985, Phys. Lett. B159, 217.

352

J. Rich et al. Experimental particle physics without accelerators

Bouchez, J., et al., 1986, Z. Phys. C 32, 499. Cabrera, B., et al., 1985, Phys. Rev. Lett. 55, 25. Caldwelt, DO., et al., 1986, Phys. Rev. D33, 2737. CaIdwell, DO., 1987, in: [Moriond 1987]. Carlson, ED., 1986, Phys. Rev. D34, 1454. Cavaignac, iF.. et al., 1984, Phys. Lett. B148. 387. Cavaignac, iF., 1986, in: [Moriond 1986]. Chen, H.H., 1985, Phys. Rev. Lett. 55, 1534. Cherry. ML., et al., 1986, II Nuovo Cimento 9C. 210. Ching, C. and T. Ho, 1984, Phys. Report U2, 1. Coron, N., et al., 1985, Nature 314, 75. Cowsik, R. and i. McClelland, 1972. Phys. Rev. Lett. 29. 669. Cribier, M., et al., 1986a, Phys. Lett. Bi82, 89. Cribier, M., et al., 1986b, in: [Sendai 1986]. Cribier, M., et al., 1987, Phys. Lett. B. 188. 168. Dar, A. and Y. Melina, 1986, Inst. Adv. Study Preprint IAS-PUB-000l. Dar, A., et al., 1986, Israel Inst. of Tech. - Haifa Preprint TECHNION-PH-86-29. Dc Rujula, A., 1981, Nuct. Phys. B188. 414. Dicus, D.. et at. 1977, Phys. Rev. Lett. 39. 168. Doi, M., et al., 1985, Prog. Theor. Phys. Suppl. 83. Drukier, A. and L. Stodolsky, 1984, Phys. Rev. DM1, 2295. Dydak, F., et al., 1984, Phys. Lett. B134, 281. Ejiri, H., et al., 1986, in: [Sendai 1986]. Elliott, SR., et al., 1986, Phys. Rev. Lett. 56, 2582. Fackler, 0., et al., 1985, Phys. Rev. Lett. 55. 1388. Faulkner, J., et al., 1986, Nature 321, 226. Fiorini, E. and TO. Ninikoski, 1984, NucI. Inst. and Meth. 224. 83. Forster, A., et al., 1984, in: The Time Projection Chamber. ed. J.A. Macdonald (AlP Conf. Proc. 108, New York, 1984). Freedman, D., et al., 1977, Ann. Rev. Nucl. Sci. 27. 167. Fritschi, M., et al., 1986, Phys. Lett. B173, 485. Gaisser, T.K., et al., 1986, Phys. Rev. D33, 1233. Gelmini, GB., et al., 1987. NucI. Phys. B281. 726. Grotz, K., et at., 1986, Astron. Astrophys. 154, Li. Haines, T.J., et al., 1986, Phys. Rev. Lett. 57, 1986. Halprin, A., 1986, Phys. Rev. D34, 3462. Hartmann, F.X. and R.A. Naumann, 1985, Phys. Rev. C3i, 1594. Haxton, W.C. and G.J. Stephenson, 1984, Prog. Part, and NucI. Phys. 12. 409. Haxton, W.C., 1985, Phys. Rev, Lett. 55, 807. Haxton, W.C., 1986a, Comments NucI. Part. Phys. 16, 95. Haxton, W.C., 1986b, in: [Moriond 19861. Haxton, W.C., 1986c, Phys. Rev. Lett. 57, 1271. Henning, \V., et at., 1984, in: [Homestake 1984]. Hirata, K., et al., 1986, in: [Sendai 1986]. Homestake, 1984, Solar Neutrino and Neutrino Astronomy, eds. ML. Cherry et al. (AlP Conf. Proc. 126, AlP, New York). Hurst, G.S., et al., 1984, in: [Homestake 1984]. Hurst, G.S., et al., 1985, Rep. Prog. Phys. 48, 1333. Jeziorski, B., et al., 1985, Phys. Rev, A32, 2573. Kayser, B., 1981, Phys. Rev. D24, 110. Kayser. B., 1985, Comments NucI. Part. Phys. 14, 69. Kayser, B., 1987, in: [Moriond 19871. Keyes, R.W., 1986, Phys. Rev. Lett. 57, 648. Kirsten, T. and H.W. Muller, 1969, Earth Plan. Sci. Lett. 6, 271. Kirsten, T., et al., 1983, Phys. Rev. Lett. 50, 474. Kirsten, T., et at., 1986, in: Proc. Intern. Symp. on Nuclear Beta Decays and Neutrino Physics, Osaka, Japan (to be published). Kirsten, T., 1984, 11th Int. Conf. on p Phys. and Astrophys., eds. K. Kleinknecht and E. Paschos (World Scientific, Singapore). Kirsten, T., 1986, in: [Moriond 1986]. Kleinknecht, K., 1986, Comments NucI. Part. Phys. 16, 267. i~olb,E.W., et at., 1986, Phys. Lett. B175, 478.

