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Ultrahigh energy neutrino interactions
Nuclear Physics B (Proc. Suppl.) 14A (1990) 105-113 North-Holland
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G.Domokos, B.Elliott, S.Kovesi-Domokos and S.Mrenna Department of Physics and Astronomy, The Johns Hopkins University. Baltimore, MD. 21218. Ultrahigh energy neutrinos are valuable probes of physics beyond the Standard Model. Neutrinos of the highest energies are emitted by point sources in the sky . We review briefly the predictions of the Standard Model concerning neutrino interactions. We further argue that a number of preon models designed to overcome some difficulties of the Standard Model leads to a blurring of the distinction between leptons and quarks. As a consequence, at sufficiently high energies neutrinos acquire "anomalous" interactions . While this phenomenon can probably explain the observed muon excess in extensive air showers (EAS), it can be also tested by studying the absorption of the primaries on the cosmic microwave background . We discuss some observations to be performed in the search of such "new physics" beyond the Standard Model. 1. INTRODUCTION. Neutrinos are remarkable because, at least within the framework of the Standard Model, they Hence they possess only weak interactions. constitute the cleanest probes of the structure of elementary particles . In addition, due to their small masses and the weakness of their interaction , neutrinos are extremely penetrating particles capable of carrying information about rapidly varying phenomena. (At energies substantially lower than the masses of the weak gauge Bosons, their interaction cross sectrion increases linearly with the incident energy.) Hence they play an number of' astrophysical important role in a processes and can carry messages from those parts of the universe which would be otherwise For this reason, inaccessible to observation . detectors like GRANDE will play an important role in the emerging science of neutrino astronomy . Typically, neutrino astronomy utilizes relatively low energy neutrinos, simply, because in any
0920-5632/90/$03 .50 © Elsevier Science Publishers R .V . (North-Holland)
astrophysical process those are more abundant. Often, the kinematics of the process imposes a sharp cutoff on the neutrino energy, e.g. in rections taking place in our sun . At other ,locations, e.g. in an X-ray binary, the neutrino spectrum can be approximated by a power law with an exponent around 2 (hence, the exponent of the integral spectrum is around -1)1. At low energies, the event rate observed between energies El and E2 is roughly proportional to lnE2/E1, but it begins to drop with the energy once the CMS energy comes close to the gauge Boson mass. Therefore, in this energy range the best way of doing neutrino astronomy is to use the Earth as a filter in order to reduce background and this is what is being planned at GRANDE . However, at CMS energies around a TeV, the situation becomes more complicated even is the fundamental physics remains to be described by the Standard Model. The interaction of photons becomes, likewise, more complicated around such energies, purely because of phenomena present already in the Standard Model. We are not going
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to discuss photons here: Francis Halzen describes those calculations. It is perhaps less often emphasized that, in addition to doing neutrino astronomy with detectors like GRANDE, one also gains an opportunity to do particle physics with 7 and v beams by observing the interactions at the highest energies . While one may resent doing particle physics with as erratic a source as CYG X3 for example, the reality is that no terrestrial facilities are being planned in which v or -y interactions can be studied at CMS energies of several TeV. Therefore, one either gives up experimentation in this energy range or builds better detectors to observe the interactions of extraterrestrial photons and neutrinos . In the next Section, we briefly review high energy neutrino interactions whithin the framework of the Standard Model (SM). Thereafter, we show how a fairly general class of models which goes beyond the Standard Model can give rise to some interesting new phenomena in high energy neutrino physics. In Sec .4 we discuss the question of using the cosmic microwave background to filter out photons coming from point sources . Sec . 5 contains the conclusions. ENERGY NEUTRINO INTERACTIONS STANDARD MODEL . A number of authors has been dealing with the problem of high energy v interactions in matter3 . All the results available are based on leading order perturbation theory in the fine structure constant, cr, but some nonperturbative features are incorporated in the properties of nucleon structure functions3. The process all authors in ref.3 are interested in, is of the type v+Q-" 1+X, where Q is some quark inside the target nucleon . The lepton (1) emerges from a vWl or vZl vertex
and thus it is either a charged lepton of the same generation as v or its charged counterpart . The final state X emerges from the effective vertex, [Q (gauge Boson) X], which is determined, to a large extent, by strong interaction physics . The quantity relevant to most of the questions discussed at this meeting is the total cross section of the process just mentioned . By a straightforward application of the elementary "cutting rules", one realizes that at(ON) (or its Pomeranchuk-conjugate4) can be expressed a&the total cross sections of the virtual processes, W + Q and Z + Q, respectively and in terms of some perturbative vertices and propagators. This spells trouble: total cross sections of anything (W, Z, 'Y, .. .) on Q cannot be computed perturbatively : a total cross section involves all distance scales, not only the shortest ones accessible to perturbative calculations. The practical question is, of ,course, whether we should distrust the perturbative estimates given by the authors listed in ref. 3. Fortunately, the answer is that "naive" perturbative estimates of the total cross section can be trusted up to about EL N 1021 eV or so : it is at those energies that the perturbative estimates are coming close to the bounds set by unitarity: see, e.g. the results of Quigg and Reno, ref. 3. (The inadequacy of perturbation theory is manifested in the growth rate of perturbatively computed total cross sections : one verifies without any difficulty that they grow faster than (In s )2 at infinity, see ref-3, thus violating the Froissart bound. (For purists' sake, we remark that this assertion is in no contradiction with the renormalizability of the theory : the amplitudes of the elementary processes are well behaved : the trouble arises when the former are folded in with the semiphenomenological structure functions .) In the same spirit, one can trust the perturbative estimate of the interaction mean free
