A Geometric Bremsstrahlung Model with " Random Walk " Picture for Leading Particle

In a previous paper, u we have shown that the Geometric Bremsstrahlung Model (GEM) is successful for the description of longitudinal momentum spectrum of the leading proton and the associated multiplicity distributions in the reaction PP->PX at 205 GeV/c. 2l Especially, 111 our model the smooth transitions from the eli ffractive to the nondiffracti ve regions in the spectrum are reproduced in contrast with the two-component Bremsstrahlung Mode!Y However, other important observables in PP->PX such as the transverse momentum spectrum and the associated average multiplicity were not treated in the model. In this note, we try to discuss the observed Pr-dependence of the leading proton spectrum and the average multiplicity of the recoil system in the framework of the GEM, assuming the leading proton as a "random walk "<l object in the Pr-plane through the emJss1on of particles. The GBM is an infinite-component generalization of Stodolsky's bremsstrahlung modei5J based on the geometric picture for hadron collision.6 l In the impact parameter representation, the basic assumption of the GEM is that in collisions at each impact parameter b, the incident hadrons radiate clusters under Stodolsky' s condition, 5l i.e., Poissonian fluctuations with energy-momentum conservation constraint. From this assumption, cross sections are written as the integrated forms of the corresponding Stodolsky' s expression 111 the b-space. For example, the inclusi\·e and semiinclusive 2V-cluster production cross sections for the leading hadron take the following forms: u ,sJ