I. Rich et a!., Experimental particle physics without accelerators

353

Kraus, H., et al., 1986, Europhys. Lett. 1, 161. Krauss, L. and F. Wilczek, 1985, Phys. Rev. Lett. 55, 122. Krofcheck, et al., 1985, Phys. Rev. Lett. 55, 1051. Kuo, T.K. and J. Pantaleone, 1986a, Phys. Rev. Lett. 57, 1805. Kuo, T.K. and i. Pantateone, 1986b, Purdue Univ. Preprint PURD-TH-86-20. Langacker, P., 1981, Phys. Reports 72, 185. Lee, B.W. and S. Weinberg, 1977, Phys. Rev. Lett. 39, 165. Lindhard, i. and PG. Hansen, 1986, Phys. Rev. Lett. 57, 965. LoSecco, i.M., et at., 1985a, Phys. Rev. Lett. 54, 2317. LoSecco, i.M., et al., 1985b, Phys. Rev. Lett. 54, 2299. LoSecco, i.M., 1986, Phys. Rev. Lett. 57, 652. LoSecco, J.M., 1987, in: [Moriond, 1987]. Markey, i. and F. Boehm, 1985, Phys. Rev. C32, 2215. Mathews, G.J., et al., 1985, Phys. Rev. C32, 796. Messiah, A., 1986, in: [Moriond 1986]. Mikheyev, S.P. and A.Yu. Smirnov, 1985, Soy. J. Nucl. Phys. 42, 913. Mikheyev, S.P. and A.Yu. Smirnov, 1986, Il Nuovo Cimento 9, 17. Moriond, 1986, ‘86 Massive Neutrinos in Astrophysics and in Particle Physics, eds. 0. Fackler and i. Tran Thanh Van (Editions Frontieres). Moriond, 1987, Search for New and Exotic Phenomena, ed. J. Tran Thanh Van, to be published. Morrison, D.R.O., 1985, CERN reprint CERN/EP 86-44. Ohi, T., et at., 1985, Phys. Lett. B160, 322. Okun, LB., et al., 1986, ITEP report no. 20, 1986 (to be published). Parke, S., 1986, Phys. Rev. Lett. 57, 1275. Parke, S. and T.P. Walker, 1986, Phys. Rev. Lett. 57, 2322. Picciotto, C. and i. Kopac, 1985, Phys. Rev. D32, 1241. Raghavan, R.S., 1976, Phys. Rev. Lett. 37, 259. Raghavan, R.5., 1983, Phys. Rev. Lett. 51, 975. Raghavan, R.S., et a!., 1986, Phys. Rev. Lett. 57, 1801. Ravn, H.L., et at., 1983, AlP Conf. Proc. 99, 1. Reinartz, P. and L. Stodolsky, 1985, Z. Phys. C 27, 507. Reines, F. and C. Cowan, 1953, Phys. Rev. 92, 830. Rosen, S.P. and J.M. GeIb, 1986, Phys. Rev. D34, 969. Rowley, i.K., et at., 1984, in: [Homestake 1984]. Schinder, i.P. and ST. Shapiro, 1982, Astrophys. J. 259, 311. Sendai, 1986, Proc. 12th tnt. Conf. on Neutrino Physics and Astrophysics, Sendai, Japan (to be published). Shrock, RE., 1980, Phys. Lett. B96, 159. Simpson, ii., 1981, Phys. Rev. D23, 649. Simpson, i.J., 1985, Phys. Rev. Lett. 54, 1891. Simpson, ii,, 1986, Phys. Lett. B174, 113. Sinclair, D., et at., 1986, II Nuovo Cimento Serie 1 9C, 308. Smirnov, A.Yu., 1987, in: [Moriond 1987]. Sobet, H., 1986, in: [Moriond 1986]. Spergel, D. and W. Press, 1985, Astrophys. J. 294, 663. Stockdale, I.E., et al., 1984, Phys. Rev. Lett. 52, 1384, Takasugi, E., 1986, in: [Moriond 1986]. Thomas, J., 1987, in: [Moriond 1987]. Ushida, N., et at., 1986, Phys. Rev. Lett. 57, 2897. Vergados, iD., 1986, Phys. Reports 133, 1. Vogel, P, and MR. Zirnbauer, 1986, Phys. Rev. Lett. 57, 3148. Voloshin, MB. and MI. \~iotsky,1986, ITEP report no. 1. von Dincklage, R.-D., et at., 1985, Phys. Rev. C31, 1510. Waysand, G., 1984, Moriond Workshop on Massive Neutrinos. Winter, K., 1986, CERN report EP/86-61. Wolfenstein, L., 1978, Phys. Rev. D17, 2369. Yasumi, S., et a!., 1986, Phys. Lett. B181, 169. Zacek, V., et al., 1985, Phys. Lett. B164, 193. Zacek, G., et at., 1986, Phys. Rev. D34, 2621. Zeinitz, B., 1985, Prog. Part, and Nuct. Phys. 13, 445.

354

J. Rich et al., Experimental particle physics without accelerators

Chapter 3 Altarev, IS., et al., 1981, Phys. Lett. B102, 13. Ansetm, A.A., et al.. 1985, Phys. Lett. B152, 116. Avishai, Y. and M. Fabre de Ia Ripelle. 1986, Phys. Rev. Lett. 56. 2121. Baldo-Ceolin, M., 1984. 1. Phys. C3. Baldo-Ceolin, M., 1986, in: Weak and Electromagnetic Interactions in Nuclei. ed. H.V. Klabdor (Springer-Verlag, Berlin). Bialek, W., et al., 1986, Phys. Rev. Lett. 56, 1623. Bigi, 1.1. and Al. Sanda, 1985, Comments NucI. Part. Phys. 14, 149. Byrne, J., 1984, i. Phys. C3, 1. Ecg. JO., 1985, Moriond Workshop on CP violation, 287. Fermi, E.. et al., 1950, Nuclear Physics (Univ. of Chicago Press) p. 201. Fidecaro, G., et al., 1985, Phys. Lett. B156, 122. Fortson, EN. and L.L. Lewis, 1984, Phys. Reports 113, 289. Golub, R.. 1984, J. Phys. C3. Greenburger, D.M., 1983, Rev. Mod. Phys. 55, 875. Hamzaoui, C. and A. Barroso, 1985. Phys. Lett. B154, 2132. ICOMAN 1983, mt. Conf. on Matter Non Conservation, eds. F. Bellotti and S. Stipcich. INFN (Frascati). lljinov. AS., et al.. 1983, in: [ICOMAN 1983]. Jones, T.W., et al., 1984, Phys. Rev. Lett. 52. 720. Kabir, P.K., 1983, Phys. Rev. Lett. 51. 231. Lazarides, G., et al., 1986. Phys. Lett. B175, 309. Lobashev, V.M. and A.P. Serebrov, 1984. J. Phys. C3. Mohapatra, RN. and RE. Marshak, 1980, Phys. Rev. Lett. 32. 438. Nieves, 1G., et al., 1986, Phys. Rev. D33. 3324. Pendlebury, i.M., et al., 1984, Phys. Lett. B136, 327. Raab, F.J., 1987, in: The Search for New and Exotic Phenomenon, ed. J. Tran Thanh Van [Moriond 1987] to be published. Ramsey, N.F., 1980, Physics Today, July 1980. Ramsey, N.F., 1982a. Rep. Prog. Phys. 45. 95. Ramsey, N.F., 1982b, Ann. Rev. NucI. Sci. 32, 211. Rauch, H., 1986, Contemp. Phys. 27. 345. Takita, M., et al., 1986, Phys. Rev. D34. 902. VoId, TO., et al., 1984, Phys. Rev. Lett. 52. 2229. Wolfenstein, L., 1985, Comments NucI. Part. Phys. 14, 149. Wolfenstein, L., 1986, Ann. Rev. NucI. Part. Sci. 36, 137. Zee, A., 1985. Phys. Rev. Lett. 55. 2382.

Chapter 4 Ann Arbor, 1981, Proc. 2nd Workshop on Grand Unification, eds. J.P. Leveille et al. (Birkhauser, Boston, 1981). Bareyre, P., et al., 1986, II Nuovo Cimento 9C No. 2, 159. Battistoni, G.. et al., 1982, Phys. Lett. B118, 461. Battistoni, G.. et al., I983a, Phys. Lett. B133. 454. Battistoni, G., et al., 1983, NIM. Bionta, R.M., 1983, Phys. Rev. Lett. 51, 27. Btewitt, G., et al., 1985. Phys. Rev. Lett. 55, 2114. Chapel Hill, 1982, Proc. 3rd Workshop on Grand Unification, eds. P. Frampton et al. (Birkhauser, Boston, 1982). Cortez, B.. et al., 1984. Phys. Rev. Lett. 52. 1092. Gaisser, T.K., et al.. 1983, Phys. Rev. Lett. 51, 223. Georgi H. and S.L. Glashow, 1974, Phys. Rev. Lett. 32, 438. Haines, T.J., et al., 1986, Phys. Rev. Lett. 57, 1986. Krishnaswamy. MR., et al., 1981, Phys. Lett. B106, 339. Krishnaswamy. MR., et al., 1982, Phys. Lett. BuS, 349. Langacker, P., 1981, Phys. Reports 72. 185. LoSecco, J.M., 1985, Comments NucI. Part. Phys. 15. 23. Lucha, W., 1985, Fortsch. der Phys. 33. 547. Lucha, W., 1986, Comments NucI. Part. Phys. 16. 155. Meyer. H.-J.. 1986, in: 12th Int. Conf. on Neutrino Physics and Astrophysics, Sendai, Japan (to be published).

