Remarks concerning φ production in the thermodynamics picture

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REMARKS CONCERNING

~b P R O D U C T I O N

IN THE THERMODYNAMICS

3 January 1977

PICTURE*

S.C. FRAUTSCHI

California Institute of Technology, Pasadena, California 91125, USA and S. PAKVASA and S.F. TUAN

Department of Physws, Universityof Hawaiiat Manoa, Honolulu, Hawati 96822, USA Received 2 November 1976 We examine the options that central production of ¢(1.019) in hadron-hadron collisions is dominated 0) completely by Hagedorn-Frautschl thermodynamics and (il) by thermodynamics modffmd by a mdd form of Zweig suppresslon at sufficiently high energy. Predictions on o(AB ~ q~+ anything), a(AB ~ ~K+K- + anything), (~/lr), (¢lp°), (0/6o°) ratios at P.L ~ 1 GeV/c, are made where A = ~r, ~, p and B = p. These can be readily checked for Elab > 300 GeV at Fermilab and ISR.

In a recent paper [1 ], we showed that the data on the production of psions J/~ and ~' in purely hadronic reactions at high energies and in the central region remain consistent with either of the following two options. (i) The Hagedorn-Frautschi thermodynamics model [2] is fully apphcable to psion (J/~, ~') production at sufficiently high energies (Ela b ~ 300 GeV). The measured production cross section of order 1.4 X 10 -31 cm 2 for say pp --> ~(3.1) + ... corresponds to an acceptable temperature T ~ 170 MeV, while the observed p± dependence for J/if(3.1) production e x p [ - p 2 / ( G e V ) 2] is also compatible with exp [-p2/2M~ T] with T 170 MeV. Production of @'(3.684) in pp --> ff'(3.684) + ... with the same temperature, also yields o(~b')/o(tk) in reasonable accord with the 400 GeV data of Snyder et al. [3]. Hence a picture based on statistical considerations appears to be internally consistent. To wit, full thermodynamical equilibrium is attained in high energy hadron production of psions, and a dynamical detail such as the Zweig (forbidden) rule could not matter. A possible rationale has been given by Femberg [4] who proposes that the expansion time for the "hadronic fluid" increases with energy, allowing progressively more components time to come into equilibrium. * Work supported in part by the U.S. Energy Research and Development Administration uncer Contracts E(11-1)-68 and E(04-3)-511.

(ii) The thermodynamics approach is incomplete

and must be supplemented by a mild form of Zweig suppression implied by the proposal that both psions and O's are produced by the gluon constituents of the incoming hadrons, even at the highest energies. The thermal production of a massive particle M with I spin 1M and ordinary spin JM is then given by (with initial hadrons A and B) o(AB -+ M + . ) ~ XH(M) 40 mb

(1)

= X(2I M + 1)(2J M + 1)(M/mTr)3/2e -M/T, where X is the weak Zweig suppression and T the temperature. For X ~ 1/30, production characteristics of J/~b, if' can be understood approximately with T 200 MeV (note option (i) corresponds to X = 1 and T = 170 MeV). Such a picture of combining Zweig suppression with thermal statistical considerations gives a reasonable account of low energy ¢ production in pp and p~ processes [1, 5]. We propose here to sort out the physical choice between options (i) and (ii) (if only to reassure ourselves that option (i) is indeed ruled out!) by examining the ansatz that central production of ~(1.019) (which is commonly believed to share Zweig rule features) in hadron-hadron collisions is governed completely by thermodynamics (option (i)) at sufficiently high energy. ¢ Inclusive (~ inclusive) processes. The conse47

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quences are: (a) Eq. (1), apphe~l to say pp colhslons with X = 1 and T = 170 MeV (to be consistent with psion production), yields o(pp -> M~ +.. ) ~ 6.1 mb.

