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If “charm” particles exist, can they be detected?
Nuclear Physics B55 ( 1 9 7 3 ) 4 4 5 - 4 5 4 . North-Holland Publishing Company
IF " C H A R M " P A R T I C L E S EXIST, C A N T H E Y BE D E T E C T E D ? G.A. SNOW * Laboratoire de Physique Theorique et Hautes Energies, Paris ** Received 27 December 1972 (Revised 21 February 1973)
Abstract: Arguments are presented in favor of the existence of " c h a r m " particles, that is, hadronic states not classifiable in the usual three-quark model of Gellmann and Zweig. The three-triplet scheme of Han-Nambu is the most promising but, far from unique, theoretical structure for such particles. Assuming, for any of these models, that the charm quantum number is conserved in strong and electromagnetic interactions, but not in weak interactions, limits are deduced from past experiments on the possible minimum mass of charm particles and the maximum charm-changing four-fermion coupling constant. Finally several possible experimental methods of searching for charm particles are discussed. Unfortunately none are certain to discover them even if they do exist with masses less than a few GeV.
1. Introduction The recent onset of experiments with accelerators in a new energy range has stimulated theoretical discussion about how to search for many new kinds of particles, including quarks [1], magnetic monopoles [2], heavy leptons [3], heavy vector mesons [4], high-spin isomers [5], and so on. The purpose of this note is to discuss experimental methods to search for another possible, but as yet undiscovered, class of particles which we shall call *** "charm" particles [6-8]. By a charm particle we mean any hadron whose values of isospin and hypercharge are incompatible with the usual SU(3)scheme.We shall assume that it will be classifiable, at least approxi-
* On sabbatical leave from the University of Maryland, College Park, supported in part by the US Atomic Energy Commision. ** Postal address: Tour 16 - ler 6t. Universitd Paris VI, 4 Place Jussieu, 75230 Paris Cedex 05, France. *** The word " c h a r m " originated in a paper by Bjorken and Glashow (ref. [6 ]) to describe non-SU(3) particles in an SU(4) classification scheme for hadrons. It has also been used in the context of the three-triplet model by Han and Nambu (ref. [7]) and by Pati and Woo (ref. [8]). We follow their usage. Thus, the discussion of charm particles in this paper does not include states which are sometimes "also called charmed, but in the notation of ref. [8] are called particles of zero charm which are not singlets in SU(3). These states can be produced singly in electromagnetic processes.
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G.A. Snow, "Charm"particles
mately, in some larger group structure than SU(3) that contains at least one new additive quantum number (beyond 13 and Y) called charm. Granting the existence of such particles with masses higher that the well-known, low-lying nonet mesons and octet or decuplet baryons, it is necessary to consider what kinds of experiments could look for them and what limits can be set on their properties if such experiments yield no positive result. These questions can only be answered within the framework of theoretical models that are far from being uniquely specified. One such model, that we find intriguing enough to use as our basic guide, is a version of the three-triplet model of Han and Nambu [7]. The possible existence of stable or semi-stable "charm" particles in threetriplet models has already been incisively discussed by Pati and Woo [81. This note is meant to extend that work so as to bring those ideas closer to the testing point in the laboratory. We first give some general arguments as to why one might expect the existence of a larger hadronic spectrum than that based on the three quarks *. This is followed by a discussion of the possible decay properties o f " c h a r m " particles. The most promising production reactions are then listed. These considerations are then combined in an analysis of the prospects for finding "charm" particles with the newer accelerators, given that they have not been found with proton or electron accelerators below 30 GeV.
2. Why " c h a r m " particles? (1) There has never been compelling theoretical arguments to explain why the approximate hadronic symmetry group should be SU(3); rather the argument has been almost entirely an empirical one [9]. (2) The simple, three-quark model of Gell-Man and Zweig, which would exclude the existence of "charnl" particles, has several difficulties: (a) The spin -1 quarks violate the Pauli principle in the strikingly successful SU(6) classification of the baryon octet and decuplet multiplets. (b) As shown by Adler [10] and Okubo [11], the simple three-quark model does not give the correct value for the ~z0 -+ 3'3' transition probability. (c) The upper limits to the abundances of fractionally charged particles to be found at accelerators, in cosmic rays, on land, in the sea or on the moon are very lOW. (3) The recent attempts by Weinberg [12], Salam [13] and others, to construct a unified renormalizable theory of weak and electromagnetic interactions, when extended to include hadrons, all seem to require that the number of basic fermion constituents be larger than three in order to remove unphysical neutral currents or to remove theoretically damaging Adler-type anomalies [14]. * Vivid arguments along these same lines are given by tf.J. Lipkin in the Proc. of the Irvine Conf., 1971 and in ref. [15].
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447
The attractiveness of the Han-Nambu three-triplet model is that it overcomes at one blow, the three difficulties (2a, b, c) of the three-quark model given above. The (56) representation for low-lying baryons is compatible with the Pauli principle for zero orbital angular momentum states of the quark. The predicted 7r0 ~ 77 amplitude is correct, and all the unsuccessful but rigorous, searches for fractionally charged particles are irrelevant since the nine quarks in this scheme all have integral charge, namely [8] ( - 1 ) 2, (0) 5, (+1) 2. (Of course no heavy integrally charged "quark" has been found either, but the limits are less significant and even the stability of such particles is not assured.) At least one unified weak and electromagnetic theory with Han-Nambu triplets has been recently shown to exist [15]. The three-triplet model has also been applied with reasonable success to a parton interpretation of deepinelastic electron and neutrino interactions [ 16]. In sum, it is a good model to take in considering the question of how to detect "charm" particles. It should be noted however that the experimental discussion given below for the case where charm is broken only by the weak interactions, applies to a much larger class of models than just the three-triplet model.