J. Rich et al., Experimental particle physics without accelerators

355

Minneapolis, 1985, Proc. 6th Workshop on Grand Unification, eds. S. Rudaz and T.F. Walsh (World Scientific, Singapore, 1986). Park, H.S., et al., 1985, Phys. Rev. Lett. 54, 22. Pati, i., A. Satam and B. Sreekantan, 1986, Int. i. Mod. Phys. Al. Perkins, D.H., 1984, Ann. Rev. NucI. Part. Sci. 34, 1. Philadelphia, 1983, Proc. 4th Workshop on Grand Unification, eds. P. Langacker et al. (Birkhauser, Boston, 1983). Providence, 1984, Proc. 5th Workshop on Grand Unification, eds. K. Kang et al. (World Scientific, Singapore, 1984). Ross, G.G., 1981, Rep. Prog. Phys. 44, 655. Rubbia, C., et at., 1985, INFN Report AE-85/7 (September 1985). Toyama City, 1986, Proc. 7th Workshop on Grand Unification (to be published). Weinberg, S., 1979, Phys. Rev. Lett. 42, 850.

Chapter 5 Baird, PEG., et al., 1977, Phys. Rev, Lett. 39, 798. Barkov, L.M. and MS. Zolotorev, 1978, JETP Lett. 27, 357. Barkov, L.M. and MS. Zolotorev, 1979, Phys. Lett. B85, 308. Barkov, L.M. and MS. Zolotorev, 1980, Soy, Phys. JETP 52, 360. Birich, ON., et al., 1984, Soy. Phys. JETP 60, 442. Bouchiat, C., et al., 1983, Nuct. Phys. B22u, 68. Bouchiat, C., et al., 1986, Europhys. Lett. 2, 511. Bouchiat, MA. and CC. Bouchiat, 1974, Phys. Lett, B48, 111. Bouchiat, MA., et al., 1982, Phys. Lett. B117, 358. Bouchiat, MA., et at., 1984, Phys. Lett, B134, 463. Bouchiat. MA., et at., 1985, i. Phys. 46, 1897. Bouchiat, MA., et at., 1986a, i. Phys. 47, 1175. Bouchiat. MA., et al., 1986b, 1. Phys. 47, 1709. Bouchiat, MA. and L. Pottier, 1984, in: Atomic Physics 9, eds. R.5. VanDyck Jr. and EN. Fortson (World Scientific, singapore, 1984). Bouchiat. MA. and L. Pottier, 1986, Science 234, 1203. Bogdanov, Yu.V,, et al., 1980, Soy. Phys. JETP 31, 214. Brown, L.S. and G. Gabrielse, 1986, Rev. Mod. Phys. 58, 233. Bucksbaum, P., et at., 1981a, Phys. Rev. Lett. 46, 640. Bucksbaum, PH., et al., 1981b, Phys. Rev, D24, 1134. Commins, ED. and PH. Bucksbaum, 1980, Ann. Rev, NucI. Part. Sci. 30, 1. Das, B.P., 1986, in: Proc. Adriatico Research Conf. on Relativistic Many-Body Problems (Trieste, 1986) to be published in Physica Scripta. Drell, P.S. and ED. Commins, 1984, Phys. Rev. Lett. 53, 968. Drell, P.S. and ED. Commins, 1985, Phys. Rev. A32, 2196. Dzuba, V.A., et al., 1985, J. Phys. B18, 597. Emmons, T.P., et at., 1983, Phys. Rev. Lett. 51, 2089. Fortson, EN. and L.L. Lewis, 1984, Phys. Reports 113, 289. Gilbert, S.L., et at., 1985, Phys. Rev, Lett. 55, 2680. Gilbert, S.L., et al., 1986, Phys. Rev, A34, 792. Herrmann, PP., et al., 1986, i. Phys. B19, 1607. Hollister, i.H., et al., 1981, Phys. Rev. Lett. 46, 643. Johnson, W.R., et al., 1986, Phys. Rev. A34, 1043. Lewis, L.L., et al., 1977, Phys. Rev. Lett. 39, 795. Lynn, B.W., 1984, in: 1983 Trieste Conf. on Radiative Corrections in SU(2) x U(1), eds. B.W. Lynn and J.F. Wheater (World Scientific, Singapore, 1984) p. 311. Marciano, Wi. and A. Sirlin, 1983, Phys. Rev, D27, 552. Marciano, Wi. and A. Sirlin, 1984, Phys. Rev. D29, 75. Martensson, AM., et al., 1981, Phys. Rev. A24, 308. Martensson-Pendrill, AM., 1985, i. Phys. 46, 1949. Martensson-Pendrill, AM., 1986, in: Proc. Adriatico Research Conf. on Relativistic Many-Body Problems (Trieste, 1986) to be published in Physica Scripta. Neuffer, DV. and ED. Commins, 1977, Phys. Rev. A16, 844. Novikov, V.N., et al., 1977, Soy. Phys. JETP 46, 420. Prescott, C.Y., et al., 1978, Phys. Lett. B77, 347. Prescott, C.Y., et al., 1979, Phys. Lett. B84, 524. Sakurai, ii., 1967, Advanced Quantum Mechanics (Addison-Wesley, Reading, Mass., 1967).

356

J. Rich et al., Experimental particle physics without accelerators

Sandars, P.G.H., 1980, Physica Scripta 284, 21. Sushkov, OP., 1986, in: Proc. Adriatico Research Conf. on Relativistic Many-Body Problems (Trieste, 1986) to be published in Physica Scripta. Taylor, J., 1984, thesis, Oxford University.