(2)

(b) The (~/70 ratio for moderate p± (~ 1 GeV/c) is

predicted to be do(pp -> ~ + . . ) do(pp-~n+ )

(2/~M + 1)(2J~M + 1) exp(--X/p 2

+M2/T)

(2I~I + 1)(2J~l + 1) exp(--X/p 2 +M2/T)

(3)

for Pll ~ 0 (central collision). The importance of choosing p± of order 1 GeV/c is to maintain a delicate balance between the known experimental fact [6] that pion p± distribution no longer follows thermal behavior for large p± (>~ 1 GeV/c), and that p± cannot be chosen too small, compared with the q~mass, else the daughter effect comes in - at small p± the number of pions is boosted somewhat above the thermal rate of first generation production, by e.g.,/90 ~ 7rTr,etc. The advantage this gives lr's over ¢'s is less at large p±. Taking Pi = 1 GeV/c, T = 170 MeV, eq. (3) gives 24% if we consider the (~b/n) ratio for a specific pion charge state (+, - , 0) or (n + + n-)/2, and 8% if we consider the (~/n) ratio for all pions (since (2I~i + 1) = 3). (c) The daughter effect under (b) can be largely avoided (though there is a small probability for ~ p T r ) by studying (¢O/pO) or (¢O/wO) ratios. The values are respectively 38% and 40% for p± ~ 1 GeV/c and T = 170 MeV. Option (ii), with weak Zweig suppression X ~ 1/10" in eq. (1) for ~bproduction (and using T = 200 MeV needed to understand the corresponding J/if, i ' production [1]), yields o(pp ~ ~ + anything) = 1.5 mb and a (~b/rr0) or ~ to (n + + n - ) / 2 ratio of 3.6% at p± 1 GeV/c. The corresponding (~/pO) and (~b/6o0) ratios, again with p± ~ 1 GeV/c, are 4.4% and 4.5%, resp. * The choice X ~ 1/10 for ~ production (in contrast to X = 1/30 for pslon production is very crudely estimated from quark-gluon coupling c~S (= g2/4~r) counting [1]. Production of ~ in the reaction 3 gluons ~ ¢(ss-) with C = -1 reqmres only ~($), where c~S($)= 0.44. Ttus estimate appears conslstent with the measured ratio o(pp ~ 4~+ anything) to o(pp ~ p°(to °) + anything) ~ 1/12 at Ela b = 150 GeV [7]. 48

3 January 1977

A relevant question for option (i) is the energy, where we would expect ~ production to be fully thermal. It seems extremely reasonable that thermal conditions would be met for $ production, at least in the energy range where the larger mass J/if, i ' particles appear to be governed by statistical considerations, i.e., Ela b ~ 300 GeV. Hence these predictions can be best checked at the highest FNAL energies and of course at ISR energies. Of particular interest at ISE energies, is to consider 90 ° production (XF = 0) of the meson. The decay mode of ~ 1 . 0 1 9 ) ~ K+K - is very distinctive - the Q value is almost zero, so if the had p± of order several hundred MeV/c, the K-pair would have a very small opening angle and might be picked up even with counters (it is much more distinctive than say p0 ~ rr+Tr-). Most likely XF has to be very nearly zero, certainly smaller than 0.05, for this test to be truly meaningful. We can speculate that since thermodynamic conditions [1 ] for production of J/if, i ' are met at Ela b 300 GeV in pp central collisions, where (s/sth)l/2 5 (Sth is the (c.m. energy) 2 for threshold production of J/if), the same empirical (s/sth) 1/2 criterion applied to ¢ production might lead us to expect thermal production at

s 1/2 ~ 5 GeV (Ela b ~ 13 GeV) for p~ ~ ~ + anything s 1/2 ~ 10 GeV (Elab ~ 50 GeV) for zrp-+ ¢ + anything s 1/2 ~ 15 Ge,V (Elab ~ 113 GeV) for pp ~ ¢ + anything.