3. Decay of charm particles Having assumed an approximate hadron symmetry larger than that based on three quarks, there are two interesting yet fundamentally different choices that can be made for the decay properties of "charm" particles. These are: (i) "Charm" is not conserved by at least one of the two interactions medium strong and electromagnetic, nor by the weak interaction t . (ii) "Charm" is rigorously conserved in strong and electronragnetic interactions but not conserved in the weak interaction. Hypothesis (i) was favored by Nambu [7] in his original work on this subject. This hypothesis allows a single "charm" particle to couple strongly to conventional zero-charm particles, nucleons and mesons. Hence, experimentally, "charm" particles could manifest themselves as ordinary resonant states. The best way to look for the particles is then to search for exotic resonances like a Z* with quantum numbers B = +1, Y = +1. This search has been going on for many years with not very encouraging results to date. Five years ago Greenberg and Nelson [ 17] tried to fit a great many baryon resonances into the Han-Nambu scheme with hypothesis (i). They pinned their phenomenology on two, at that time, probable, Z* resonant states, plus the Roper resonance N(1470). More data has not confirmed the existence of these particular Z* states, and the electromagnetic properties of the N(1470) is not consistent with the three-triplet model assignment [ 18]. Furthermore, possible alterna-
t Models such as SU(4) in which the "charm" quantum number modifies the Gell-Mann-Nishijima formula relating Q to I3 and Y, are not of this type, but they can be of the type (ii), ref. [ 14 ]. The Han Nambu model retains the usual formula Q =/3 + ,~Y, so that it retains both option (i) and OiL ref. [8 ].
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G.A. Snow, "Charm" particles
tive theoretical explanations of the N(1470) within a conventional three-quark model have been given [19], so that the detailed level fitting of Greenberg and Nelson must be abandoned. This does not mean that Nambu's hypothesis is definitely ruled out, but rather that it has no empirical confirmation among the low-lying baryonic states, Since the simple three-quark model can tolerate baryon states in multiplets other than octets or decuplets by adding q ~ pairs to the qqq lowest configuration, the observation of a single Z* resonance does not resolve the issue. Only a detailed phenomenological classification of all observed resonances, such as was attempted by Greenberg and Nelson, can hope to shed light on the underlying hadronic symmetry. The opening up of new energy ranges is likely to have much less of an effect on this line of investigation than the increasing ability to collect and analyze massive statistics for all kinds of two-body and many-body reactions at energies below 30 GeV. Unusually narrow, high-mass resonances should be sought. Hypothesis (ii), in which charm is broken only by the weak interaction, presents a very different picture. The charm quantum number now acts like strangeness so that charm particles can be produced only in pairs via the strong or electromagnetic interactions. One presumes that the lightest charm particles will decay either nonleptonically into ordinary baryons and mesons, or leptonically into zero-charm hadrons plus an ev or/Jr pair. As the mass of the lightest charm particle increases the number of different final states increases very rapidly as does its total transition probability. For example there are eleven known S = 0 baryonic states with J ~< 23. below a mass of 2 GeV. If one assumes a charm-changing weak-interaction strength G c equal to G a s = l , then the lepton decay transition probability summed over these eleven final states is ~ 5 × 10 l0 sec - 1 ( ~ 8 0 % to neu). A 3 GeV charm particle will have a leptonic transition probability ~ 3 X 1012 s e c - l to the same eleven states ( ~ 40% to neu) t . Besides the large number of leptonic final states, there will be an even larger number of non-leptonic final states, such as charm particle -~ Nzr, N*Tr, N*ezr, etc. Unlike the hyperons with their special phase-space effects near threshold there is no reason to suppose that leptonic decays make up only a tiny fraction of non-leptonic decays of charm particles if their masses are >~ 2 GeV. It is more plausible to assume that the fraction of leptonic decays is in the 1 0 - 5 0 % range (not unlike the situation with intermediate vector mesons), ref. [3]. Furthermore there is no a priori compelling reason why the charm-changing weak-interaction coupling constant could not be much larger than the strangeness-changing coupling constant, in fact as large as GFerm i. One important experimental point is clear from this discussion: charm particles produced at high energy might be visible as decaying tracks, for example in a bubble chamber, if their masses were < 3 GeV and if G~xce 0 G G a s ~ O" For heavier particles, or larger coupling strengths, even 300 GeV protons could not produce chain1 particles with enough energy in the laboratory to go more than a fraction of a centimeter before decaying. [E.g. r c = 10-13 sec, 3,c =(Eo/Mc)=50 -~ 7cCrc = 0.15 cm]. The non-leptonic decay modes of a massive charm particle will f These estimates are made with all transition matrix elements set equal to one.
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be distributed over a very large array of states with relatively little concentration on transitions to two-body final states which are easiest to analyze.
4. Production of charm particles * The assumption of charm conservation in strong and electromagnetic interactions implies that charm particles must be produced in pairs except in high-energy neutrino interactions. Typical reactions to produce charmed baryons and mesons (B c and m c respectively) might be (la) P+P -+Bc + m c + a n y t h i n g , + B 'C + anything,
(lb)
O m c + m ' c + anything,
(lc)
~ B c + m c + anything,
(2a)
e - + e + -+mc + m c + anything,
(2b)
+ anything.
