Quark model and pi+p-pp multiplicity difference

Volume

82B, number

1

PHYSICS

QUARK MODEL AND %+p-pp MULTIPLICITY

LETTERS

DIFFERENCE

12 March 1979

*

Mehmet A. CIRIT Physics Department (83), Hacettepe University, Ankara, Turkey Received 30 August 1978 Revised manuscript received

4 December

1978

Hadron interactions at high energy are sensitive to the space-time structure of the parton model. Based on this structure we propose a model of particle production in which collective collisions among the constituents can take place. We show that the a+p-pp multiplicity difference and the asymmetry in n+p collisions should decrease with rising energy.

In hadron-hadron collisions the quark-parton model has been applied mainly to the large-pT processes [ 11. Feynman gave a qualitative description of the low-pT region [2], which has been generally the domain of the multiperipheral and statistical models, as arising from the interaction of “wee” partons, but not much work has been done on the subject. There has been a resurgence of interest recently in a constituent model of low-p-r particle production and various quark-quark [3] and quark-gluon [4] models have been proposed. In such models the leading particles emerge quite naturally. The asymmetry observed in n+p collisions is a strong hint that constituents play an important role in the low-p, region as well [5]. The empirical relationship between the shape of the pion distribution in the fragmentation region in a pp inclusive reaction and the quark distribution in a proton observed by Ochs [6] further supports this hypothesis. With some assumptions as to the energy dependence of the multiplicity KNO scaling [7] follows trivially once it is assumed that the relevant collision is the collision of partons [3]. One can also predict accurately the particle ratios in the central region in a quark-quark model [8]. We shall make here some remarks on the quarkquark collision tention

model

and would

to the importance

like to draw the at-

of the space-time

develop-

* Partially supported by the Scientific and Technical Research Council of Turkey.

ment of parton interactions for particle production: (1) Pointlike quarks are unlikely to be responsible for particle production as assumed by Gel1 and Eilam and Tavernier [3]. In the Field-Feynman fit to the quark distribution functions a valence quark in the proton carries approximately 14% of the momentum of the proton. Thus with pointlike quarks we would expect K = 0.14, where K is the coefficient of inelasticity which is known to have the constant value K = 0.5 independent of energy [lo]. (2) Even if we assume that the collision agents are not the bare quarks but the dressed quarks [ 111 the model is still not satisfactory. For pp collisions, assuming that the momentum is equidistributed among the valence quarks, the coefficient of inelasticity would be K = l/3 which is still not compatible with the data. Furthermore as pointed out by Morse et al. [12] the expected n+p-pp multiplicity difference in this model is too big compared to the experimental difference. If we assume that multiplicity is given by N=clnsqq, c being a universal constant independent of quark flavour [ 131 with the numerical value c = 1.8 for the charged multiplicity [14], N,+p - Npp = 1.8 ln(9/6) = 0.7 which is larger than the measured difference 0.26 + 0.09 [12] at 100 GeV. (3) We want to point out in general that the spacetime development of the parton-parton interaction is being neglected in these models. A high energy parton scattering involves a sequence of basic momentumnearest-neighbour interactions. Each basic interaction 123

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PHYSICS LETTERS

requires a time interval ~ l / m in its rest flame (for lack of another scale), and in a high velocity frame this basic time interval is dilatated by a factor ~ p / m [15]. We might be facing here the same situation as in the collision of a hadron with a nucleus, as stressed by Gottfried [ 16], where hadron-nucleon collisions are spread over a large space-time region and before they can reach their asymptotic form interactions with the other nucleons of the target are likely. In the same way, before a p a r t o n - p a r t o n interaction fully develops and the recombination with the spectators occurs, it migh interact with the other partons falling into the interaction region. Thus a high energy collision should be a collective collision of patrons. We shall show here that some features of high energy collisions can be understood more easily if we take into account the space-time development of the parton interactions. This introduces much complication to the simple p a r t o n - p a r t o n collision model, as the various contituents in varying numbers can be found in the interaction region. In order to have a working model we shall make several simplifying assumptions: (1) We shall assume that the collision agents are the dressed valence quarks among which the momentum of the hadron is equidistributed [11]. With this assumption we hope to take into account the gluon component of the hadron which is neglected in the q u a r k - q u a r k models. Equidistribution is not essential to our conclusions so long as all the quarks can be represented by the same distribution function. It has been remarked that this is not the case for the strange quarks [19]. We shall confine ourselves to the interactions of the nonstrange quarks. (2) We shall assume that the number of quarks taking part in the collision from each hadron has a binomial probability distribution. This may not be a good assumption at low energies where the interaction occurs in a comparatively narrow space and short time interval and single quark-quark collisions might be favoured over others. Mso in the other limit of extremely high energy all the constituents of the hadrons might be involved in the collision. In this case the coefficient of inelasticity becomes exactly equal to one, contrary to the results from cosmic ray experiments [10]. Mso in this case there should not be any multiplicity difference between n+p and pp collisions. In view of this, a binomial distribution might be a good assumption at high energies. 124