G. Domokos et al./ Ultrahigh energy neutrino interactions path (mfp) of neutrinos or antineutrinos up to about the same energy. One finds that the mfp of vN interactions becomes of the order of the Earth's diameter around EL ~ 1015 eV. Thus, the standard technique of looking for neutrinos coming from underfoot in search of new phenomena may well become useless at about the energy region where the real fun is expected to begin. (One should remember that a PeV in the lab . system corresponds to about a TeV in the CMS ; one expects that the mechanism responsible for the breaking of the elctroweak gauge symmetry and, hence, for the mass generation of quarks, leptons, etc. will reveal itself around this energy.) There is very little one can do about this. From the theoretical point of view, the result is practically unassailable : it is well within the energy region where perturbation theory can be trusted . (The uncertainty arising from one's imprecise knowledge of the nucleon structure functions is unlikely to affect the results substantially.) From the experimental point of view, it requires some rethinking of the ways one would like to detect new reactions induced by cosmic v beams. In particular, one has to reassess the usefulness of looking towards the center of the Earth in search of "new physics" or UHE v sources in the sky . We have no good solution to the problem to offer: we do believe, however, that the problem deserves a very serious consideration by all those involved. Perhaps looking "sideways" will help, but one has to make sure that enough of the absorber is left in order to filter out atmospheric neutrinos . This is a quantitative question and the appropriate calculations will have to be done before the new detectors become operational . As a last item in the review of the SM predictions, let us mention that the calculations reported in zef. 3 verify Pomeranchuk's theorem : if
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one superimposes neutrino and antinentrino cross sections, as computed, e.g. by Quigg and Reno, ref. 3, their ratio is found to be very dose to unity. This is, of course, expected : after all, Pomeranchuk's theorem states that the ratio of Pomeranchuk-conjugate cross sections tends to unity at infinite energy. While one is not surprised at finding the theorem verified in perturbation theory, the rapid onset of "asymptopia" is both pleasing and practically important. (Roughly speaking, one can save about 50% of a computation of cross sections by invoking Pomeranchuk's theorem.) 3. NEW PHYSICS AT A TeV? Speculations abound about the onset of some kind of "new physics" at CMS energies of the order of a TeV . We mentioned already in the previous Sections that most of these speculations are concerned either with the symmetry breaking mechanism of the electroweak symmetry or with questions not addressed within the framework of the SM, such as the question of generations . It is impossible to review all the various attempts in this direction within the space available. Let us, all of them were designed to however, mention that cure two unsatisfactory features of the SM: i) The symmetry breaking sector of the SM as proposed by the "founding fathers" in terms of an elementary Higgs field is very sick. First of all, Wilson has shown rather long ago that a 94 theory in four dimensions does not exist: the renormalized coupling vanishes5. It is not clear what happens if tl.^ Higgs field is coupled to other fields (as it is the case in the Ski), but even if the extra couplings invalidate the "no-minteraction" result, the theory is badly behaved due to its quadratic divergences : it is very sensitive to the choice of its input parameters. This is
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the infamous "fine tuning problem": it has been reviewed by Jackiw in a volume on dynamical symmetry breakinge . ii) The SM, strictly speaking, has no room for a family structure of quarks and leptons . The families are put in by hand, the mass matrix is largely arbitrary and, hence the model contains an undesirably large number of input parameters . Yet, in most theorists' opinion, the existence of families is an important clue from Nature and it should not be ignored. There have been many cures proposed for the ailments of the SM; neither one of them is entirely convincing or spectacularly successful. There are several broad categories into which the proposed cures fall. Some of them postulate the existence of new Fermion generations with their uew kind of gauge interactions (technicolor theories, see the volume quoted in ref. 6). Other theories propose that the presently seen quarks and leptons are not the ultimate elementary Fermions used by Nature as building blocks of the observed particles : these are, broadly speaking, the preon models ; they, at least, offer the hope of understanding the family problem together with the problem of symmetry breaking, whereas technicolor theories, typically, ire concerned with problem i) only; for a review, see, e.g. ref. 7. [It seems that superstring theories, even if they are combined with some phenomenological assumptions, are not quite capable (yet) to make predictions in this energy range.] Whatever the solution to the problems of the SM, it is fairly clear that "something new" will be srien around CMS energies of the order of a TeV. There is a (very old) and fairly modelindependent way of estimating this; the method has been applied to the problem at hand by Appelquist and Chanowitz8. Briefly, the method in the present
context requires adding explicit symmetry breaking terms to a low energy effective Lagrangian. Such a theory violates unitarity : by computing some elastic partial wave amplitude, it grows with energy too rapidly. One can estimate the characteristic energy associated with the onset of the "new physics" by determining the CMS energy at which the unitarity bound on the amplitude is violated. Depending on the process considered, one gets different estimates, of course. However, under reasonable assumptions about the top mass, etc. one invariably ends up in the range of a few TeV . [If you think that this is a very poor way of doing physics, try to compute some low-J amplitude of, say, ve -+ ve in the old V-A theory and determine some average mass of W and Z from the energy where the amplitude hits the unitarity bound . In this case we already know the answer, so the computation serves as a useful check of the method.] This sounds like a very nice theoretical speculation, but do we have some experimental Present and future hadronic handle on it? machines (TEVATRON, SSC) are nice, but dirty: typically one is swamped with soft QCD processes, like the production of low-PT pious, etc. (The
discovery of the weak gauge Bosons at the CERN collider was made possible by the fact that one could make relatively reliable theoretical production rates and predictions about distributions.) In this case, we are less lucky : there is no trustworthy theory around, so one needs guidance from experiments . Clearly, LEP2 and HERA will be of some help, but not quite adequate as far as the available energy is concerned . As we indicated previously, one can hope to perform semileptonic experiments by utilizing point sources in the sky. This is very different from the particle physics we are used to in the second half of this century :