(3)
~B
7+p
u
#
+n
C
~/a-+B
c
Clearly as the minimum masses for Bc and m c go up the probability of having made these particles at the older accelerators goes down rapidly. Exactly how rapidly cannot be estimated precisely since reliable strong interaction dynamical models that including charm particles do not exist. However crude estimates can be made. For example for reaction ( l a ) one can use a simple model of diffraction dissociation such as that of Gottfried and Kofoed-Hansen [20]. In their model the differential cross section for making a mass M in the forward direction is approximately K(M-Mo)-2 exp ( - b ' l t l ) where b' ~ 5 GeV -1. To make charm particles the total mass in the diffraction blob must be larger than the sum of the masses of the lightest baryon and meson charm particles, Bc + m c. If we assume this number is ~> 4 GeV, then the cross section for charm particle production is very small for 30 GeV pp collisions but can be non-negligible at 200 GeV or higher. "Non-negligible" here means a cross section ~ 0.1 - 0.3% of the total cross section. Such an estimate implies a charm particle cross section between one and two orders of magnitude smaller than the associated production YK cross sections [21]. Other models and other regions of phase space can give much more pessimistic estimates for charm-particle production. For example if one makes a dual-model estimate of reaction ( l b ) or ( l c ) in the central region (x ~ 0), one expects [22] a factor exp ( - 4 p 2) or equivalently exp ( 4 M 2 ) , where M is the mass of B c or m c. For M ~ 2 GeV, this exponential is ~ 1 0 - 7. A similar pessimistic estimate would arise from a strict thermodynamic model a la Hagedorn. However we believe that the diffraction dissociation model estimate is the most reasonable one for the production of charm via strong interactions. Contin* A qualitatively similar discussion has been given by Glashow et al. [ 14].
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G.A. Snow, "Charm"particles
uing with our assumption that charm is strictly conserved in strong and electromagnetic interactions, one expects high-energy photoproduction cross sections of pairs of charm particles, to be smaller than the total photo-hadronic cross section by two or three orders of magnitude * [23] Let us now consider neutrino-production processes as in eq. (3). Tile high-energy cross section depends directly on the square of the ratio of coupling constants (;ACe-0/(;Fenni" The threshold is determined by the mass of the lightest charmed baryon, M(Bc). For neutrino energies, Ev, a few hundred MeV above M(Bc)--M(p), one could expect a total charm-particle cross section.
o(v +n ~ Bc +,u
, . , , , , ,,\ ' G 2 + a n y t h i n g ) ~ 0 . 5 ( E v E v t h r e ~ ' ° l d- ) /-- - ~ U ) X 10 3 8 c m(4) 2.
Whenever the charmed baryon decays promptly (~< 1 0 - I t see), and non-leptonically, there is no way for the neutrino experimentors to distinguish such an event from an ordinary deep inelastic neutrino event. However when Bc decays leptonically, the neutrino event becomes distinguishable from the usual inelastic event by the presence of two l e p t o n s A search for such events is similar but not identical to the search for intermediate vector bosons and heavy leptons. I have re-examined all published neutrino experiments at CERN and Brookhaven to determine what limits these set on the mass and coupling constant of charnmd baryons. It appears that the most sensitive experiment in this regard is the neutrino heavy liquid bubble chamber experiment carried out at CERN from 1963 to 1967, ref. [241. One can ask how many possible (/a, e) events there are, and compare this with the number of v events in which enough energy is transferred to the hadrons (v > Vmin) so as to be able to comfortably produce a charlned baryon of assumed massM(Bc). Table 1 shows the number of inelastic neutrino events (deduced from ref. [24d1) with hadronic energy, v, greater than various m i n i n m m values. These minilnum values correspond to 0.500 GeV above the energy needed to produce charmed baryons with M(Bc) = 2.0, 2.5 and 3.0 GeV respectively. An approximate calculation, integrating over the neutrino spectrum, converts these numbers to expected numbers of charmed particles produced assuming eq. (4) and GAC~O -- (;t.'enni (4th row of table 1). If one adopts a value for the branching ratio of Bc decay into electrons or positrons of 10% one gets the expected number of obsen, ed (/1 , e ±) events in the stone sample (row 5), with Gz~c~ O/(;Femil = 1. The actual number of ( ~ , e -+) candidates observed is 1 [24a, b ] Hence the 90% confidence limit for ((;AC~o/GF) at each mass value M(Bc) can be easily c~culated and is given in row 6 This CERN experiment is then compatible with the existence of charm particles in the mass range ~> 2 GeV and with a weak, charm-changing, coupling constant of the same order as the Fermi * Carlson and Freund have discussed tile possibility of detecting heavy vector mesons via photoproduction, where these vector mesons are related to qcqc states of charmed quarks, qc From the experiment',d point of view however, it is not easy to distinguish such objects, with their zero charm, from the expected higher mass vector mesons in conventional theories
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G.A. Snow. "Charm "particles
Table l Present limits from CERN neutrino experiment [24] on charm-changing weak-interaction coupling constant versus the mass of charmed baryon M(Bc) (see text for explanations) M(Bc) (GeV)
2.0
2.5
3.0
Neutrino threshold energy (GeV) Approx. minimum hadron excitation energy (GeV) Number of B.C. events Number of expected (~t, e) events from charm particles for GdxC4:0 = GF
1.86
3.14
4.64
90% upper limit for GAC¢O/GF
1.5 210
2.7 65
4.2 25
12.6
3.3
1.0
1.1
2.0
0.56
coupling constant. One can make similar analyses for double muon, neutrino events both in spark chambers and in bubble chambers. However, one find that none of the existing published experiments [25] give upper limits more restrictive than the (~t, e) search in the heavy liquid chamber. An analysis along these lines o f the current neutrino bubble chamber experiment at CERN can improve the statistical situation, perhaps by a significant factor.
5. Conclusions " I f charm particles exist, can they be detected?" The answer is - perhaps, but only with great difficulty. A search for two lepton events in higher energy neutrino experiments, such as those planned at NAL, could certainly improve the limits on GaC¢ o and M(Bc) given in table I. The background from n O induced electrons or positrons and decay muons from pions will probably determine the ultimate limit of this approach. Perhaps one can reach G a c ~ o ~ Gzxs¢ o" If in fact the charm-changing weak interaction is less than, or of the same order as, the strangeness-changing weak interaction, there is some small experimental hope in a completely different direction, namely to observe the path of a charmed particle before it decays. As long as the mass M(Bc) ~ 2.5 GeV the lifetime of Be could be long enough ( ~ 10 -12 sec), so that decay paths of 1 cm would not be hnprobable, when the gamma of the charmed particle were large compared to one. But this is just the condition that we expect to prevail when a pair of charmed particles are produced via diffraction. Therefore a very careful study of the vertices of high energy pp collisions, as can be done in the 30-inch bubble-chamber experiments at NAL, should be made, since this is one of the few practical ways to search for charmed particles t .
t Footnote: see next page.