Chapter 6 Adams, P.i., et al., 1983, Phys. Rev. D28, 1822. Bahcall, iN. and M. Schmidt, 1967, Phys. Rev, Lett, 19, 1294. Barnet, C., et al., 1985, Astrophys. J. 295, 24. Baum, WA. and R. Florentin-Nietsen, 1976, Astrophys. J. 209, 319. Bekenstein, J.D., 1982, Phys. Rev, D25, 1527. Dyson, F.i., 1967, Phys. Rev, Lett, 19, 1291. Dyson, F.i., 1972, in: Aspects of Quantum Theory, eds. A. Salam and E.P. Wigner (Cambridge University, Cambridge). Dyson, F.i., 1978, Variation of Constants, in: Current Trends in the Theory of Fields, eds. i.E. Lannutti and P.K. Williams (American Institute of Physics, New York) pp. 163—167. Gleiser, M. and i.G. Taylor, Phys. Rev. D31. 1904. Hellings, R.W., et al., 1983, Phys. Rev, Lett, 51. 1609. Irvine, J.M., 1983, Contemp. Phys. 24, 427. Irvine, i.M. and R. Humphreys, 1986, Prog. in Part, and NucI. Phys. 17, 59. Khare, P., 1986, Phys. Rev. D34, 1936. KoIb, E.W., et al., 1986, Phys. Rev. D33. 869. Lindner, M., et al., 1986, Nature 320, 246. Luck, J.-M. and Ci. Atlegre, 1983, Nature 302, 130. Mansfield, V.N. and S. MaIm, 1976, Astrophys. i. 209, 335. Marciano, Wi., 1984, Phys. Rev. Lett. 52, 489. Maurette, M., 1976, Ann. Rev. NucI, Sci. 26, 319. Norman, E.B., 1986, Am. J. Phys. 54, 317. Shlyakhter, Al., 1976, Nature 264, 340. Solheim, J.E., et al., 1976, Astrophys. J. 209, 330. Tubbs, AD. and AM. Wolfe, 1980, Astrophys. i. 236, L105. Turneaure, i.P. and SR. Stein, 1976, in: Atomic Masses and Fundamental Constants, vol. 5, eds. Sanders and Wapstra (Plenum, New York). Turneaure, i.P., et al,, 1983, Phys. Rev, D27, 1705. Weiss, N., 1986, Phys. Lett, B172, 180. Wu, Y.-S. and Z. Wang, 1986, Phys. Rev. Lett, 57, 1978.

Chapter 7 Baltrusaitis, R.M., et al., 1984, Phys. Rev, Lett. 52, 1380. Baltrusaitis, R.M., et al., 1985, Phys. Rev, D31, 2192. Bartelt, J., et at,, 1985, Phys. Rev, D32. 1630. Bartol, 1978, Cosmic Rays and Particle Physics, 1978 (Bartol Conf.), ed. T.K. Gaisser (Alp. New York, 1979). Battistoni, G., et at., 1983, Phys. Lett. B133, 454. Battistoni, G., et al., 1985, Phys. Lett. B155, 465. Berezinsky, VS., et al., 1986, Phys. Lett. B172, 423. Berger, C., et al,, 1986, Phys. Lett. B174, 118. Bhat et al., 1986, Ap. i. 306, 587. Bionta, R.M., et al., in: [Moriond 1986] p. 521. Cassiday, G.L., 1985, Ann. Rev. NucI. Part. Phys. 35, 321. Chardin, G., 1987, unpublished Ph.D. Thesis, University of Paris XI. Chardin, G. and G. Gerbier, 1985, Saclay report DPhPE 85-10. Dickey, i.M., 1983, Astrophys. J. 273, L71. D’Ettore Piazzoti, B., 1985, in: [ICRC 1985] 9, 455. D’Ettore Piazzoti, B., 1986, Summer study on SSC. Fontaine, 0., 1987, in: Search for New and Exotic Phenomena. ed, J. Tran Thanh Van, in: [Moriond 1987] to be published. Gaisser, T.K., et al., 1978, Rev. Mod. Phys. 50, 859. Gaisser, T.K. and GB. Yodh, 1980, Ann. Rev, NucI. Part. Phys. 30, 475. Gaisser, T.K. and F. Ha!zen, 1986, in: [Moriond 1986]. Greider, P.K.F., 1986, in: Neutrinos and the Present Day Universe, CEN, Saclay, 1986, eds, T. Montmerte and M. Spiro.

J. Rich et al. Experimental particle physics without accelerators

Halzen, F., et al., 1986, Phys. Rev, D34, 2061. Hermsen, W., et al., 1985, in: [ICRC 1985] 1, 95. Hil!as, AM., 1985, in: [ICRC 1985] 9, 407. ICRC, 1973, Proc. 13th Int. Cosmic Ray Conf., Denver, 1973 (ColoradoUniversity Boulder, 1973). ICRC, 1979, Proc. 16th Int. Cosmic Ray Conf., Kyoto, 1979 (Inst. of Cosmic Ray Res., Univ. of Tokyo, Tokyo, 1979). ICRC, 1983, Proc. 18th Int. Cosmic Ray Conf., Bangalore, 1983, eds. N. Durgaprasad et al, (Tata Inst. of Fund. Ret., Bombay, 1983). ICRC, 1985, Proc. 19th mt. Cosmic Ray Conf., La Jolla, 1985, eds. F.C. Jones et al. (NASA, Washington DC, 1985). Jones, LW., 1985, in: [ICRC 1985] 9, 323. Khristiansen, GB., 1979, in: [ICRC 1979] 14, 360. Krishnaswamy, MR., et al,, 1976, in: Proc. Int. Neutrino Conf., Aachen, eds. H. Faissner et al,, p. 197. Krishnaswamy, MR., et al., 1977, Pramana 5, 59. Lamb, R.C., et al., 1977, Astrophys. J. Lett. 212, L63. Lattes, C.M.G., et al., 1973, in: [ICRC 1973] 3, 2227; 4, 2671. Lattes, C.M.G., et al,, 1980, Phys. Reports 65, 151. MACRO, 1986, Il Nuovo Cimento 9C, No. 2, 281. Marshak, ML., 1985, in: [Minneapolis1985] p. 89. Marshak, ML., et al., 1985a, Phys. Rev. Lett. 54, 2079. Marshak, ML., et al.. 1985b, Phys. Rev, Lett. 55, 1965. McCusker, C.B.A., 1975, Phys. Reports 20, 229. Midorikawa, S. and S. Yoshimoto, 1986, Phys. Lett. B171, 239. Mincer, A., et al,, 1985, Phys. Rev. D32, 541. Minneapolis, 1985, Proc. 6th Workshop on Grand Unification, eds. S. Rudaz and T.F. Walsh (World Scientific, Singapore, 1986). Molteni, D., et at., 1980, Astron. Astrophys. 87, 88. Moriond, 1986, Progress in Electroweak Interactions, Moriond, 1986, ed. I. Tran Thanh Van (Editions Frontieres, Gif-sur-Yvette) p. 541. Ochs, W. and L. Stodolsky, 1986, Phys. Rev. D33, 1247. Robinett, R.W., 1986, Phys. Rev. D33, 1239. Samorski, M. and W. Stamm, 1983, in: [ICRC 1983] 11, 244. van der Klis, M. and i.M. Bonnet-Bidaud, 1981, Astron, Astrophys. 95, L5. Watson, A.A., 1985, in: [ICRC 1985] 9, 111. Wolfendale, AM., 1984, Rep. Frog. Phys. 47, 655. Wosiek, B., 1985, in: [ICRC 1985] 9, 509. Yock, P.C.M., 1986, Phys. Rev. D34, 698. Yodh, GB., et al., 1972, Phys. Rev. Lett. 28, 1005. Yodh, GB., et al,, 1983, Phys. Rev. D27, 1183.