G. Domokos et al./ Ultrahigh energy neutrino interactions the particles we are likely to observe have been emitted some 104 years ago or more (depending on which source we consider) ; hence, no experimental group has a chance to ask for a pure -f or pure v beam or for a tuning of the accelerator . However, the situation is a lot better than it was in the forties, when "particle physics" was identical with "cos-mic ray physics". Thanks to modern detection techniques, it is now possible to focus on point sources, thus to reduce the omnipresent "soft" background by narrowing acceptance, using the time structure of the source, etc. How can we hope to discover some "new physics" by such means? In order to aid the imagination, in the papers of ref.9 we created some "strawmen", which, we hope, reflect some of the features of the predictions of a better theory yet to be constructed. First of all, we have to worry about the conservation of probability . Assume that we believe that a process explains a given experimental result . Given the primary and the target, we have to determine the fraction of events in which we see the new phenomenon. Let the cross section of the new process be Ao,, whereas the total cross section of the known ("uninteresting") processes is Q. Then the fraction, F, of "interesting" events at a given energy is obviously given by the formula: F = 00,/(0' + Oa) . (1) interactions of To quote an example, consider photons with air nuclei. Here, a is dominated by electron pair production, so in the atmosphere, x--500 mb. Let Ao stand for the enhancement in the photoproduction cross section, see Francis Halzen's talk at this meetings. If we want to make roughly every other EAS muon rich, i.e. F_0.5, this means that we have to crank up the photoproduction cross section to something like 35 mb/nucleon, compared to = 0.1 mb/nucleon,
observed at presently available energies. Jordan Goodman reported at this meetinglo that the CYGNUS collaboration finds the average muon contents of an EAS associated with a point source like CYG X3 or HER X1, roughly equal to that of a hadron induced shower at CMS energies of the order of 2 TeV. Assuming (as in ref.2) that all those showers are induced, one needs photoproduction cross sections much larger than 35 mb/nucleon! This example illustrates that probability conservation imposes nontrivial constraints on proposed theoretical schemes. In ref. 9 we proposed a mechanism for detecting a composite structure of leptons and quarks whithin the framework of a "generic" preon model. Our main point was that, in the spirit of eq .(1), one should look for new processes in channels where the competition from processes already contained in the SM is minimal . Neutrino-4nduced reactions come to mind naturally, cf. Sec. 1. What came as a surprise was the fact that some of the processes which are likely to be allowed by a class of reasonable preon models can also lead to a natural explanation of the muon excess in EAS associated with point sources. Whithout going into technical details, the basic idea of the papers in ref. 9 is easy to describe. Consider vAnduced reactions: competition from reactions allowed by the SM is negligible. If all leptons and quarks are composite objects, leptons will contain some constituents carrying color (i.e. the charges associated with the gauge group of strong interactions). Although leptons are overall colorless, if we probe them at short distances, we should be able to detect this hidden color. We argued previously that the characteristic energy scale of the "new physics", fl, should be of the order of 1 TeV. Therefore, we have to probe neutrinos at distances N1/A . Fig .1 shows a sketch of such a process. An incident neutrino exchanges a
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oup of colored preons with the target quark (heavy wavy line in Fig .1), while emitting an observed particle (e.g. a muon) of large transverse moment
explain a part of the muon excess observed in EAS: one expects the jet emerging from the hard preon-quark interaction to have essentially the same characteristic as any ordinary hadronic jet . "Hard" interactions of neutrinos at sufficiently high energies resemble hadronic interactions. The important point to emphasize is that the discovery of a phenomenon of this type, with A=1 TeV, is almost impossible by means of terrestrial facilities: cosmic ray particle physics has the leading edge in this area.
FIGURE 1. Sketch of a z.-induced process with the exchange of colored preons.
4. PeV ABSORPTION SPECTOSCOPY. One of the problems associated with doing utilizing "he:,vertly particle physics the accelerators" is that the beam is, not pure: presumably, we are getting a mixture of 7 and v primaries"; at low energies, the photons are absorbed more efficiently at the source, so the neutrino intensity is considerably higher . At higher energies, however, if the neutrino cross section increases as we conjectured in the preceding Section, the neutrinos also suffer from the absorption at the source . As a rough guess, we can put the high energy fluxes equal at the highest energies . If one were convinced that neutrino interactions are entirely governed by the SM, the question of separating primaries would be a moot one: for all practical purposes, the interaction mfp of neutrinos in the atmosphere is infinite as compared to photons . If, however, neutrinos begin to interact strongly at some characteristic energy, it is a task of some importance to determine whether or not a certain fraction of the observed EAS is induced by neutrinos . The only way this can be done in a modelindependent way is by studying the absorption characteristics of the source on the microwave background . Neutrinos, for all practical purposes, do not interact with the background,
In an inclusive reaction one sums over the components of the jet emitted in the preon-quark interaction ; thus, the entire inclusive cross section is proportional to the total preon--quark interaction, see Fig .2.
FIGURE 2. The inclusive cross section is proportional to the total preon-quark cross section. e estimated the magnitude of the preon-quark cross scetion and found that, contrary to naive dimensional analysis, that cross section can be quite substantial; on can take typically 10% of some hadronic cross section as a first guess . This mechanism, if its existence is verified by further theoretical investigation, is capable, in principle, to
G. Domokos et al./ Ultrahigh energy neutrino interactions whereas the absorption of photons has been calculated by a number of authors . The modern computational procedure is described by Protheroela, where references to earlier works can be found . Basically, the absorption due to pair production has a broad maximum around E = 2 PeV ; there the absorption mfp is approximately 6 kpc. From the point of view of the physics involved, the only important thing to keep in mind is that all the physics involved is very standard: in fact, the thermal average of the CMS energy is around a few MeV . Nobody expects any trouble with QED or weak interactions in that energy range. Thus, absorption on the microwave background is a reliable tool: it allows to study new physics by using very reliable "old physics" only. The disadvantage of the technique is that absorption is almost totally negligible outside of the energy interval,l PeV < E <3 PeV . However, we have no other absorber between a celestial source and a detector, so we have to live with what we have. The objective of the following considerations is to create a PeV absorption spectroscopy routine: we suggest that a number of sources be analyzed by using the same procedure . It is in this way only that one will be able to extract some useful physics information from a set of sparse data samples . Given a set ofobservations of some source, we propose that the absorption on the microwave background be characterized in terms of a single parameter, the apparent distance of the source . henceforth denoted by d . Assuming that all primaries emitted by a given celestial source are photons, d provides a good measure of the absorption on the microwave background . (In fact, if we knew for sure that nothing but photons are emitted by a given source, the distance measured at
