Transverse Momenta and Overlap Functions in Multiperipheral Models

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Abstract
The multi-Regge model is studied, with particular emphasis on the predicted slope of the elastic diffraction peak, and the average transverse momentum of the produced particles. The slope of the diffraction peak is proportional to the mean-square impact parameter, and in the multi-Regge model the total impact parameter is built up in a random walk, with each link in the multiperipheral chain corresponding to a step in the walk. A simple Chew-Pignotti model is incapable of fitting the inclusive production data at high energies: It predicts too slow an increase in the multiplicity of produced pions, and too rapid a shrinkage of the diffraction peak. To cure this problem, one must introduce "clustering" effects such as to reduce the over-all spread in impact parameter, and increase the density of produced pions in longitudinal-momentum space. Such effects were to be expected, in fact, because of resonance formation. A multiperipheral cluster model is introduced, in which the decay of the clusters is described via the statistical bootstrap model of Hagedorn and Frautschi. A crude fit to the high-energy data, in which all the clusters are given a common mass, shows that the average cluster mass is at least a couple of GeV, a surprisingly large figure. This provides some a posteriori justification for Hagedorn's thermodynamic model. The calculations are carried out using both approximate analytical methods and a Monte Carlo numerical program.