Chapter 8 Ahlen, S. and G. Tarte, 1983, Phys. Rev. D27, 688. Alexeyev, EN., et al., 1985, in: Proc. 19th tnt. Cosmic Ray Conf., La Jolla, Vol. 8, p. 250. Bartelt, i., et al,, 1983, Phys. Rev, Lett. 50, 655. Barwick, SW., et al., 1983, Phys. Rev. D28, 2338. Bermon, 5., et at., 1985, Phys. Rev, Lett. 55, 1850. Bonarelti, R., et al,, 1983, Phys. Lett. B126, 137. Cabrera, B., 1982, Phys. Rev. Lett. 48, 1378. Cabrera, B., et al., 1983, Phys. Rev, Lett. 51, 1933. Callan, C.G., 1982, Phys. Rev, D25, 2141. Caplmn, AD., et al., 1985, Nature 317, 234. Caplin, AD., et al,, 1986, Nature 321, 402. Carrigan, R.A. and W.P. Trower, 1983, Nature 305, 673. Craigie, N.S., et al,, 1986, Theory and Detection of Magnetic Monopotes in Gauge Theories (World Scientific, Singapore). Cromar, MW., et al., 1986, Phys. Rev. Lett. 56, 2561. Dimopoulos, S., et al,, 1982, Phys. Lett. B119, 320. Doke, T., et al., 1983, Phys. Lett. B129, 370. Drell, S.D., et al., 1983, Phys. Rev. Lett. 50, 644. Errede, S., et al., 1983, Phys. Rev, Lett. 51, 245. Freese, K., et al,, 1983, Phys. Rev. Lett. 51, 1625. Frisch, H.J., 1983, Monopole ‘83, ed. iL. Stone (Plenum Press, New York). Giacomelli, G., 1984, La Riv, del Nuovo Cim. 7, 1.

357

358

J. Rich et al,, Experimental particle physics without accelerators

Giacomelti, G., 1986, Invited paper at 7th WOGU./ICOBAN, Toyoma, Japan. Groom, G.E., 1986, Phys. Reports 140, 323. Hara, T., et al., 1986, Phys. Rev. Lett. 56, 553. Incandela, J., et al., 1984, Phys. Rev. Lett. 53, 2067. Incandeta, J., et al., 1986, Phys. Rev. D34, 2637. Kajino, F., et al., 1984, Phys. Rev, Lett. 52, 1373. KoIb, E.W., et al,, 1982, Phys. Rev. Lett. 49, 1373. Krishnaswamy, MR., et al., 1984, Phys. Lett, B142, 99. Liss, TM., et al., 1984, Phys. Rev, D30, 884. MACRO, 1986, II Nuovo Cimento 9C, No. 2, 281. Masek, G.E., et al., 1985, in: Proc. 19th lot. Cosmic Ray Conf., La Jolla, vol. 8, eds. F.C. Jones et al. (NASA, Washington DC, 1985) p. 253. Mashimo, T., et al., 1983, Phys. Lett. B128, 327. Musset, P., 1986, Il Nuovo Cimento 9, 559. Parker, EN., 1970, Astrophys. J. 160, 383. Parker, EN., 1983, Monopole ‘83, ed. J.L. Stone (Plenum Press. New York) p. 125. Polyakov, AM., 1974, JETP Lett. 20, 194. Preskilt, J., 1984, Ann. Rev, NucI. Part. Sci. 34, 461. Price, M., 1983, Monopole ‘83, ed. J.L. Stone (Plenum Press, New York). Price, PB., 1984, Phys. Lett. 140B, 112. Price, PB. and M.H. Salamon, 1986, Phys. Rev. Lett. 56, 1226. Rubakov, V., 1981, JETP Lett. 33, 644. ‘t Hooft, 0., 1974, NucI. Phys. B79, 276.

Chapter 9 Chupka, WA., et at., 1966, Phys. Rev. Lett. 17, 60. Getl-Mann, M., 1964, Phys. Lett. 8, 214. Hirsch, G., et al,, 1979, LBL preprint 9350. Hodges, C., et al., 1981, Phys. Rev, Lett. 47, 1651. Ingelman, G. and C. Wetterich, 1986, Phys. Lett, B174, 109. Jones, LW., 1977, Rev. Mod. Phys. 49, 717. Joyce, D.C., et at., 1983, Phys. Rev. Lett, 51, 731. Kawagoe, K., et at., 1984, Lett. al Nuovo Cim. 41, 604. Kim, Y.S., 1973, Contemp. Phys. 14, 289. Kutschera, W., 1984, Phys. Rev, D29, 791. Lackner, KS. and G. Zweig, 1983, Phys. Rev. D28, 1671. LaRue, OS., et al., 1981, Phys. Rev, Lett. 46, 967. Lewin, iD. and P.F. Smith, 1985, Phys. Rev. D32, 1177. Liebowitz, D., et al., 1983, Phys. Rev. Lett. 50, 1640. Lindgren, MA., et al., 1983, Phys. Rev. Lett. 51, 1621. Lyons, L., 1985, Phys. Reports 129. 225. Marinelli, M. and 0. Morpurgo, 1982, Phys. Reports 85, 161. Marinelli, M. and G. Morpurgo, 1984, Phys. Lett. B137, 439. Mashomo, T., et al., 1983, Phys. Lett. B128, 327. Mitner, R.G., et al,, 1985, Phys. Rev. Lett, 54, 1472. Morpurgo, G., 1986, in: Congrès Nationale de Nice, September, 1985, ed. M. Le Bellac (Societe Francaise de Ia Physique). Price, iC., 1985, SLAC report SLAC-288. Price, IC., et al., 1986, SLAC-PUB-3938. Savage, ML., et al., 1986, Phys. Lett. B167, 481. Smith, P.F., et al., 1985, Phys. Lett. B153, 188. Smith, P.F., et al,, 1986a, Phys. Lett. B171, 129. Smith, P.F., et al,, 1986b, Phys. Lett. B181, 407. Steigman, 0., 1979, Ann. Rev, Nuct. Part. Sci. 29, 313. Zweig, G., 1964, CERN-TH 412 (unpublished).

Chapter 10 Alvager, T. and R.A. Naumann, 1967, Phys. Lett. B24, 647. Bahcall, iN., et al., 1982, Rev. Mod, Phys. 54, 767.

J. Rich et a!., Experimental particle physics without accelerators

359

Barbiellini, G., et at., 1983, CERN Report, EP 83-09. Boyd, RN., et al., 1978, Phys. Lett. B72, 484. Cahn, RN. and S.L. Glashow, 1981, Science 213, 607. Dick, Wi., et at., 1984, Phys. Rev. Lett. 53, 431.

Dick, Wi., et al., 1986, Phys. Rev. D33, 32. Dover, C.B., et al., 1979, Phys. Rev, Lett. 42, 1117. Haxton, W.C., 1986, in: ‘86 Massive Neutrinos in Astrophysics and in Particle Physics [Moriond19861, eds. 0. Fackler and I. Tran Thanh Van (Editions Frontieres). Ho!t, Ri., et al., 1976, Phys. Rev. Lett. 36, 183. Isgur, N. and S. Wolfram, 1979, Phys. Rev. D19, 234. Kirsten, T., 1986, Moriond Conference on Massive Neutrinos. Klein, i., et al., 1981, in: Symp. Accelerator Mass Spectrometry, Argonne National Lab., p. 136. Lee, B.W. and 5. Weinberg, 1977, Phys. Rev, Lett. 39, 165.