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G.A. Snow, "Charm "particles
What about the more powerful electronic techniques that can handle enormously greater fluxes than can the bubble chambers? One possibility might be to exploit the leptonic decay modes of the charm particles, produced for example in pp collisions. This suggests a high energy experiment such as carried out by Wanderer et al. [26], at BNL with 30 GeV protons, in which one searches for nmons produced directly in a target, as distinguished from those from a decay region downstreanl from the target. In fact the unpublished data from that experiment, containing the number of directly produced muons of lower momenta than used in the W search, could provide interesting limits on the product of (production moss section) × (muonic decay rate) for charmed particles. Another interesting possibility would be to search for apparently directly produced leptons in pp collisions at the ISR over a large solid angle. The current large angle, large momentum transfer search for electrons, positrons and nmons [27] could only collect a very small fraction of the leptons from charmed particle decay, because the longitudinal m o m e n t u m of a charmed particle is large, and the typical transverse momentum of a decay lepton is modest ('~ 1 GeV). (As the massM(Bc) or M(mc) increases one expects that even the leptonic decays will be dominated, not by transitions to the ground state such as M(Bc) ~ n + ~ + v, but by transitions to excited states, such asM(Bc) ~ N* + ~ + v, since the number of these excited states increases rapidly with energy.) Again this charm particle detection method is severely limited by the secondary leptonic background from ordinary 7r and K production. Except for the actual path length observation method described above, all of the other methods hinge on detecting leptons from charmed particle decays. It is a severe challenge to devise an experiment to detect charmed particles via their non leptonic decay modes, given the expected characteristics of high mass, many decay channels and production in pairs via the strong interaction. If the mass of charmed particles were ~ 2 GeV, and their decay rates to leptons were very much smaller than to hadrons, then charm particles may be produced in appreciable abundance in high energy collisions without detection. Alongside the persistent searches for quarks, monopoles, intermediate vector mesons and heavy leptons, an intensive search for charm particles is necessary $ [28]. I would like to thank Professor D.H. Perkins and J. Mulvey of Oxford University for their interest and hospitality this past summer when this work was begun. I am + One might hope to have obtained a strict lifetime upper limit from a search of cosmic ray interactions in nuclear emulsions. Itowever the small number of carefully studied, very high energy cosmic ray events when combined with background difficulties, does not "allowan interesting limit to be deduced, l am indebted to Prof. D.H. Perkins for a pertinent discussion of this point. The statistic'a] difficulty could be overcome with an exposure of nuclear emulsion to 300 GeV protons at NAL. $ We have assumed throughout this article that charm particles are unstable with short lifetimes. Negative, long-lived, charm particles can only exist if their masses were greater than 3Mp due to the searches carried out at Serpukhov [28].
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also i n d e b t e d to m y colleagues at the L a b o r a t o i r e de P h y s i q u e T h e o r i q u e e t H a u t e s Energies and at the Ecole P o l y t e c h n i q u e for i n t e r e s t i n g discussions and t o Professors M. Levy, R. V i n h Man a n d B. G r e g o r y for their gracious h o s p i t a l i t y .
References [1] J. Sculli and T.O. While, Phys. Rev. Letters 27 (1971) 619. [21 J.L. Newmayer and J.S. Tref'fl, Phys. Letters 38B (1972) 524. ]3] M.L. Perl, SLAC-PUB 1062 (1972); Y.S. Tsai, Phys. Rev. D4 (1971) 2821; J.D. Bjorken and C.H. Llewellyn Smith, Phys. Rev. D7 (1973) 887. [4] T.D. Lee and C.N. Yang, Phys. Rev. 119 (1960) 1410; R.W. Brown and J. Smith, Phys. Rev. D3 (1971) 207. [5] B. Pontecorvo, Phys. Letters 39B (1972) 346. [6] J.D. Bjorken and S. Glashow, Phys. Letters 11 (1964) 255. [71 M. Han and Y. Nambu Phys. Rev. 139 (1965) B1006; Y. Nambu, in Preludes in theoretical physics, ed. A. de Shalit, H. Feshbach and L. Van Hove (North Holland, Amsterdam, 1966) p. 133. [8] J.C. Pati and C.H. Woo, Phys. Rev. D3 (1971) 1173. [91 L. O'Raifeartaigh, in Group theory and its applications, ed. M. Loebl (Academic Press, New York, 1968) p. 469. [10] S. Adler, Phys. Rev. 177 (1969) 2426. [11] S. Okubo, Phys. Rev. 179 (1969) 1629. [121 S. Weinberg, Phys. Rev. Letters 19 (1967) 1264; 27 (1971) 1688. [13] A. Salam, Elementary particle theory, ed. N. Svartholm (Almquist and Forlag, Stockholm, 1968) p. 367. [14] S.L. Glashow, J. lliopoulos and k. Maiani, Phys. Rev. D2 (1970) 1285; B. Zumino, Cargese Summer Institute July 1972, to be published (CERN Theory preprint 1550). [ 15] H. Georgi and S.L. Glashow, Harvard preprint (1972); H.J. Likpin, NAL-Thy-85 (1972) to be published in Phys. Rev.; R.N. Mohopatra, University of Maryland report 72- 022 (1972), to be published in Nuovo Cimento Letters. [ 16] R. Budny ct al., Nucl. Phys. B44 (1972) 618; H.J. Lipkin, Phys. Rev. Letters 28 (1972) 63; T.H. Chang and D.K. Chroudbury, Nuovo Cimento Letters 5 (1972) 727; M. Koca and M.S.K. Razmi, Trieste preprint IG/72/132 (1972). [ 17] O.W. Greenberg and C.A. Nelson, Phys. Rev. Letters 20 (1968) 604. [18] G. Karl and E. Obryk, Nucl. Phys. B6 (1968) 102. [ 19] Y.S. Kim and M.E. Noz, Nuovo Cimento 11A (1972) 313. [20] K. Gottfried and O. Kofoed-Hansen, Phys. Letters 41B (1972) 195. [2l] E.L. Berger et al., Phys. Rev. Letters 28 (1972) 322. [22] Chan-Li Jen, K. Kang et al., Ann. of Phys. 72 (1972) 548; R.C. Arnold and E.L. Berger, Phys. Rev. D5 (1972) 2733. [23] C.E. Carlson and P.G.O. Freund, Phys. Letters 39B (1972) 342. [241 (a) M.M. Bloch et al., Phys. Letters 12 (1964) 281; (b) G. Bernardini et al., Nuovo Cimento 38 (1966) 608; (c) 1. Budagov et al., Phys. Letters 30B (1969) 364; (d) G. Myatt and D.H. Perkins, Phys. Letters 34B (1971) 542.
