Wide-angle behavior of a double-scattering diagram

Abstract

Landshoff has recently pointed out that in composite models for hadron-hadron wide-angle scattering, processes where the constituents remain close to their mass shells throughout the scattering can dominate the wide-angle cross sections. We use a Feynman parametric integral to estimate the phase space for such a process and confirm Landshoff's result. The differential cross section for elastic $\pi -\pi$ scattering at fixed c.m. angle is found to fall off as $s^{-5\mathrm{}}$, rather than as $s^{-6\mathrm{}}$, which is predicted by the dimensional-counting rules.