Middleton, R., et al,, 1979, Phys. Rev, Lett. 43, 429. Muller, R., et at., 1977, Science 196, 521. Nitz, D., et al., 1986, University of Michigan preprint UM HE 86-16. Pichard, B., et al., 1986, CEN Sactay, DPhPE, preprmnt. Rowley, i.K, et al, 1984, in: Solar Neut. and Neut. Astr. Conf., Homestake AlP Conf. Proc. No. 126, eds. ML. Cherry et at. (AlP, New York, 1985).

Smith, P.F., et al., 1982, NucI. Phys. B206, 333. Sur, B. and RN. Boyd, 1985, Phys. Rev, Lett. 54, 485. Turkevitch, A., et a!., 1984, Phys. Rev. D30, 1876. Wolfram, 5., 1979, Phys. Lett, B82, 65.

Chapter 11 Aronson, S.H., et al., 1986a, Phys. Rev. Lett. 56, 1342. Aronson, S.H., et al,, 1986b, Phys. Rev, Lett. 56, 2334. Barr, SM. and RN. Mohapatra, 1986, Phys. Rev. Lett, 57, 3129. Bars, I. and M. Visser, 1986, Phys. Rev. Lett. 57, 25. Bizzeti, P.O., 1986, Florence Univ. preprint DFF 86 No. 31. Bizzeti, PG., 1987, in: [Moriond 1987]. Bouchiat, C. and J. Itiopoulos, 1986, Phys. Lett. B169, 447. Bragmnski, V.G. and VI. Panov, 1972, Soy. Phys. JETP 34, 463. Cavasinni, V., et al., 1986, Phys. Lett. A116, 157. Chan, HA., et al., 1982, Phys. Rev, Lett. 49, 1745. Chang, D., et at., 1985, Phys. Rev, Lett. 55, 2835. Chen, Y.T., et at., 1984, Proc. R. Soc. Lond. A394, 47. Chu, S.Y. and RH. Dicke, 1986, Phys. Rev. Lett. 57, 1823. De Rujula, A., 1986a, CERN preprint TH. 4466/86. Dc Rujula, A., 1986b, Phys. Lett, B180, 213.

De Rujula, A., 1987, in: [Moriond19871. Eckhardt, D.H., 1986, Phys. Rev. Lett. 57, 2868. Fayet, P., 1986, Phys. Lett, B171, 261. Fischbach, E., et al., 1986a, Phys. Rev. Lett. 56, 3. Fischbach, E., et al,, 1986b, Phys. Rev, Lett. 56, 2424 and 2426. Fischbach, E., et al., 1986c, Phys. Rev. Lett, 57, 1959.

Fischbach, E., et al., 1986d, Phys. Rev. Lett. 57, 2869. Gabrielse, G., et al., 1986, Phys. Rev, Lett. 57, 2504. Gibbons, G.W. and B.F. Whiting, 1981, Nature 291, 636. Goldman, T., Ri. Hughes and MM. Nieto, 1986, Phys. Lett. B171, 217.

Holding, S.C., et al., 1986, Phys. Rev. D33, 3487. Hoskins, i.K., et al., 1985, Phys. Rev, D32, 3084. Keyser, PT., et al., 1986, Phys. Rev. Lett. 56, 2425. Kim, YE., 1986, Phys. Lett. B177, 255. Kuroda, K. and H. Hirakawa, 1985, Phys. Rev. D32, 342. Kuroda, K., 1987, in: [Moriond1987]. Long, DR., 1976, Nature 260, 417. Mikkelsen, DR. and Mi. Newman, 1977, Phys. Rev, D16, 919.

360

J. Rich et a!., Experimental particle physics without accelerators

Milgrom, M., 1986, NucI. Phys. B277, 509. Moody, i.E. and F. Wilczek, 1984, Phys. Rev. D30, 130. Moriond, 1987, The Search for New and Exotic Phenomena, ed. J. Tran Thanh Van, to be published. Neufeld, D.A., 1986, Phys. Rev, Lett, 56, 2344. Newman, RD., 1983, in: Proc. Third Marcel Grossman Meeting on General Relativity, ed. Hu Ning (North-Holland). Newman, RD., 1987, in: [Moriond 1987]. Nussinov, S., 1986, Phys. Rev. Lett. 56, 2350. Ogawa, Y., et al,, 1982, Phys. Rev. D26, 729. Panov, V.1. and V.N. Frontov, 1979, Soy. Phys. JETP 50. 852. Raab, F.i., 1987, in: [Moriond 1987]. Rapp, RH., 1974, Geophys. Res. Lett. 1. 35. Rapp, RH., 1977, Bull. Geod, 51, 301. Roll, PG., et al,, 1967, Ann. Phys. (NY) 26, 442. Smith, D.E., et al,, 1985, 1. Geophys. Res. 90, Bli, 9221. Speake, CC. and TI. Quinn, 1986, Nature 321, 567. Stacey, F.D., et al., 1981, Phys. Rev, D23, 1683. Stacey, F.D., 1983, in: Science Underground, eds. MM. Nieto et al. (Am. Inst. of Phys., New York). Stacey, F.D., et al., 1986, University of Queensland Report: Geophysics and the Law of Gravity, Rev. Mod, Phys., to be published. Stacey, F.D., 1987, in [Moriond 1987]. Suzuki, M., Phys. Rev. Lelt. 56, 1339. Thieberger, P., 1986, Phys. Rev. Lett. 56, 2347. Thieberger, P., 1987, in: [Moriond 1987]. Thodberg, H.H., 1986, Phys. Rev. Lett. 56, 2423.