(4) Hence the earher low-energy ¢ production data [5] may be too low in energy to be decisive on whether thermal production need or need not be supplemented with some form of Zweig suppression. However, the more recent data of Anderson et al. [7] on ¢ production at 150 GeV by 7r+ mesons and protons do bear on the validity of eq. (4). The rough equality between o(pp ~ ~b+ anything) (-~0.66 + 0.20 mb) and o(n+p ~b+ anything) ( ~ 0 . 5 6 + 0.17 mb) is certainly supportive o f the thermal picture - i.e., production cross sections independent of the characters of the initial state. However, the data do not support predictions (2) and (3) (for p± ~ 1 GeV/c, T = 170 MeV). The cross section is too small by an order of magnitude, while an estimate of the "measured" ¢ to (rr+ + 7r-)/2 ratio (using the pion measurements of the ChicagoPrinceton group on hydrogen at 200 GeV [8] ) hovers

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around 4 to 6% (with error of -+2%). Option (ii) is much more compatible with data at 150 GeV [7] (though the prediction for a(pp -+ p0(co0) + anything) becomes less satisfactory, being a factor of 3 larger than the measured 8.6 -+ 2.5 mb of ref. [7]. We must emphasize, however, that the effective energy threshold proposed in eq. (4) is purely an empirical guess. It is possible that the noted rise in reclusive 4~production in pp collision from (158 + 35)/ab at 24 GeV [9] to (660 -+ 200)/2b at 150 GeV [7] will persist at still higher energies. Accurate ¢ measurements at the highest FNAL energies and at the ISR are needed to make a clear-cut choice between the options. KK and D19 inclusive. Experiments on KK have always required some nonstatlstical suppression. Note in this regard that the K/rr ratio remains below statistical at all s that have been observed. This impfies that at least for the total cross section integrated over x F, KK production requires a nonstatimcal suppression at all s. Furthermore at ISR there are data [10] specifically at small x, large s which shows the K+/Tr+ ratio still down around 10%. Hence a nonstatistical suppression, not necessarily the exotic one (under option (ii)) but possibly related to it, persists at the highest s studied. The experimental limits on charmed DI3 production in proton-nucleus collisions [11 ] at 400 GeV/c are close to a decisive test of option (ii). The order-ofmagnitude estimate for DI) production can be obtained from eq. (1) by replacing the right-hand side of (1) by H2(MD) and setting X = 1 as appropriate to a Zweig-allowed process. Taking into account that production here may benefit from a spin weight factor as large as 9, the estimated DD production (assuming a mass of 2 GeV each) is of order 10 -30 cm 2 for option 0i) with T = 200 MeV [1 ]. The corresponding prediction for option (i) with T = 170 MeV is about 5 × 10 -32 cm 2. (~KK Inclusive (and t~DD inclusive} process. One can also discuss the process pp ~ ~Kg. + anything. This is Zweig-allowed at sufficiently high energy in the central region. The thermal cross section can be obtained by replacing the r.h.s, of eq. (1) by H(M¢)H2(MK) and setting X = 1 since this is a Zweigallowed process. For option (1) with T = 170 MeV, the predicted pp -~ ~bK+K- + . cross section is about 0.8 mb - close to the experimental rate for pp -+

3 January 1977

+ anything quoted above [7]. This process has a high threshold, however, because KK must be included. The effective threshold in pp ~ ~bKg. + anything may be even higher because here it is Zweig-allowed only at small x < x 0, hence the effective threshold is determined by

xosl/2 > 5(2Mp +Me + 2MK).

(4')

Current wisdom suggests that x 0 is about 0.1 for sea partons to be important in generating the Zweig-allowed process. Hence s 1/2 ~> 200 GeV from eq. (4'). The extra Kg.'s implied by this mechanism in the pp reaction are therefore not expected to be accessible to the present generation of particle accelerators. Processes pl5 ~ CK+K - + anything and np ~ 4~K+K+ anything share the same thermal cross section (~ 0.8 mb) as pp; however, their effective thresholds are not inhibited by x < x 0 and are at s 1/2 ~ l0 GeV (Ela b ~ 50 GeV) for p~ and s 1/2 ~ 15 GeV (Ela b >~ 113 GeV) for 7rp respectively. Since the experimental cross section for 7r+p ~ q~+ anything at 150 GeV [7] of 0.56 + 0.17 mb is quite close to this thermal prediction, search for the extra KK.'s implied by central production of CKK at close to the mb level, will

be of great interest here. For the Zweig-allowed ~bK+K- combination, option (li) with T = 200 MeV predicts o(pp -~ ~bK+K- + .. ) ~ cr(p~ -~ CK+K - + ...)

