Asymptotic Behavior of Particle Distributions in Hadron Collisions

Abstract

The distribution functions for the "inclusive" production of $N$ specified particles plus anything else are treated from a $J$-plane point of view. The variables relevant to the exhibition of the asymptotic behavior of these distributions are chosen during a group-theoretic discussion of the matrix elements involved. After the variables are located in this fashion, a crossed-channel partial-wave analysis is carried out to exploit the $\mathrm{SO}(1,3)\mathrm{}$ symmetry of the production cross sections, and in the context of this partial-wave structure the multi-Regge asymptotics are presented. Such features as pionization and limiting fragmentation are treated, as are certain phenomena involving the approach to limiting distributions, including the rate of approach and specific dependences on certain variables related to longitudinal momenta. Single- and double-particle production is treated in detail, and then a set of numerical estimates is made for proton-proton collisions with incident lab momenta of about 200-500 $\frac{\mathrm{GeV}}{c}$ to give an indication where many of the phenomenological results might be tested. A mathematical appendix is provided for those interested in group theory.