Chapter 12 Abbott, L.F. and P. Sikivie, 1983, Phys. Lett. B120. 133. Ahten, S.F., et al,, 1986, Harvard-Smithsonian Center for Astrophysics, preprint no. 2292. Alcock, C. and E. Farhi, 1985, Phys. Rev. D32, 1273. Alcock, C., et al., 1986, Phys. Rev. Lett. 57, 2088. Auriemma, G., et al,, 1985, INFN (Rome) Report no, 447. Avignone, FT., et al., 1986, SLAC-PUB-3872. Bardeen, WA., 1986, MPI (Munich) Report MPI/PTH56/86. Bergstrom, L. and H. Snellman, 1986, University of Stockholm Report no, TRITA-TFY-86-09. Bjorken, iD. and L.D. McLerran, 1979, Phys. Rev. D20, 2353. Blumenthal, G.R., et al., 1984, Nature 311, 517. Cabibbo, N., et al. 1981, Phys. Lett, BiOS, 155. Cabibbo, N. and L. Maiani, 1982, Phys. Lett, B114, 115. Cabrera, B., et al., 1985, Phys. Rev, Lett. 55, 25. CaIdwell, DO., 1987, in: [Moriond 1987]. CaIdwell, JAR. and iF. Ostriker, 1981, Ap. J. 251, 61. Campbell, BA., et at., 1986, Phys. Lett, B173. 270. Caplin, D., 1987, in: [Moriond 19871. Chasman, C., et al., 1965, Phys. Rev, Lett. 15, 245. Coron, N., et al,, 1985, Nature 314, 75. Coron, N., 1987, in: [Moriond 1987]. DeGrand, T., et al., 1986, Phys. Rev. D33, 910. Dc Rujuta, A. and S.L. Glashow, 1980, Phys. Rev, Lett. 45, 942. Dc Rujula, A. and S.L. Glashow, 1984, Nature 312, 734. Dimopoulos, S., et al., 1986, Phys. Lett, B168, 145. Dine, M. and W. Fischler, 1983, Phys. Lett, B120, 137. Dolgov, AD. and Ya.B, Zeldovich, 1981, Rev, Mod, Phys. 53, 1. Drukier, A. and L. Stodotsky, 1984, Phys. Rev. D30, 2295. Drukier, AK., et at., 1986, Phys. Rev. D33, 3495. Ellis, i. et al, 1984, NucI. Phys. B238, 453. Faber, SM. and J.S. Gallagher, 1979, Ann, Rev. Astron, Astrophysics 17, 135. Farhi, E. and R.L. Jaffe, 1984, Phys. Rev, D30, 2379. Farhi, E. and R.L. Jaffe, 1985, Phys. Rev. D32, 2452.

J.

Rich et a!., Experimental particle physics without accelerators

361

Farhi, E. and R.L. Jaffe, 1986, Phys. Rev, D32, 2452. Farhi, E., 1986, Comments NucI, Part. Phys. 16, 289. Fiorini, E. and TO. Niinikoski, 1984, NucI. Inst. and Meth, in Phys. Res, 224, 83. Freese, K., 1986, Phys. Lett. B167, 295. Gaisser, T.K., et al., 1986, Phys. Rev. D34, 2206. Gotdberg, H. and Li. Hall, 1986, Phys. Lett. B174, 151. Goodman, MW. and E. Witten, 1985, Phys. Rev, D31, 3059. Gunn, J.E., et at., 1978, Ap. J. 223, 1015. Hagetin, J.S., et al., 1984, NucI. Phys. B241, 638. Hagelmn, J.S., et al., 1986, University of Minnesota preprmnt UMN-TH-566/86. Hagelin, iS. and G.L. Kane, 1986, Nuel, Phys. B263, 399. Haines, Ti., et a!., 1986, Phys. Rev, Lett, 57, 1986. Halzen, F. and H.C. Liu, 1985, Phys. Rev. D32, 1716. Ibanez, L.E., 1984, Phys. Lett, B137, 160. Ipser, i. and P. Sikivie, 1983, Phys. Rev, Lett. 50, 925. Kane, G.L. and I. Kani, 1986, NucI, Phys. B277, 525. Kephart, T.W. and T.J. Weiler, 1987, Phys. Rev. Lett. 58, 171. Keyes, R.W., 1986, Phys. Rev, Lett. 57, 648. Krauss, L., et at., 1985, Phys. Rev, Lett. 55, 1797. Krauss, L.M., et al., 1986, Phys. Rev. D33, 2079. Kuznick, B., 1987, in: [Moriond 1987]. Langacker, P., et al., 1983, Phys. Rev. D27, 1228. Le Gros, M., et al., 1986, to be published in IEEE-NS. LoSecco, J.M., 1987, in: [Moriond 1987]. Maalampi, i., et at., 1986, Phys. Rev, Lett. 56, 1031. Madsen, i., et al., 1986, Phys. Rev. D34, 2947. Moriond, 1987, Search for New and Exotic Phenomena, ed. J. Tran Thanh Van, to be published. Morris, D.E., 1984, Lawrence Berkeley Lab report LBL-17915. Nakamura, K., et al., 1985, Phys. Lett. B161, 417. Olive, K.A. and D.N. Schramm, 1985, Comments Nuct. Part. Phys. 15, 69. Olive, K.A. and J. Silk, 1985, Phys. Rev. Lett. 55, 2362. Pagets, HR., 1985, Comments Nuct, Part, Phys. 14, 289. Pantziris, A. and K. Kang, 1986, Phys. Rev, D33, 3509. Peccei, RD. and HR. Quinn, 1977, Phys. Rev. Lett. 38, 1440. Preskill, i., et at., 1983, Phys. Lett. B120, 127. Pretzl, K., 1987, in: [Moriond 1987]. Primack, JR., 1984, SLAC-PUB-3387. Raffelt, G.G., 1986a, Phys. Lett. B166, 402. Raffett, G.G., 1986b, Phys. Rev. D33, 897. Raffelt, G.G., 1986c, Phys. Rev. D34, 3927. Rudaz, S., 1986, Phys. Rev. Lett. 56, 2128. Sadoulet, 1987, in: [Moriond 1987]. Sandage, A. and GA. Tammann, 1983, in: Proc. first ESO-CERN Symp., eds. G. Setti and L. Van Hove. Sikivie, P., 1983, Phys. Rev. Lett. 51, 1415. Sikivie, P., 1984, Phys. Rev. Lett. 52, 695. Sikivie, P., 1985, Phys. Rev. D32, 2988. Sikivie, P., 1987, in: [Moriond 1987]. Silk, i. and M. Srednicki, 1984, Phys. Rev. Lett. 53, 624. Silk, i., et al., 1985, Phys. Rev, Lett. 55, 257. Stonczewski, iC., 1985, Phys. Rev. D32, 3338. Smith, P.F. and iD. Lewin, 1985, Acta Physica Polonica B16, 837. Smith, P.F., 1986a, in: Cosmology, Astronomy, and Fundamental Physics (ESO, Garching, March 1986); and Rutherford-Appleton Lab report RAL-86-029. Smith, P.F., 1986b, Z. Phys. C 31, 265. Smith, P.F., 1987, in: [Moriond 1987]. Spergel, D.N. and W.H. Press, 1985, Ap. i. 294, 663. Spiro, M., 1987, in: Search for New and Exotic Phenomenon, ed. J. Tran Thanh Van [Moriond1987] to be published. Srednicki, M., 1985, Nuel. Phys. B260, 689.

