Scaling and nonscaling of inclusive pion production in nuclear collisions

An examination is made of the degree of scaling observed in inclusive pion production from high energy nuclear collisions. While apparent scaling does occur for forward pion production, the scaling limit is not reached in backward $\pi$ production between 0.7-8 GeV/nucleon. We show that the shapes of the pion inclusive cross sections in both the forward and backward directions can be explained by a simple, hard scattering model employing elementary proton-proton $\pi$ production rates, or alternatively, in terms of elementary proton-light cluster $\pi$ production rates. The essential features of this model are an invariant parametrization of the elementary subprocess, the proper handling of kinematical effects, and the use of a long-tailed internal momentum distribution function for nucleons or clusters. We find that much of the "apparent" scaling in the forward direction can be attributed to kinematical effects. The importance of final state interactions on the interpretation of the internal momentum (Fermi) distribution is emphasized, and the connection to quasi-two-body scaling is examined.