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[25] G. Danby et al., Phys. Rev. Letters 9 (1962) 36; J.K. Bienlein et al., Phys. Letters 13 (1964) 80; R. Burns et al., Phys. Rev. Letters 15 (1965) 42. [26] P.J. Wanderer et al., Phys. Rev. Letters 23 (1969) 729. [27] Report of the Int. High Energy Physics Conference at Batavia, 1972, to be published. [28] Yu Antipov et al., NucL Phys. B31 (1971) 235; F. Binon et al., Phys. Rev. Letters 30B (1969) 510.
IF " C H A R M " P A R T I C L E S EXIST, C A N T H E Y BE D E T E C T E D ? G.A. SNOW * Laboratoire de Physique Theorique et Hautes Energies, Paris ** Received 27 December 1972 (Revised 21 February 1973)
Abstract: Arguments are presented in favor of the existence of " c h a r m " particles, that is, hadronic states not classifiable in the usual three-quark model of Gellmann and Zweig. The three-triplet scheme of Han-Nambu is the most promising but, far from unique, theoretical structure for such particles. Assuming, for any of these models, that the charm quantum number is conserved in strong and electromagnetic interactions, but not in weak interactions, limits are deduced from past experiments on the possible minimum mass of charm particles and the maximum charm-changing four-fermion coupling constant. Finally several possible experimental methods of searching for charm particles are discussed. Unfortunately none are certain to discover them even if they do exist with masses less than a few GeV.
1. Introduction The recent onset of experiments with accelerators in a new energy range has stimulated theoretical discussion about how to search for many new kinds of particles, including quarks [1], magnetic monopoles [2], heavy leptons [3], heavy vector mesons [4], high-spin isomers [5], and so on. The purpose of this note is to discuss experimental methods to search for another possible, but as yet undiscovered, class of particles which we shall call *** "charm" particles [6-8]. By a charm particle we mean any hadron whose values of isospin and hypercharge are incompatible with the usual SU(3)scheme.We shall assume that it will be classifiable, at least approxi-
* On sabbatical leave from the University of Maryland, College Park, supported in part by the US Atomic Energy Commision. ** Postal address: Tour 16 - ler 6t. Universitd Paris VI, 4 Place Jussieu, 75230 Paris Cedex 05, France. *** The word " c h a r m " originated in a paper by Bjorken and Glashow (ref. [6 ]) to describe non-SU(3) particles in an SU(4) classification scheme for hadrons. It has also been used in the context of the three-triplet model by Han and Nambu (ref. [7]) and by Pati and Woo (ref. [8]). We follow their usage. Thus, the discussion of charm particles in this paper does not include states which are sometimes "also called charmed, but in the notation of ref. [8] are called particles of zero charm which are not singlets in SU(3). These states can be produced singly in electromagnetic processes.
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G.A. Snow, "Charm"particles
mately, in some larger group structure than SU(3) that contains at least one new additive quantum number (beyond 13 and Y) called charm. Granting the existence of such particles with masses higher that the well-known, low-lying nonet mesons and octet or decuplet baryons, it is necessary to consider what kinds of experiments could look for them and what limits can be set on their properties if such experiments yield no positive result. These questions can only be answered within the framework of theoretical models that are far from being uniquely specified. One such model, that we find intriguing enough to use as our basic guide, is a version of the three-triplet model of Han and Nambu [7]. The possible existence of stable or semi-stable "charm" particles in threetriplet models has already been incisively discussed by Pati and Woo [81. This note is meant to extend that work so as to bring those ideas closer to the testing point in the laboratory. We first give some general arguments as to why one might expect the existence of a larger hadronic spectrum than that based on the three quarks *. This is followed by a discussion of the possible decay properties o f " c h a r m " particles. The most promising production reactions are then listed. These considerations are then combined in an analysis of the prospects for finding "charm" particles with the newer accelerators, given that they have not been found with proton or electron accelerators below 30 GeV.
2. Why " c h a r m " particles? (1) There has never been compelling theoretical arguments to explain why the approximate hadronic symmetry group should be SU(3); rather the argument has been almost entirely an empirical one [9]. (2) The simple, three-quark model of Gell-Man and Zweig, which would exclude the existence of "charnl" particles, has several difficulties: (a) The spin -1 quarks violate the Pauli principle in the strikingly successful SU(6) classification of the baryon octet and decuplet multiplets. (b) As shown by Adler [10] and Okubo [11], the simple three-quark model does not give the correct value for the ~z0 -+ 3'3' transition probability. (c) The upper limits to the abundances of fractionally charged particles to be found at accelerators, in cosmic rays, on land, in the sea or on the moon are very lOW. (3) The recent attempts by Weinberg [12], Salam [13] and others, to construct a unified renormalizable theory of weak and electromagnetic interactions, when extended to include hadrons, all seem to require that the number of basic fermion constituents be larger than three in order to remove unphysical neutral currents or to remove theoretically damaging Adler-type anomalies [14]. * Vivid arguments along these same lines are given by tf.J. Lipkin in the Proc. of the Irvine Conf., 1971 and in ref. [15].
