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High-Energy Multiparticle Reactions UC Irvine UC Irvine Previously Published Works Title High-energy multiparticle reactions Permalink https://escholarship.org/uc/item/4cg994v7 Journal Reviews of Modern Physics, 44(2) ISSN 0034-6861 Authors Frazer, WR Ingber, L Mehta, CH et al. Publication Date 1972 DOI 10.1103/RevModPhys.44.284 License https://creativecommons.org/licenses/by/4.0/ 4.0 Peer reviewed eScholarship.org Powered by the California Digital Library University of California REVIEWS OF MODERN PH Y SI C S VOLUME 44, NUMBER 2 AP RIL 197 2 ::—:;ig.'x-.'nergy ', 0:u..tipartic. .e 'reactions W. R. FRAZER, L. INGBER, C, H. MEHTA, C. H. POON, D. SILVERMAN, f K. STOWE, P. D. TING, H. J. YESIAN) DePartment of Physics, University of California, San Diego, La Jolla, California 92037 {June, 1971) (Revised January 1972) Hadronic multiparticle reactions at very high energies are reviewed with emphasis on current theoretical pictures and models. CONTENTS energies. Two new facilities are or soon will be in opera- I. Introduction. ~. 284 tion: the CERN-ISR, intersecting storage rings pro- II. General Features of Multiparticle Reactions. 285 viding proton —proton collisions at up to 60 GeV center A. Some Very General Observations ~. 285 of mass energy (the equivalent of 1900 GeV lab energy B. Longitudinal Kinematics. 285 on a stationary and the NAL ac- 1. Longitudinal and Transverse Momenta. ~ . 285 impinging proton); 2. Longitudinal Phase Space Plots. 286 celerator providing a proton beam at energies up to 500 3. Choice of Longitudinal Variables. , . 289 .. this review will back- C. Inclusive Spectra. ~. .. 292 GeV. We hope that provide 1. Definitions and Conventions. ~ 292 ground material useful in the interpretation of data 2. Normalization and Sum Rules ~. 292 from these machines. 3. Limiting Fragmentation and Scaling. 292 We begin, in Sec. with general features of multi- D. Short-Range Correlation Hypothesis. , . ~ . 293 II, 1. Correlation Length Hypothesis. 293 particle reactions, trying to emphasize considerations 2. Speculations Concerning Asymptotic Energies . 295 which are not. tied specific models. this review 3. Central Plateau and Logarithmic Growth of to If Multiplicities. , . , . , . 296 shouM have any effect on future choices of measure- 4. Two-Particle Correlations. , . , . ~. 297 ments to be made, we would like it to help "maximize E. Mueller Analysis of Inclusive Reactions. 297 the possibility that the experimental data collected will 1. Generalized Optical Theorem. ~. ~ . 297 2. Central Region; Double-Regge Limit. 298 remain useful despite continuing changes in theoretical 3. Fragmentation Regions; Single-Regge Limit. 298 fashions. '" We defer to Sec. III the description of 4. Approach to Limit; Secondary 'Trajectories. 298 5. Factorization. .. ~. 300 specific models, very obviously influenced in our choice 6. Phase Space Boundary; Triple-Regge Limit. 301 by current theoretical trends. In Sec. IV we summarize 7. Two-Particle Inclusive Spectra; Correlations. 303 the predictions of these models, as well the more F. Partial Cross Sections and Multiplicity Distribu- as tions. .. 303 general considerations of Sec. II, and attempt a com- III. Models of Multiparticle Reactions. ~. , 305 parison with emphasis on those experiments which dis- A. Multiperipheral. Model. 305 criminate most effectively between models. B. Diffractive Fragmentation Model. , . 309 C. Feynman Diagram-Summing Models. .. 310 Although we have tried to emphasize general con- D. Statistical- Thermodynamical Model ~. 312 siderations and have tried to give an adequate presen- IV. Summary of Predictions of Models. , . 316 tation of other models, we caution the reader that all I. INTRODUCTION of us are theorists, and that we have among us invested several man years in the study of the multiperipheral The motivation for this review grew out of the feeling model. This paper is primarily theoretical; the experi- that the field of multiparticle reactions is growing in- mental data presentation is illustrative, not exhaustive. creasingly coherent, and increasingly likely to yield Conversations with our colleagues over the course of fundamental information about the nature of hadrons. the past few years were of course essential to the forma- Widespread agreement has developed as to some im- tion of this review, but it is impossible to enumerate portant questions to be asked of the experimental data, them all. Some of the most extensive and recent help and excitement increases as partial answers to some of has come from J. S. Ball, T. Betlach, G. F. Chew, these questions become available. Nevertheless, it T. Ferbel, S. C. Frautschi, R. L. Lander, B. %. Lee, seemed to us as we began this work that this excitement A. Mueller, R. Sugar, C. I. Tan, L. Van Hove, and was not widely shared among particle physicists, much L.L. Wang. Finally, the detailed criticism of our Editor, less among the larger physics community. For