12 March 1979

With these simplifying assumptions we can immediately write down the average multiplicity expected from the collision of two hadrons made up of A and B valence quarks each: A B (N)(2 A - 1)(2 B - 1) a = 1 ~=l~a,l~b, t A B

2A - 1 B 2B--1 b=l

B "

Here a and b denote the number of valence quarks taking part in the collision from each hadron. From this formula we obtain the 7r+p-pp charged multiplicity difference to be ~V?~.p - ~ f ) p p = 0.33 in excellent agreement with experiment. The coefficient of inelasticity can be found easily as well. The maximum amount of energy going into particle creation in the center of mass frame of the produced particles is % / ~ q q . But this frame is shifted in rapidity with respect to the center of mass frame of the parent hadrons by ~(a, b) = in(aB/Ab ) .

(2)

Assuming all the available energy goes into particle creation, the average energy in the center of mass frame of the colliding hadrons is found to be A B (2 A - 1 ) ( 2 B - 1 ) a= 1

x ch ~(a, b),

(3)

from which we obtain (K) = 2A-1/(eA -- 1) + 2 B - 1 / ( 2 B - 1). For pp collisions this formula gives (K) = 4/7 which is compatible with the data. As we pointed out earlier the formulae above should be regarded as asymptotic formulae in the sense that at low energies single quark-quark collisions might be dominant. In this case we can expect the coefficient of inelasticity in pp collisions to rise slowly with energy from K ~ 1/3 to K ~ 4/7. The 7r+p-pp multiplicity difference should, for the same reason, decrease with rising energy to the value expected from eq. (1). Our model is also in qualitative agreement with

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the gradual loss of asymmetry in n+p collisions with rising energy [18]. At low energies where q u a r k quark collisions dominate the rapidity peak occurs at y = (1/2) in (3/2) = 0.2 while at higher energies where collective collisions dominate the peak is shifted to y = qv~)/~

= 0.08.

I would like to thank the Scientific and Technical Research Council of Turkey for financial support.

References [ 1] D. Sivers, S.J. Brodsky and R. Blankenbecler, Phys. Rep. 23C (1976) 1. [2] R.P. Feynman, Photon-hadron interactions (Benjamin, New York, 1972). [3] G. Eilam and Y. Gell, Phys. Rev. D10 (1974) 3634; S.P.K. Tavernier, Nucl. Phys. BI05 (1976) 241. [4] S. Pokorski and L. Van Hove, Nucl. Phys. B86 (1975) 243. [5] J.W. Elbert, A.R. Erwin and W.D. Walker, Phys. Rev. D3 (1971) 2042; M. Deutschmann, Proc. Amsterdam Intern. Conf. on Elementary particles (1971), eds. A.G. Tenner and

12 March 1979

M.J.G. Veltman (North-Holland, Amsterdam, 1972). [6] W. Ochs, Nucl. Phys. Bl18 (1977) 397. [7] Z. Koba, H.B. Nielsen and P. Olesen, Nucl. Phys. B40 (1974) 317. [8] V.V. Anisovich and V.M. Shekhter, Nuch Phys. B55 (1973) 455; J.D. Bjorken and G.R. Farrar, Phys. Rev. D9 (1974) 1449. [9] R.D. Field and R.P. Feynmann, Phys. Rev. D15 (1977) 2590. [10] E.L. Feinberg, Phys. Rep. 5C (1972) 237. [11] H. Satz, Phys. Lett. 25B (1967) 220; Nuovo Cimento 37A (1977) 141. [12] W.M. Morse et al., Phys. Rev. D15 (1977) 66. [13] S.J. Brodsky and J.F. Gunion, Phys. Rev. Lett. 37 (1976) 402. [14] J. Whitmore, Phys. Rep. 10C (1974) 275. [15] J. Kogut, D.K. Sinclair and L. Susskind, Phys. Rev. D7 (1973) 3637; J. Koplik and A.H. Mueller, Phys. Rev. D12 (1975) 3638. [16] K. Gottfried, Phys. Rev. Lett. 32 (1974) 957. [17] P. Stix and T. Ferbel, Univ. of Rochester preprint COO3065-153 (1977). [18] V.G. Grishin et al., Soy. J. Nuel. Phys. 24 (1976) 311. [19] A.R. Erwin et al., Phys. Rev. Lett. 36 (1976) 636.

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