a few PeV would be a lot more reliable than the one determined from the absorption at 21 cm. Paradoxically, we know a lot more about the microwave background than we know about the distribution of, say, intergalactic Hydrogen...) As it is, however, a particle physicist has to accept a standard of distance to a given source, determin by some, supposedly reliable, method, e.g. by absorption at A = 21 cm. We call this the "true distance" to the source, d. Given d and assuming that d is determined from a fit to high energy EAS data, one has to consider the following possibilities. 1) One finds d# = d. This means "no news": all primaries are photons . 2) The result of the analysis is d* < d. This is the physically interesting case: it indicates that not all primaries are absorbed by the microwave background. 3) An analysis resulting in d > d would indicate an inconsistency in the fitting procedure. It has to be remarked that the distance determination is rather sensitive to the temperature used. However, small errors in the value of the temperature can be easily corrected; one has to remember that d is, in essence, determined by the data points near the absorption maximum. Keeping this in mind, one finds that if öT is the error we committed in the value of the temperature, the resulting error 6d in the apparent distance is given by the approximate formula: öd*/d# N - 38T/T. Assuming that one found d < d, one can approximately determine the interaction cross section near the absorption maximum, Eo = 2 PeV. (For the sake of definiteness, we assume that the non absorbed component is made up of neutrinos.) It is easily shown that a., the interaction cross section of neutrinos on nucleons is given by the formula,
G. Domok-os et a!./ Ultrahigh energy neutrino interactions jirV =
P Cr7 [
*/L -
. /L]/A
Here A stands for the effective atomic number of air, L for the absorption mfp ar Bo and Q for the 7
total cross section of photons in air. The quantity R is the ratio of the fiuxx of photons to that of neutrinos at the source . Assuming an analysis according to the SM, 1ne gets R to be substantially less than unity; R=Q.2 is not an unreasonable estimate, see Todor Stanevlz computations 13. If, hwvever, neutrinos begin to interact strongly, they are also absorbed on the material around a source and R gets closer to unity. In order to illustrate the procedure, we analyzed all the available high energy data, (E>1TeV) on CVG X3. Somewhat to our surprise, we found''-4 a rather small apparent distance, d -6kpc. Fig.3 exhibits our results in the energy region where absorption is substantial. The best fit
1
FIGURE 3. Data points on CYG X3 around lfeV primary energy, together with various fits. from which the apparent distance was determined is
given by the upper dashed line, while the fit with a true distance of 12kpc is given by the lower dashed line. (Using the true distance gives a likelihood ratio of v1074with respect to the best fit.) The solid lines show the results of the fits with some simplified modeïs . The upper solid curve gives the result for a neutrino component interacting with ov 6mb and characteristic energy A=1TeV. The model corresponding to the lower solid curve is of the type as described by F. Halzen at this meeting2. It is obvious from the Figure that at least some non absorbed component is needed in order to achieve a good fit. Details of the procedure are described in ref. 14. It appears that the data exhibit another anomaly besides the muon excess in EAS . We believe that both anomalies are connected with each other and both can be explained by the onset of a new regime of interactions . However, similar analyses should be carried out on other sources as well before the case for strongly interacting neutrinos (or some other type of new phenomenon) becomes a convincing one. 5. DISCUSSION. In discussing neutrino interactions, we have concentrated upon the particle physics aspects of this topic . Apart from these authors , personal prejudices, we have done so because neutrino astronomy is much written about these days. By contrast, doing particle physics with cosmic rays (with the help of the much improved techniques which became availabe during this decade) is stil in its infancy . We hope to have demonstrated that there are questions of particle physics for which the answers are likely to come from experiments done with high energy neutrino beams . Since such beams will not be available at terrestrial accelerators in
G. Domokos et al./ Ultrahigh energy neutrino interactions the foreseeable suture, we have to rely upon cosmic neutrino beams. Clearly, the outstanding questions include a separation of photon and neutrino induced showers when point sources are looked at. Ideally, one would like to do this on a shower-by shover basis ; however, this requires much more theoretical work and a considerable improvement of the experimental techniques. Without pretending to be original, we wish to emphasize that a new generation of detectors will clearly bring us closer to the the goal of doing modern particle physics by using extraterrestrial primary particles . ACKNOWLEDGEMENT . Two of us (G.D. and S.K.D.) would like to thank the organizers, particularly Gaurang Yodh and Don Wold, for the opportunity of discussing important physics in a very pleasant atmosphere provided by this workshop. We also thank Sophia K. Domokos for her help in drawing the Figures . This research was supported in part by the U.S. Energy under Grant Department of No. DE-FG02A5ER40211 . REFERENCES. 1 . See, for instance, R.J. Protheroe, Rapporteur talk in Proc. Twentieth ICRC, Moscow, USSR, 1987. Edited by V.A. Kozyarivsky et al. Nauka, Moscow, 1987. 2. F. Halzen, these Proceedings and references quoted there. 3. D.W. McKay and J.P. Ralston, Phys . Lett. 167B (1986) 103 . C. Quigg, M.H. Reno and T.P. Walker, Phys . Rev. Lett. 57 (1986) 774 . T.K . Gaisser and A.F. Grillo, Phys. Rev . D36 (19870 2752. M.H. Reno and C. Quigg, Phys. Rev. D37 (1988) 657.
4. See e.g. A.D. Martin and T .D. S "Elementary Particle Theory", (American Elsevier, New York, 1970). Ch. 6. 5. K.G. Wilson in "Phase Transition and Criti Phenomena", Edited by C. Domb and J.L. Lebowitz. (Academic Press, New York, 1976). Vol. 6. 6. R. Jackiw, in "Dynamical Gauge Symmetry Breaking", Edited by E. Farhi and R. Ja (World Scientific, Singapore, 1982.) 7. H. Harari, in "Fundamental Forces", i,lited by D. Frame and K.J. Peach. (SUSSP, Edinburgh University, Edinburgh, 1985.) 8. T. Appelquist and M.S. Chanowitz, Phys. Rev. Letters 59 (1987) 2405. 9. G. Domokos and S. Nussinov, Phys . Letters (1987) 372, G. Domokos and S. Kovesi-Domokos, Phys. Rev. D38 (1988) 2833. 10. J. Goodman, these Proceedings . 11. T.K . Gaisser, in "Accretion Processes in Astrophysics", Edited by J. Audouze and J . Tran Thanh Van . (Editions Frontieres, Gif-surYvette, 1986.) 12. R.J. Protheroe, Mon. Not. Roy . Astr. Soc . 22 1 (1986) 769 . 13. T. Stanev, these Proceedings. 14. G. Domokos, B. Elliott, S. KovesiDomokos and S. Mrenna, Johns. Hopkins University preprint, JHUTIPAC 8901 (1989) .
(This paper was presented E-mail : SKD@JHUP .BITNET; phone: (301) 338 7377.)