G.A. Snow, "Charm "particles
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The attractiveness of the Han-Nambu three-triplet model is that it overcomes at one blow, the three difficulties (2a, b, c) of the three-quark model given above. The (56) representation for low-lying baryons is compatible with the Pauli principle for zero orbital angular momentum states of the quark. The predicted 7r0 ~ 77 amplitude is correct, and all the unsuccessful but rigorous, searches for fractionally charged particles are irrelevant since the nine quarks in this scheme all have integral charge, namely [8] ( - 1 ) 2, (0) 5, (+1) 2. (Of course no heavy integrally charged "quark" has been found either, but the limits are less significant and even the stability of such particles is not assured.) At least one unified weak and electromagnetic theory with Han-Nambu triplets has been recently shown to exist [15]. The three-triplet model has also been applied with reasonable success to a parton interpretation of deepinelastic electron and neutrino interactions [ 16]. In sum, it is a good model to take in considering the question of how to detect "charm" particles. It should be noted however that the experimental discussion given below for the case where charm is broken only by the weak interactions, applies to a much larger class of models than just the three-triplet model.
3. Decay of charm particles Having assumed an approximate hadron symmetry larger than that based on three quarks, there are two interesting yet fundamentally different choices that can be made for the decay properties of "charm" particles. These are: (i) "Charm" is not conserved by at least one of the two interactions medium strong and electromagnetic, nor by the weak interaction t . (ii) "Charm" is rigorously conserved in strong and electronragnetic interactions but not conserved in the weak interaction. Hypothesis (i) was favored by Nambu [7] in his original work on this subject. This hypothesis allows a single "charm" particle to couple strongly to conventional zero-charm particles, nucleons and mesons. Hence, experimentally, "charm" particles could manifest themselves as ordinary resonant states. The best way to look for the particles is then to search for exotic resonances like a Z* with quantum numbers B = +1, Y = +1. This search has been going on for many years with not very encouraging results to date. Five years ago Greenberg and Nelson [ 17] tried to fit a great many baryon resonances into the Han-Nambu scheme with hypothesis (i). They pinned their phenomenology on two, at that time, probable, Z* resonant states, plus the Roper resonance N(1470). More data has not confirmed the existence of these particular Z* states, and the electromagnetic properties of the N(1470) is not consistent with the three-triplet model assignment [ 18]. Furthermore, possible alterna-
t Models such as SU(4) in which the "charm" quantum number modifies the Gell-Mann-Nishijima formula relating Q to I3 and Y, are not of this type, but they can be of the type (ii), ref. [ 14 ]. The Han Nambu model retains the usual formula Q =/3 + ,~Y, so that it retains both option (i) and OiL ref. [8 ].
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G.A. Snow, "Charm" particles
tive theoretical explanations of the N(1470) within a conventional three-quark model have been given [19], so that the detailed level fitting of Greenberg and Nelson must be abandoned. This does not mean that Nambu's hypothesis is definitely ruled out, but rather that it has no empirical confirmation among the low-lying baryonic states, Since the simple three-quark model can tolerate baryon states in multiplets other than octets or decuplets by adding q ~ pairs to the qqq lowest configuration, the observation of a single Z* resonance does not resolve the issue. Only a detailed phenomenological classification of all observed resonances, such as was attempted by Greenberg and Nelson, can hope to shed light on the underlying hadronic symmetry. The opening up of new energy ranges is likely to have much less of an effect on this line of investigation than the increasing ability to collect and analyze massive statistics for all kinds of two-body and many-body reactions at energies below 30 GeV. Unusually narrow, high-mass resonances should be sought. Hypothesis (ii), in which charm is broken only by the weak interaction, presents a very different picture. The charm quantum number now acts like strangeness so that charm particles can be produced only in pairs via the strong or electromagnetic interactions. One presumes that the lightest charm particles will decay either nonleptonically into ordinary baryons and mesons, or leptonically into zero-charm hadrons plus an ev or/Jr pair. As the mass of the lightest charm particle increases the number of different final states increases very rapidly as does its total transition probability. For example there are eleven known S = 0 baryonic states with J ~< 23. below a mass of 2 GeV. If one assumes a charm-changing weak-interaction strength G c equal to G a s = l , then the lepton decay transition probability summed over these eleven final states is ~ 5 × 10 l0 sec - 1 ( ~ 8 0 % to neu). A 3 GeV charm particle will have a leptonic transition probability ~ 3 X 1012 s e c - l to the same eleven states ( ~ 40% to neu) t . Besides the large number of leptonic final states, there will be an even larger number of non-leptonic final states, such as charm particle -~ Nzr, N*Tr, N*ezr, etc. Unlike the hyperons with their special phase-space effects near threshold there is no reason to suppose that leptonic decays make up only a tiny fraction of non-leptonic decays of charm particles if their masses are >~ 2 GeV. It is more plausible to assume that the fraction of leptonic decays is in the 1 0 - 5 0 % range (not unlike the situation with intermediate vector mesons), ref. [3]. Furthermore there is no a priori compelling reason why the charm-changing weak-interaction coupling constant could not be much larger than the strangeness-changing coupling constant, in fact as large as GFerm i. One important experimental point is clear from this discussion: charm particles produced at high energy might be visible as decaying tracks, for example in a bubble chamber, if their masses were < 3 GeV and if G~xce 0 G G a s ~ O" For heavier particles, or larger coupling strengths, even 300 GeV protons could not produce chain1 particles with enough energy in the laboratory to go more than a fraction of a centimeter before decaying. [E.g. r c = 10-13 sec, 3,c =(Eo/Mc)=50 -~ 7cCrc = 0.15 cm]. The non-leptonic decay modes of a massive charm particle will f These estimates are made with all transition matrix elements set equal to one.