(5) o0r p -~ ~bK+K- +

) = 5 mb.

We expect here again, that the effective threshold condition (4') will preclude a test of this prediction in pp collisions. However, it will be interesting to sort out the roughly comparable predictions for the weakly Zweig-inhibited production of ¢ (~ 1.5 mb) and the Zweig-allowed q~K+K- (~ 5 mb) with only thermal inhibition in 7rp and ~p processes (where the effective thresholds can be much lower). The only clean way to disentangle these two mechanisms seems to be the detection of the extra K+K - pair. We confess to a certain degree of uneasiness that the prediction (5) is nearly ten times larger than the experimental total 7r+p cross section for all ~bproduction at 150 MeV [7] unless the effective threshold for ~KK. is much higher than our guess. It is possible that CKK. production under optxon (ii) must be supplemented by an extra suppression due to the presence of KK. pair. This was 49

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n o t e d earlier in c o n n e c t i o n w i t h K K p r o d u c t i o n alone up to the highest s at I S R * . In conclusion we need to reiterate that the final experimental verdict m a y n o t confirm either (i) or (ii) in every essential detail. However, we have sketched out here a list o f tests in the statistical picture, whtch when the data are in, wall enable us to determine which o f the two options is m o r e nearly correct, thus supplying the necessary building blocks for a more c o m p l e t e t h e o r y in the future. Two o f us (S.C.F. and S.F.T.) w o u l d like to thank the Aspen Center for Physics for its hospitality, and their colleagues J.W. Cronin, S.D. Ellis, G. F o x , and J. Rosner for useful discussions * It would be mterestmg to speculate that a simdar suppression may also be present in inclusive DI3 and CDI) processes. This will help option (11) where the experimental limits on DI) production (ref. [11]) are already ti..ghtening. The problem is academic at this moment for CDD, since the predicted cross section with T = 200 MeV is < 10 -34 cm 2 for M D = 2 GeV.

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3 January 1977

References [11 S.C. Frautschl, S. Pakvasa and S.F. Tuan, CALT 68-562 (1976), submitted to Nucl. Phys. B. [2] R. Hagedorn, Nuovo Cim. Suppl. 3 (1965) 147; R. Hagedorn and J. Ranft, Nuovo Cim. Suppl. 6 (1968) 169, S. Frautschl, Phys. Rev. D3 (1971) 2821. [3] H.D. Snyder et al., Phys. Rev. Lett. 36 (1976) 1415. [4] E.L. Feinberg, CERN preprint TH 2156 (1976). [5] C.J. Hamer, Nuovo Cim. 12A (1972) 162; R.A. Donald et al., Phys. Lett. 61B (1976) 210; V. Blobel et al., Phys. Lett. 59B (1975) 88. [6] D.R.O. Morrlson, m: Proc. of the Fifth Hawaii Topical Conf. m Particle physics, 1973, eds. P.N. Dobson, Jr., V.Z. Peterson and S.F. Tuan (Umv. Press of Hawah, Honolulu, Hawaii, 1974) p. 189. [7] K.J. Anderson et al., Phys. Rev. Lett. 37 (1976) 799. [8] J.W. Cronin, private communication. [9] V. Blobel et al., of ref. [5]. [10] See fig. 5.14 of P. Caplluppi et al., Nucl. Phys. B79 (1974) 189. [11] D. Bintmger et al., Phys. Rev. Lett. 37 (1976) 732.