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G.Domokos, B.Elliott, S.Kovesi-Domokos and S.Mrenna Department of Physics and Astronomy, The Johns Hopkins University. Baltimore, MD. 21218. Ultrahigh energy neutrinos are valuable probes of physics beyond the Standard Model. Neutrinos of the highest energies are emitted by point sources in the sky . We review briefly the predictions of the Standard Model concerning neutrino interactions. We further argue that a number of preon models designed to overcome some difficulties of the Standard Model leads to a blurring of the distinction between leptons and quarks. As a consequence, at sufficiently high energies neutrinos acquire "anomalous" interactions . While this phenomenon can probably explain the observed muon excess in extensive air showers (EAS), it can be also tested by studying the absorption of the primaries on the cosmic microwave background . We discuss some observations to be performed in the search of such "new physics" beyond the Standard Model. 1. INTRODUCTION. Neutrinos are remarkable because, at least within the framework of the Standard Model, they Hence they possess only weak interactions. constitute the cleanest probes of the structure of elementary particles . In addition, due to their small masses and the weakness of their interaction , neutrinos are extremely penetrating particles capable of carrying information about rapidly varying phenomena. (At energies substantially lower than the masses of the weak gauge Bosons, their interaction cross sectrion increases linearly with the incident energy.) Hence they play an number of' astrophysical important role in a processes and can carry messages from those parts of the universe which would be otherwise For this reason, inaccessible to observation . detectors like GRANDE will play an important role in the emerging science of neutrino astronomy . Typically, neutrino astronomy utilizes relatively low energy neutrinos, simply, because in any
0920-5632/90/$03 .50 © Elsevier Science Publishers R .V . (North-Holland)
astrophysical process those are more abundant. Often, the kinematics of the process imposes a sharp cutoff on the neutrino energy, e.g. in rections taking place in our sun . At other ,locations, e.g. in an X-ray binary, the neutrino spectrum can be approximated by a power law with an exponent around 2 (hence, the exponent of the integral spectrum is around -1)1. At low energies, the event rate observed between energies El and E2 is roughly proportional to lnE2/E1, but it begins to drop with the energy once the CMS energy comes close to the gauge Boson mass. Therefore, in this energy range the best way of doing neutrino astronomy is to use the Earth as a filter in order to reduce background and this is what is being planned at GRANDE . However, at CMS energies around a TeV, the situation becomes more complicated even is the fundamental physics remains to be described by the Standard Model. The interaction of photons becomes, likewise, more complicated around such energies, purely because of phenomena present already in the Standard Model. We are not going
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to discuss photons here: Francis Halzen describes those calculations. It is perhaps less often emphasized that, in addition to doing neutrino astronomy with detectors like GRANDE, one also gains an opportunity to do particle physics with 7 and v beams by observing the interactions at the highest energies . While one may resent doing particle physics with as erratic a source as CYG X3 for example, the reality is that no terrestrial facilities are being planned in which v or -y interactions can be studied at CMS energies of several TeV. Therefore, one either gives up experimentation in this energy range or builds better detectors to observe the interactions of extraterrestrial photons and neutrinos . In the next Section, we briefly review high energy neutrino interactions whithin the framework of the Standard Model (SM). Thereafter, we show how a fairly general class of models which goes beyond the Standard Model can give rise to some interesting new phenomena in high energy neutrino physics. In Sec .4 we discuss the question of using the cosmic microwave background to filter out photons coming from point sources . Sec . 5 contains the conclusions. ENERGY NEUTRINO INTERACTIONS STANDARD MODEL . A number of authors has been dealing with the problem of high energy v interactions in matter3 . All the results available are based on leading order perturbation theory in the fine structure constant, cr, but some nonperturbative features are incorporated in the properties of nucleon structure functions3. The process all authors in ref.3 are interested in, is of the type v+Q-" 1+X, where Q is some quark inside the target nucleon . The lepton (1) emerges from a vWl or vZl vertex
and thus it is either a charged lepton of the same generation as v or its charged counterpart . The final state X emerges from the effective vertex, [Q (gauge Boson) X], which is determined, to a large extent, by strong interaction physics . The quantity relevant to most of the questions discussed at this meeting is the total cross section of the process just mentioned . By a straightforward application of the elementary "cutting rules", one realizes that at(ON) (or its Pomeranchuk-conjugate4) can be expressed a&the total cross sections of the virtual processes, W + Q and Z + Q, respectively and in terms of some perturbative vertices and propagators. This spells trouble: total cross sections of anything (W, Z, 'Y, .. .) on Q cannot be computed perturbatively : a total cross section involves all distance scales, not only the shortest ones accessible to perturbative calculations. The practical question is, of ,course, whether we should distrust the perturbative estimates given by the authors listed in ref. 3. Fortunately, the answer is that "naive" perturbative estimates of the total cross section can be trusted up to about EL N 1021 eV or so : it is at those energies that the perturbative estimates are coming close to the bounds set by unitarity: see, e.g. the results of Quigg and Reno, ref. 3. (The inadequacy of perturbation theory is manifested in the growth rate of perturbatively computed total cross sections : one verifies without any difficulty that they grow faster than (In s )2 at infinity, see ref-3, thus violating the Froissart bound. (For purists' sake, we remark that this assertion is in no contradiction with the renormalizability of the theory : the amplitudes of the elementary processes are well behaved : the trouble arises when the former are folded in with the semiphenomenological structure functions .) In the same spirit, one can trust the perturbative estimate of the interaction mean free