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be distributed over a very large array of states with relatively little concentration on transitions to two-body final states which are easiest to analyze.
4. Production of charm particles * The assumption of charm conservation in strong and electromagnetic interactions implies that charm particles must be produced in pairs except in high-energy neutrino interactions. Typical reactions to produce charmed baryons and mesons (B c and m c respectively) might be (la) P+P -+Bc + m c + a n y t h i n g , + B 'C + anything,
(lb)
O m c + m ' c + anything,
(lc)
~ B c + m c + anything,
(2a)
e - + e + -+mc + m c + anything,
(2b)
+ anything.
(3)
~B
7+p
u
#
+n
C
~/a-+B
c
Clearly as the minimum masses for Bc and m c go up the probability of having made these particles at the older accelerators goes down rapidly. Exactly how rapidly cannot be estimated precisely since reliable strong interaction dynamical models that including charm particles do not exist. However crude estimates can be made. For example for reaction ( l a ) one can use a simple model of diffraction dissociation such as that of Gottfried and Kofoed-Hansen [20]. In their model the differential cross section for making a mass M in the forward direction is approximately K(M-Mo)-2 exp ( - b ' l t l ) where b' ~ 5 GeV -1. To make charm particles the total mass in the diffraction blob must be larger than the sum of the masses of the lightest baryon and meson charm particles, Bc + m c. If we assume this number is ~> 4 GeV, then the cross section for charm particle production is very small for 30 GeV pp collisions but can be non-negligible at 200 GeV or higher. "Non-negligible" here means a cross section ~ 0.1 - 0.3% of the total cross section. Such an estimate implies a charm particle cross section between one and two orders of magnitude smaller than the associated production YK cross sections [21]. Other models and other regions of phase space can give much more pessimistic estimates for charm-particle production. For example if one makes a dual-model estimate of reaction ( l b ) or ( l c ) in the central region (x ~ 0), one expects [22] a factor exp ( - 4 p 2) or equivalently exp ( 4 M 2 ) , where M is the mass of B c or m c. For M ~ 2 GeV, this exponential is ~ 1 0 - 7. A similar pessimistic estimate would arise from a strict thermodynamic model a la Hagedorn. However we believe that the diffraction dissociation model estimate is the most reasonable one for the production of charm via strong interactions. Contin* A qualitatively similar discussion has been given by Glashow et al. [ 14].
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G.A. Snow, "Charm"particles
uing with our assumption that charm is strictly conserved in strong and electromagnetic interactions, one expects high-energy photoproduction cross sections of pairs of charm particles, to be smaller than the total photo-hadronic cross section by two or three orders of magnitude * [23] Let us now consider neutrino-production processes as in eq. (3). Tile high-energy cross section depends directly on the square of the ratio of coupling constants (;ACe-0/(;Fenni" The threshold is determined by the mass of the lightest charmed baryon, M(Bc). For neutrino energies, Ev, a few hundred MeV above M(Bc)--M(p), one could expect a total charm-particle cross section.
o(v +n ~ Bc +,u
, . , , , , ,,\ ' G 2 + a n y t h i n g ) ~ 0 . 5 ( E v E v t h r e ~ ' ° l d- ) /-- - ~ U ) X 10 3 8 c m(4) 2.
Whenever the charmed baryon decays promptly (~< 1 0 - I t see), and non-leptonically, there is no way for the neutrino experimentors to distinguish such an event from an ordinary deep inelastic neutrino event. However when Bc decays leptonically, the neutrino event becomes distinguishable from the usual inelastic event by the presence of two l e p t o n s A search for such events is similar but not identical to the search for intermediate vector bosons and heavy leptons. I have re-examined all published neutrino experiments at CERN and Brookhaven to determine what limits these set on the mass and coupling constant of charnmd baryons. It appears that the most sensitive experiment in this regard is the neutrino heavy liquid bubble chamber experiment carried out at CERN from 1963 to 1967, ref. [241. One can ask how many possible (/a, e) events there are, and compare this with the number of v events in which enough energy is transferred to the hadrons (v > Vmin) so as to be able to comfortably produce a charlned baryon of assumed massM(Bc). Table 1 shows the number of inelastic neutrino events (deduced from ref. [24d1) with hadronic energy, v, greater than various m i n i n m m values. These minilnum values correspond to 0.500 GeV above the energy needed to produce charmed baryons with M(Bc) = 2.0, 2.5 and 3.0 GeV respectively. An approximate calculation, integrating over the neutrino spectrum, converts these numbers to expected numbers of charmed particles produced assuming eq. (4) and GAC~O -- (;t.'enni (4th row of table 1). If one adopts a value for the branching ratio of Bc decay into electrons or positrons of 10% one gets the expected number of obsen, ed (/1 , e ±) events in the stone sample (row 5), with Gz~c~ O/(;Femil = 1. The actual number of ( ~ , e -+) candidates observed is 1 [24a, b ] Hence the 90% confidence limit for ((;AC~o/GF) at each mass value M(Bc) can be easily c~culated and is given in row 6 This CERN experiment is then compatible with the existence of charm particles in the mass range ~> 2 GeV and with a weak, charm-changing, coupling constant of the same order as the Fermi * Carlson and Freund have discussed tile possibility of detecting heavy vector mesons via photoproduction, where these vector mesons are related to qcqc states of charmed quarks, qc From the experiment',d point of view however, it is not easy to distinguish such objects, with their zero charm, from the expected higher mass vector mesons in conventional theories
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G.A. Snow. "Charm "particles
Table l Present limits from CERN neutrino experiment [24] on charm-changing weak-interaction coupling constant versus the mass of charmed baryon M(Bc) (see text for explanations) M(Bc) (GeV)
2.0
2.5
3.0
Neutrino threshold energy (GeV) Approx. minimum hadron excitation energy (GeV) Number of B.C. events Number of expected (~t, e) events from charm particles for GdxC4:0 = GF
1.86
3.14
4.64
90% upper limit for GAC¢O/GF
1.5 210
2.7 65
4.2 25
12.6
3.3
1.0
1.1
2.0
0.56
coupling constant. One can make similar analyses for double muon, neutrino events both in spark chambers and in bubble chambers. However, one find that none of the existing published experiments [25] give upper limits more restrictive than the (~t, e) search in the heavy liquid chamber. An analysis along these lines o f the current neutrino bubble chamber experiment at CERN can improve the statistical situation, perhaps by a significant factor.
