Multiplicity Distributions in Impact Parameter Space

Abstract

A definition for the average multiplicity of pions as a function of momentum transfer and total energy in the high energy proton-proton collisions is proposed by using the n-pion production differential cross section with the given momentum transfer from a proton to other final products and the given energy of the latter. Contributions from nondiffractive and diffractive processes are formulated in a multi-Regge model. We define a relationship between impact parameter and momentum transfer in the sense of classical theory for inelastic processes and we obtain the average multiplicity of pions as a function of impact parameter and total energy from the corresponding quantity afore­ mentioned. By comparing this quantity with the square root of the opaqueness at given impact parameter, we conclude that the overlap of localized constituents is important m determining the opaqueness at given impact parameter in a collision of two hadrons. Experiments for high energy particle collisions revealed the structure deep inside the hadrons and the distributions of their constituents in impact parameter space. Typical phenomena which appeared in such investigations would be a scal­ ing behaviour in the structure functions for the deep inelastic electron-proton scat­ tering1J and the interesting results given by a geometrical analysis of the scattering amplitudes in an elastic PP collision. A recent work 2J showed that at extremely high energies each colliding hadron has, in the c.m. system, two interaction regions: (1) A highly absorptive core (pionization region) and (2) a partially absorptive fringe, where diffractive dissociation occurs, which has a large interaction radius and large transparancy, and which is responsible for the increase in the pp total cross section shown in ISR experiments. 3J In this paper we extend such a geometrical description to inelastic processes. That is, we propose a definition for the average multiplicity of pions produced at high energy PP collisions in impact parameter space and look at its behaviour as the impact parameter changes from zero to infinity, in other words as one goes from a violent collision to a peripheral one. For this purpose we first define the average multiplicity of pions as a function of momentum transfer and total energy in § 2. The n-pion production differential cross section with the given momentum transfer from a proton to other final products and the given total energy of the latter is defined in the multi-Regge formalism by Chew, Goldberger and Low. 4 J Nondiffractive and diffractive processes