G. Domokos et al./ Ultrahigh energy neutrino interactions path (mfp) of neutrinos or antineutrinos up to about the same energy. One finds that the mfp of vN interactions becomes of the order of the Earth's diameter around EL ~ 1015 eV. Thus, the standard technique of looking for neutrinos coming from underfoot in search of new phenomena may well become useless at about the energy region where the real fun is expected to begin. (One should remember that a PeV in the lab . system corresponds to about a TeV in the CMS ; one expects that the mechanism responsible for the breaking of the elctroweak gauge symmetry and, hence, for the mass generation of quarks, leptons, etc. will reveal itself around this energy.) There is very little one can do about this. From the theoretical point of view, the result is practically unassailable : it is well within the energy region where perturbation theory can be trusted . (The uncertainty arising from one's imprecise knowledge of the nucleon structure functions is unlikely to affect the results substantially.) From the experimental point of view, it requires some rethinking of the ways one would like to detect new reactions induced by cosmic v beams. In particular, one has to reassess the usefulness of looking towards the center of the Earth in search of "new physics" or UHE v sources in the sky . We have no good solution to the problem to offer: we do believe, however, that the problem deserves a very serious consideration by all those involved. Perhaps looking "sideways" will help, but one has to make sure that enough of the absorber is left in order to filter out atmospheric neutrinos . This is a quantitative question and the appropriate calculations will have to be done before the new detectors become operational . As a last item in the review of the SM predictions, let us mention that the calculations reported in zef. 3 verify Pomeranchuk's theorem : if
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one superimposes neutrino and antinentrino cross sections, as computed, e.g. by Quigg and Reno, ref. 3, their ratio is found to be very dose to unity. This is, of course, expected : after all, Pomeranchuk's theorem states that the ratio of Pomeranchuk-conjugate cross sections tends to unity at infinite energy. While one is not surprised at finding the theorem verified in perturbation theory, the rapid onset of "asymptopia" is both pleasing and practically important. (Roughly speaking, one can save about 50% of a computation of cross sections by invoking Pomeranchuk's theorem.) 3. NEW PHYSICS AT A TeV? Speculations abound about the onset of some kind of "new physics" at CMS energies of the order of a TeV . We mentioned already in the previous Sections that most of these speculations are concerned either with the symmetry breaking mechanism of the electroweak symmetry or with questions not addressed within the framework of the SM, such as the question of generations . It is impossible to review all the various attempts in this direction within the space available. Let us, all of them were designed to however, mention that cure two unsatisfactory features of the SM: i) The symmetry breaking sector of the SM as proposed by the "founding fathers" in terms of an elementary Higgs field is very sick. First of all, Wilson has shown rather long ago that a 94 theory in four dimensions does not exist: the renormalized coupling vanishes5. It is not clear what happens if tl.^ Higgs field is coupled to other fields (as it is the case in the Ski), but even if the extra couplings invalidate the "no-minteraction" result, the theory is badly behaved due to its quadratic divergences : it is very sensitive to the choice of its input parameters. This is
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the infamous "fine tuning problem": it has been reviewed by Jackiw in a volume on dynamical symmetry breakinge . ii) The SM, strictly speaking, has no room for a family structure of quarks and leptons . The families are put in by hand, the mass matrix is largely arbitrary and, hence the model contains an undesirably large number of input parameters . Yet, in most theorists' opinion, the existence of families is an important clue from Nature and it should not be ignored. There have been many cures proposed for the ailments of the SM; neither one of them is entirely convincing or spectacularly successful. There are several broad categories into which the proposed cures fall. Some of them postulate the existence of new Fermion generations with their uew kind of gauge interactions (technicolor theories, see the volume quoted in ref. 6). Other theories propose that the presently seen quarks and leptons are not the ultimate elementary Fermions used by Nature as building blocks of the observed particles : these are, broadly speaking, the preon models ; they, at least, offer the hope of understanding the family problem together with the problem of symmetry breaking, whereas technicolor theories, typically, ire concerned with problem i) only; for a review, see, e.g. ref. 7. [It seems that superstring theories, even if they are combined with some phenomenological assumptions, are not quite capable (yet) to make predictions in this energy range.] Whatever the solution to the problems of the SM, it is fairly clear that "something new" will be srien around CMS energies of the order of a TeV. There is a (very old) and fairly modelindependent way of estimating this; the method has been applied to the problem at hand by Appelquist and Chanowitz8. Briefly, the method in the present
context requires adding explicit symmetry breaking terms to a low energy effective Lagrangian. Such a theory violates unitarity : by computing some elastic partial wave amplitude, it grows with energy too rapidly. One can estimate the characteristic energy associated with the onset of the "new physics" by determining the CMS energy at which the unitarity bound on the amplitude is violated. Depending on the process considered, one gets different estimates, of course. However, under reasonable assumptions about the top mass, etc. one invariably ends up in the range of a few TeV . [If you think that this is a very poor way of doing physics, try to compute some low-J amplitude of, say, ve -+ ve in the old V-A theory and determine some average mass of W and Z from the energy where the amplitude hits the unitarity bound . In this case we already know the answer, so the computation serves as a useful check of the method.] This sounds like a very nice theoretical speculation, but do we have some experimental Present and future hadronic handle on it? machines (TEVATRON, SSC) are nice, but dirty: typically one is swamped with soft QCD processes, like the production of low-PT pious, etc. (The
discovery of the weak gauge Bosons at the CERN collider was made possible by the fact that one could make relatively reliable theoretical production rates and predictions about distributions.) In this case, we are less lucky : there is no trustworthy theory around, so one needs guidance from experiments . Clearly, LEP2 and HERA will be of some help, but not quite adequate as far as the available energy is concerned . As we indicated previously, one can hope to perform semileptonic experiments by utilizing point sources in the sky. This is very different from the particle physics we are used to in the second half of this century :