5. Conclusions " I f charm particles exist, can they be detected?" The answer is - perhaps, but only with great difficulty. A search for two lepton events in higher energy neutrino experiments, such as those planned at NAL, could certainly improve the limits on GaC¢ o and M(Bc) given in table I. The background from n O induced electrons or positrons and decay muons from pions will probably determine the ultimate limit of this approach. Perhaps one can reach G a c ~ o ~ Gzxs¢ o" If in fact the charm-changing weak interaction is less than, or of the same order as, the strangeness-changing weak interaction, there is some small experimental hope in a completely different direction, namely to observe the path of a charmed particle before it decays. As long as the mass M(Bc) ~ 2.5 GeV the lifetime of Be could be long enough ( ~ 10 -12 sec), so that decay paths of 1 cm would not be hnprobable, when the gamma of the charmed particle were large compared to one. But this is just the condition that we expect to prevail when a pair of charmed particles are produced via diffraction. Therefore a very careful study of the vertices of high energy pp collisions, as can be done in the 30-inch bubble-chamber experiments at NAL, should be made, since this is one of the few practical ways to search for charmed particles t .
t Footnote: see next page.
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G.A. Snow, "Charm "particles
What about the more powerful electronic techniques that can handle enormously greater fluxes than can the bubble chambers? One possibility might be to exploit the leptonic decay modes of the charm particles, produced for example in pp collisions. This suggests a high energy experiment such as carried out by Wanderer et al. [26], at BNL with 30 GeV protons, in which one searches for nmons produced directly in a target, as distinguished from those from a decay region downstreanl from the target. In fact the unpublished data from that experiment, containing the number of directly produced muons of lower momenta than used in the W search, could provide interesting limits on the product of (production moss section) × (muonic decay rate) for charmed particles. Another interesting possibility would be to search for apparently directly produced leptons in pp collisions at the ISR over a large solid angle. The current large angle, large momentum transfer search for electrons, positrons and nmons [27] could only collect a very small fraction of the leptons from charmed particle decay, because the longitudinal m o m e n t u m of a charmed particle is large, and the typical transverse momentum of a decay lepton is modest ('~ 1 GeV). (As the massM(Bc) or M(mc) increases one expects that even the leptonic decays will be dominated, not by transitions to the ground state such as M(Bc) ~ n + ~ + v, but by transitions to excited states, such asM(Bc) ~ N* + ~ + v, since the number of these excited states increases rapidly with energy.) Again this charm particle detection method is severely limited by the secondary leptonic background from ordinary 7r and K production. Except for the actual path length observation method described above, all of the other methods hinge on detecting leptons from charmed particle decays. It is a severe challenge to devise an experiment to detect charmed particles via their non leptonic decay modes, given the expected characteristics of high mass, many decay channels and production in pairs via the strong interaction. If the mass of charmed particles were ~ 2 GeV, and their decay rates to leptons were very much smaller than to hadrons, then charm particles may be produced in appreciable abundance in high energy collisions without detection. Alongside the persistent searches for quarks, monopoles, intermediate vector mesons and heavy leptons, an intensive search for charm particles is necessary $ [28]. I would like to thank Professor D.H. Perkins and J. Mulvey of Oxford University for their interest and hospitality this past summer when this work was begun. I am + One might hope to have obtained a strict lifetime upper limit from a search of cosmic ray interactions in nuclear emulsions. Itowever the small number of carefully studied, very high energy cosmic ray events when combined with background difficulties, does not "allowan interesting limit to be deduced, l am indebted to Prof. D.H. Perkins for a pertinent discussion of this point. The statistic'a] difficulty could be overcome with an exposure of nuclear emulsion to 300 GeV protons at NAL. $ We have assumed throughout this article that charm particles are unstable with short lifetimes. Negative, long-lived, charm particles can only exist if their masses were greater than 3Mp due to the searches carried out at Serpukhov [28].
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also i n d e b t e d to m y colleagues at the L a b o r a t o i r e de P h y s i q u e T h e o r i q u e e t H a u t e s Energies and at the Ecole P o l y t e c h n i q u e for i n t e r e s t i n g discussions and t o Professors M. Levy, R. V i n h Man a n d B. G r e g o r y for their gracious h o s p i t a l i t y .
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[25] G. Danby et al., Phys. Rev. Letters 9 (1962) 36; J.K. Bienlein et al., Phys. Letters 13 (1964) 80; R. Burns et al., Phys. Rev. Letters 15 (1965) 42. [26] P.J. Wanderer et al., Phys. Rev. Letters 23 (1969) 729. [27] Report of the Int. High Energy Physics Conference at Batavia, 1972, to be published. [28] Yu Antipov et al., NucL Phys. B31 (1971) 235; F. Binon et al., Phys. Rev. Letters 30B (1969) 510.