example, J. D. Jackson, led to most of the improvements in this despite their simplicity, single-particle inclusive spectra. revised manuscript. were explored very little even at existing accelerator We conclude this introduction with a guide to some * of the other reviews of multiparticle hadronic reactions This work was supported in part by the U.S. Atomic Energy Commission. which have appeared recently, and which, because of f Present address: Department of Physics, University of their differing emphases, will help the rea. der to ob- California, Irvine. f Present address: Department of Physics, University of Calif ornia, Berkeley. ' K. G. Wilson (1970). W. R. FRAzER et ul. High-Energy MNltipurticle Reactions 285 tain a balanced picture of the field. Lander (1971), PT(Ge Y/C) augmented by Krisch (1971), provides comprehensive -- I.O coverage of data on inclusive reactions as of September 1971. A brief phenomenological review was I given by I -50 5.0 Frazer (1971a), and a more comprehensive one by Pl.(G e Y IC ) — Berger (1971).Theoretical reviews with very different -- I 0 emphasis from the present one are those by Van Hove l2. 5 GeY (1971) and Bjorken (1971).Reviews which very con- Pn. 2.2 Contours of constant cross section as a function of siderably overlap this one are those of Frazer longitudinal and transverse momentum of secondary particle, (1971b), for various beam momenta in pp~m X. The contour at 12.5 Quigg (1971), and Arnold (1971). Older reviews GeVjc is taken from Akerlof et al. (1971);the others are estimated. which have been useful to us are Wroblewski (1970a), Czyzewski (1968), and the entire proceedings of the International Conference on Expectations for Particle (2) Low multiplicity of particles produced: The aver- Reactions at New Accelerators (Madison, 1970) and age number— of particles produced grows slowly with of the 1969 Stony Brook Conference )High Energy energy much more slowly than would be the case if Collisions, edited by C. N. Yang et al. (Gordon and most of the available energy were converted into par- Breach, New York, 1969)]. ticles. The data on the multiplicity of charged particles from the Echo Lake cosmic ray experiment (Jones, 1970) shown in Fig. 2.1 are well fit by a logarithmic II. GENERAL FEATURES OF MULTIPARTICLE increase with energy REACTIONS (u,i)=A+B ln s, (2.1) A. Some Very General Observations where the values of the parameters for this and other Two empirical rules concerning the nature of multi- similar its are given in Table 2.1. particle reactions are so well accepted and so inAuential We shall return in Sec. II.F to a more detailed de- in both phenomenology and the construction of models scription of multiplicity distributions, but at the mo- as to deserve priority of presentation. They are ment we are mainly concerned with observing that the (1) Smallness of trarssverse momenta: The number multiplicity of particles produced is growing much less of particles produced falls off very rapidly as a function rapidly than the available energy would allow. This fact, with mo- of q&, the magnitude of momentum transverse to the together the rule of smallness of transverse incident beam (compatible with exponential or Gauss- menta, implies that most of the available energy goes ian fits). The average value, (qi) 0.3 to 0.4 GeV/c, into longitudinal motion (along the incident beam is approximately independent of the incident energy, direction), and the average longitudinal momentum and does not depend strongly on the type of particle increases rapidly with incident energy, or multiplicity of particles produced. See, for example, &Vii) s'"/ln s»&V ). (2.2) Smith et aL (1969) or Elbert et al. (1968). Figure 2.2 sketches the elongation in q~I of a typical contour of constant cross section as s increases. Thus E (GeV) the longitudinal momenta are the only variables which 10 I 00 IOOO change rapidly with energy, and great kinematical sim- I I I t I i I I I I I I I l I I plifications can be obtained by recognizing this fact, as we shall discuss in the next sections. B. Longitudinal Kinematics l. J.oegitldinal aed Transverse JI/Iomerlta The kinematics of a many-particle system is gen- erally quite involved. Great simplifications result, however, in the region of very high-energy scattering. As we have seen in the previous sections, the final-state I I I I I I l I particles of such scattering processes are characterized IO IOO I 000 by small mean transverse momenta 0.4 GeV/c), s (GeV) ( which become independent of the incident energy as FIG. 2.1. Average multiplicity of charged secondaries as a func- the latter becomes large. This, as already noted, sug- tion of energy in the Echo Lake cosmic ray experiment {Jones, 1970). High-energy points (s)200) are cosmic ray data; low- gests a differential treatment for the longitudinal and energy points are accelerator data, transverse momentum dependence of the scattering am- 286 REvIEws QP MQDERN PHYsIcs ' APRIL 1972 TABLE 2.
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