G. Domokos et al./ Ultrahigh energy neutrino interactions the particles we are likely to observe have been emitted some 104 years ago or more (depending on which source we consider) ; hence, no experimental group has a chance to ask for a pure -f or pure v beam or for a tuning of the accelerator . However, the situation is a lot better than it was in the forties, when "particle physics" was identical with "cos-mic ray physics". Thanks to modern detection techniques, it is now possible to focus on point sources, thus to reduce the omnipresent "soft" background by narrowing acceptance, using the time structure of the source, etc. How can we hope to discover some "new physics" by such means? In order to aid the imagination, in the papers of ref.9 we created some "strawmen", which, we hope, reflect some of the features of the predictions of a better theory yet to be constructed. First of all, we have to worry about the conservation of probability . Assume that we believe that a process explains a given experimental result . Given the primary and the target, we have to determine the fraction of events in which we see the new phenomenon. Let the cross section of the new process be Ao,, whereas the total cross section of the known ("uninteresting") processes is Q. Then the fraction, F, of "interesting" events at a given energy is obviously given by the formula: F = 00,/(0' + Oa) . (1) interactions of To quote an example, consider photons with air nuclei. Here, a is dominated by electron pair production, so in the atmosphere, x--500 mb. Let Ao stand for the enhancement in the photoproduction cross section, see Francis Halzen's talk at this meetings. If we want to make roughly every other EAS muon rich, i.e. F_0.5, this means that we have to crank up the photoproduction cross section to something like 35 mb/nucleon, compared to = 0.1 mb/nucleon,
observed at presently available energies. Jordan Goodman reported at this meetinglo that the CYGNUS collaboration finds the average muon contents of an EAS associated with a point source like CYG X3 or HER X1, roughly equal to that of a hadron induced shower at CMS energies of the order of 2 TeV. Assuming (as in ref.2) that all those showers are induced, one needs photoproduction cross sections much larger than 35 mb/nucleon! This example illustrates that probability conservation imposes nontrivial constraints on proposed theoretical schemes. In ref. 9 we proposed a mechanism for detecting a composite structure of leptons and quarks whithin the framework of a "generic" preon model. Our main point was that, in the spirit of eq .(1), one should look for new processes in channels where the competition from processes already contained in the SM is minimal . Neutrino-4nduced reactions come to mind naturally, cf. Sec. 1. What came as a surprise was the fact that some of the processes which are likely to be allowed by a class of reasonable preon models can also lead to a natural explanation of the muon excess in EAS associated with point sources. Whithout going into technical details, the basic idea of the papers in ref. 9 is easy to describe. Consider vAnduced reactions: competition from reactions allowed by the SM is negligible. If all leptons and quarks are composite objects, leptons will contain some constituents carrying color (i.e. the charges associated with the gauge group of strong interactions). Although leptons are overall colorless, if we probe them at short distances, we should be able to detect this hidden color. We argued previously that the characteristic energy scale of the "new physics", fl, should be of the order of 1 TeV. Therefore, we have to probe neutrinos at distances N1/A . Fig .1 shows a sketch of such a process. An incident neutrino exchanges a
G. Domokos et al./ Ultrahigh
--energy neutrino interactions
oup of colored preons with the target quark (heavy wavy line in Fig .1), while emitting an observed particle (e.g. a muon) of large transverse moment
explain a part of the muon excess observed in EAS: one expects the jet emerging from the hard preon-quark interaction to have essentially the same characteristic as any ordinary hadronic jet . "Hard" interactions of neutrinos at sufficiently high energies resemble hadronic interactions. The important point to emphasize is that the discovery of a phenomenon of this type, with A=1 TeV, is almost impossible by means of terrestrial facilities: cosmic ray particle physics has the leading edge in this area.
FIGURE 1. Sketch of a z.-induced process with the exchange of colored preons.
4. PeV ABSORPTION SPECTOSCOPY. One of the problems associated with doing utilizing "he:,vertly particle physics the accelerators" is that the beam is, not pure: presumably, we are getting a mixture of 7 and v primaries"; at low energies, the photons are absorbed more efficiently at the source, so the neutrino intensity is considerably higher . At higher energies, however, if the neutrino cross section increases as we conjectured in the preceding Section, the neutrinos also suffer from the absorption at the source . As a rough guess, we can put the high energy fluxes equal at the highest energies . If one were convinced that neutrino interactions are entirely governed by the SM, the question of separating primaries would be a moot one: for all practical purposes, the interaction mfp of neutrinos in the atmosphere is infinite as compared to photons . If, however, neutrinos begin to interact strongly at some characteristic energy, it is a task of some importance to determine whether or not a certain fraction of the observed EAS is induced by neutrinos . The only way this can be done in a modelindependent way is by studying the absorption characteristics of the source on the microwave background . Neutrinos, for all practical purposes, do not interact with the background,
In an inclusive reaction one sums over the components of the jet emitted in the preon-quark interaction ; thus, the entire inclusive cross section is proportional to the total preon--quark interaction, see Fig .2.
FIGURE 2. The inclusive cross section is proportional to the total preon-quark cross section. e estimated the magnitude of the preon-quark cross scetion and found that, contrary to naive dimensional analysis, that cross section can be quite substantial; on can take typically 10% of some hadronic cross section as a first guess . This mechanism, if its existence is verified by further theoretical investigation, is capable, in principle, to
G. Domokos et al./ Ultrahigh energy neutrino interactions whereas the absorption of photons has been calculated by a number of authors . The modern computational procedure is described by Protheroela, where references to earlier works can be found . Basically, the absorption due to pair production has a broad maximum around E = 2 PeV ; there the absorption mfp is approximately 6 kpc. From the point of view of the physics involved, the only important thing to keep in mind is that all the physics involved is very standard: in fact, the thermal average of the CMS energy is around a few MeV . Nobody expects any trouble with QED or weak interactions in that energy range. Thus, absorption on the microwave background is a reliable tool: it allows to study new physics by using very reliable "old physics" only. The disadvantage of the technique is that absorption is almost totally negligible outside of the energy interval,l PeV < E <3 PeV . However, we have no other absorber between a celestial source and a detector, so we have to live with what we have. The objective of the following considerations is to create a PeV absorption spectroscopy routine: we suggest that a number of sources be analyzed by using the same procedure . It is in this way only that one will be able to extract some useful physics information from a set of sparse data samples . Given a set ofobservations of some source, we propose that the absorption on the microwave background be characterized in terms of a single parameter, the apparent distance of the source . henceforth denoted by d . Assuming that all primaries emitted by a given celestial source are photons, d provides a good measure of the absorption on the microwave background . (In fact, if we knew for sure that nothing but photons are emitted by a given source, the distance measured at