362

J. Rich ci al.. Experimental particle physics without accelerators

Srednicki, M.. Ct al., 1986, Phys. Rev. Lett. 56, 263. Srednicki. M., et al., 1987, NucI. Phys. B279, 804. Sleeker. F.W. and Q. Shafi. 1983. Phys. Res. Lctt. 50, 921. Stecker, F.W., et al., 1985, Phys. Rev. Lett. 55, 2622. Stecker. F.W.. 1986. Phys. Rev. Lett. 56, 255! and accompanying response of Olive and Silk. Steigman. 0.. 1979. Ann. Rev. Nuel. Part. Sc). 29. 313. Steigman, G.. et al.. 1978. Astron. J. 83. 1050. Tremaine, S. and i.E. Gunn. 1979, Phys. Rev. Lett. 42. 41)7. Tupper, 0.. Ct al.. 1987. Phys. Rev. D35. 394. Turner. MS.. 1986a. Phys. Rev, D33. 889. Turner, MS.. 1986b. Phys. Rev. D34. 192!. Wasserman, 1.. 1986, Phys. Rev. D33. 2071. Weiler, T., 1982, Phys. Rev. Lett. 49. 234. Weinberg, 5.. 1978, Phys. Rev. Lett. 40. 223. Wilczek, F., 1978. Phys. Rev. Lett. 40. 279. Wilczek. F., 1984. in: TASI Lectures in Elementary Particle Physics (TASI publIcations, Ann Arbor). Witten, E.. 1984, Phys. Rev. D30. 272. Wolfram. 5.. 1979, Phys. Lett. B82. 65. Yang, J., et al., 1984, Ap. J. 281. 493. Zehnder, A., 1983. SIN Report No. PR-83.03.

Notes added in proof 1. Neutrinos The observation of ~ from the supernova SN1987a by the Kamiokande [Hirata et al. 1987] and 1MB [Bionata et a!. 1987] experiments has provided information about the mass and lifetime of the mass eigenstates forming i~.The arrival at earth of large numbers of i~implies that at least one neutrino mass eigenstate that couples strongly to electrons has rim> i03 yr MeV - , This rules out the neutrino decay explanation of the solar-neutrino problem unless there is a large mixing angle for two mass eigenstates forming v~.Furthermore, several people (e.g. Bahcall and Glashow [1987], Arnett and Rosner [1987], and Roos [1987]) have pointed out that the observation by Kamiokande of eight neutrinos of differing energies over a period of 2 sec places constraints on the mass the dominant component of ~e’ For a given neutrino mass, the emission time of each observed i~can be calculated (since its energy is measured). If the i~’~ had a mass of 20 eV (as suggested by the experiment of Boris et a!. [19851),the emission times of the eight neutrinos would have been spread out over 14 see, and their near coincidence on Earth would be an accident. While such a conspiracy cannot be ruled out, it seems rather implausible. Requiring that the transit-time difference due to the mass do not compress the length of the neutrino pulse by more than a factor of two, Bahcall and Glashow report that the Kamiokande data require m < 11 eV. The solar MSW effect for three neutrino species has been studied by Toshev [1987]; Kim and Sze [1987]; Kim, Nussinov and Sze [1987]; and Baldini and Giudice [1987]. The implications of the MSW solution to the solar neutrino problem for seesaw mass generation schemes have been discussed by Langacker, Petcov, Steigman and Toshev [1987]; Kang and Shin [19871;and Langacker, Peccei and Yanagida [1986]. The 1MB experiment has published a study of the MSW effect using cosmic-ray neutrinos [LoSecco et a!. 1987a]. Their data rule out sin22O >0.08 for ~m2 i0~eV2. Evidence for the double43 decay of 76Ge with the emission of a majoron has been reported by Avignone et a!. [1987]. The data of Caidwell et a!. [1987],coming from a similar germanium-crystal spectrometer, do not support this claim. -~

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2. Neutrons The Leningrad group [Altarev et al. 1986] has published a tantalizing value for the neutron 25cm. Bigi and electric-dipole moment that is 2.3 standard deviations from zero: = (—1.4 ±0.6) X 10 Sanda [1987]have discussed the theoretical significance of a non-zero value of this magnitude. 3. Time variation of the fundamental constants Barrow [1987]has placed limits on the rate of change of extra spatial dimensions in Kaluza—Klein and superString theories by considering some of the prehistoric processes discussed in chapter 6. 4. Heavy particles bound in nuclei Norman, Gazes and Bennett [1987]have searched for heavy X particles bound in iron nuclei using methods similar to those of Turkevich et al. [19841.Their limits are near 10t2 X per nucleon. They point out that iron is a good place to look for heavy X if the particles have been processed in stars. 5. Galactic dark matter. The 1MB collaboration [LoSecco et al. 1987b] has published limits on the flux of high energy neutrinos from the annihilation of dark matter particles trapped in the Sun. Ng et al. [1986] have concluded that these limits cannot be used to eliminate photinos as dark matter candidates, primarily because of uncertainties in the local density of halo particles. The theoretical evaporation and annihilation rates of massive weakly-interacting particles in the Sun have been studied by Griest and Secke! [1987]and by Gould [1987]. Drukier [1987]has presented some design considerations for cryogenic detectors of cold dark matter candidates.

References Attarev, IS., et al., 1986, Lett. JETP 44 (8), 360—362. Arnett, W.D. and iL. Rosner, 1987, Phys. Rev, Lett. 58, 1906. Avignone, FT., et at., 1987, University of South Carolina preprint. Bahcall, iN. and S.L. Glashow, 1987, Nature 326, 476. Baldini, A. and G.F. Giudice, 1987, Phys. Lett. B186, 211. Barrow, iD., 1987, Phys. Rev. D35, 1805. Bigi, 1.1. and Al. Sanda, 1987, Phys. Rev, Lett. 58, 1604. Bionata, R.M., et at., 1987, Phys. Rev, Lett, 58, 1494. Boris, S., et al., 1985, Phys. Lett. B159, 217. Catdwell, DO., et al., 1987, in: Searches for New and Exotic Phenomena, ed, i. Tran Thanh Van, to be published. Drukier, AK., 1987, Inst. for Adv, Study preprint, submitted to Noel. Inst. and Meth. Gould, A., 1987, SLAC-PUB-4162, submitted to Astrophysical Journal. Grlest, K. and D. Seckel, 1987, NucI. Phys. B283, 681. Hirata, K., et al., 1987, Phys. Rev. Lett. 58, 1490. Kang, K. and M. Shin, 1987, Phys. Lett, B185, 163. Kim C.W. and W.K. Sze, 1987, Phys. Rev, D35, 1404. Kim C.W., S. Nussinov and W.K. Sze, 1987, Phys. Lett. B184, 403. Langacker, P., RD. Peccei and T. Yanagida, 1986, DESY 86—141. Langacker, P., ST. Petcov, G. Steigman and S. Toshev, 1987, NucI. Phys. B282, 589. LoSecco, J.M., et al,, 1987a, Phys. Lett. B184, 305. .

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J. Rich ci a!.. Experimental particle physics without accelerator,s

LoSecco, J.M., et a!., 1987b, Phys. Lett. B188. 388. Mg. K.-W., et a!.. 1986, University of Minnesota preprint UMN-TH-589/86. Norman. E.B.. SB. Gazes and D.A. Bennett. 1987. Phys. Rev. Lett. 58, 1403. Roos, M., 1987, University of Helsinki preprint HU-TFT-87-10. Toshev, S., 1987, Phys. Lett. B185, 177. Turkevich. A.. et al.. 1984. Phys. Rev. D30, 1406.