a few PeV would be a lot more reliable than the one determined from the absorption at 21 cm. Paradoxically, we know a lot more about the microwave background than we know about the distribution of, say, intergalactic Hydrogen...) As it is, however, a particle physicist has to accept a standard of distance to a given source, determin by some, supposedly reliable, method, e.g. by absorption at A = 21 cm. We call this the "true distance" to the source, d. Given d and assuming that d is determined from a fit to high energy EAS data, one has to consider the following possibilities. 1) One finds d# = d. This means "no news": all primaries are photons . 2) The result of the analysis is d* < d. This is the physically interesting case: it indicates that not all primaries are absorbed by the microwave background. 3) An analysis resulting in d > d would indicate an inconsistency in the fitting procedure. It has to be remarked that the distance determination is rather sensitive to the temperature used. However, small errors in the value of the temperature can be easily corrected; one has to remember that d is, in essence, determined by the data points near the absorption maximum. Keeping this in mind, one finds that if öT is the error we committed in the value of the temperature, the resulting error 6d in the apparent distance is given by the approximate formula: öd*/d# N - 38T/T. Assuming that one found d < d, one can approximately determine the interaction cross section near the absorption maximum, Eo = 2 PeV. (For the sake of definiteness, we assume that the non absorbed component is made up of neutrinos.) It is easily shown that a., the interaction cross section of neutrinos on nucleons is given by the formula,
G. Domok-os et a!./ Ultrahigh energy neutrino interactions jirV =
P Cr7 [
*/L -
. /L]/A
Here A stands for the effective atomic number of air, L for the absorption mfp ar Bo and Q for the 7
total cross section of photons in air. The quantity R is the ratio of the fiuxx of photons to that of neutrinos at the source . Assuming an analysis according to the SM, 1ne gets R to be substantially less than unity; R=Q.2 is not an unreasonable estimate, see Todor Stanevlz computations 13. If, hwvever, neutrinos begin to interact strongly, they are also absorbed on the material around a source and R gets closer to unity. In order to illustrate the procedure, we analyzed all the available high energy data, (E>1TeV) on CVG X3. Somewhat to our surprise, we found''-4 a rather small apparent distance, d -6kpc. Fig.3 exhibits our results in the energy region where absorption is substantial. The best fit
1
FIGURE 3. Data points on CYG X3 around lfeV primary energy, together with various fits. from which the apparent distance was determined is
given by the upper dashed line, while the fit with a true distance of 12kpc is given by the lower dashed line. (Using the true distance gives a likelihood ratio of v1074with respect to the best fit.) The solid lines show the results of the fits with some simplified modeïs . The upper solid curve gives the result for a neutrino component interacting with ov 6mb and characteristic energy A=1TeV. The model corresponding to the lower solid curve is of the type as described by F. Halzen at this meeting2. It is obvious from the Figure that at least some non absorbed component is needed in order to achieve a good fit. Details of the procedure are described in ref. 14. It appears that the data exhibit another anomaly besides the muon excess in EAS . We believe that both anomalies are connected with each other and both can be explained by the onset of a new regime of interactions . However, similar analyses should be carried out on other sources as well before the case for strongly interacting neutrinos (or some other type of new phenomenon) becomes a convincing one. 5. DISCUSSION. In discussing neutrino interactions, we have concentrated upon the particle physics aspects of this topic . Apart from these authors , personal prejudices, we have done so because neutrino astronomy is much written about these days. By contrast, doing particle physics with cosmic rays (with the help of the much improved techniques which became availabe during this decade) is stil in its infancy . We hope to have demonstrated that there are questions of particle physics for which the answers are likely to come from experiments done with high energy neutrino beams . Since such beams will not be available at terrestrial accelerators in
G. Domokos et al./ Ultrahigh energy neutrino interactions the foreseeable suture, we have to rely upon cosmic neutrino beams. Clearly, the outstanding questions include a separation of photon and neutrino induced showers when point sources are looked at. Ideally, one would like to do this on a shower-by shover basis ; however, this requires much more theoretical work and a considerable improvement of the experimental techniques. Without pretending to be original, we wish to emphasize that a new generation of detectors will clearly bring us closer to the the goal of doing modern particle physics by using extraterrestrial primary particles . ACKNOWLEDGEMENT . Two of us (G.D. and S.K.D.) would like to thank the organizers, particularly Gaurang Yodh and Don Wold, for the opportunity of discussing important physics in a very pleasant atmosphere provided by this workshop. We also thank Sophia K. Domokos for her help in drawing the Figures . This research was supported in part by the U.S. Energy under Grant Department of No. DE-FG02A5ER40211 . REFERENCES. 1 . See, for instance, R.J. Protheroe, Rapporteur talk in Proc. Twentieth ICRC, Moscow, USSR, 1987. Edited by V.A. Kozyarivsky et al. Nauka, Moscow, 1987. 2. F. Halzen, these Proceedings and references quoted there. 3. D.W. McKay and J.P. Ralston, Phys . Lett. 167B (1986) 103 . C. Quigg, M.H. Reno and T.P. Walker, Phys . Rev. Lett. 57 (1986) 774 . T.K . Gaisser and A.F. Grillo, Phys. Rev . D36 (19870 2752. M.H. Reno and C. Quigg, Phys. Rev. D37 (1988) 657.
4. See e.g. A.D. Martin and T .D. S "Elementary Particle Theory", (American Elsevier, New York, 1970). Ch. 6. 5. K.G. Wilson in "Phase Transition and Criti Phenomena", Edited by C. Domb and J.L. Lebowitz. (Academic Press, New York, 1976). Vol. 6. 6. R. Jackiw, in "Dynamical Gauge Symmetry Breaking", Edited by E. Farhi and R. Ja (World Scientific, Singapore, 1982.) 7. H. Harari, in "Fundamental Forces", i,lited by D. Frame and K.J. Peach. (SUSSP, Edinburgh University, Edinburgh, 1985.) 8. T. Appelquist and M.S. Chanowitz, Phys. Rev. Letters 59 (1987) 2405. 9. G. Domokos and S. Nussinov, Phys . Letters (1987) 372, G. Domokos and S. Kovesi-Domokos, Phys. Rev. D38 (1988) 2833. 10. J. Goodman, these Proceedings . 11. T.K . Gaisser, in "Accretion Processes in Astrophysics", Edited by J. Audouze and J . Tran Thanh Van . (Editions Frontieres, Gif-surYvette, 1986.) 12. R.J. Protheroe, Mon. Not. Roy . Astr. Soc . 22 1 (1986) 769 . 13. T. Stanev, these Proceedings. 14. G. Domokos, B. Elliott, S. KovesiDomokos and S. Mrenna, Johns. Hopkins University preprint, JHUTIPAC 8901 (1989) .
(This paper was presented E-mail : SKD@JHUP .BITNET; phone: (301) 338 7377.)
by
G.Domokos,