Model calculations of electroproduction and inclusive annihilation cross sections

Abstract

We have studied "deep-inelastic electroproduction" and "inclusive $e^{+}{e}^{-}$ annihilation" in massless ${\phi }^4$ theory in the ladder approximation. The relevant Bethe-Salpeter-type equations can be completely solved and the physically important asymptotic limits are studied. The behavior of the moments of the structure functions is analyzed, and the "anomalous dimensions" which govern the asymptotic power behavior of the moments in the two cases are found. The anomalous dimensions are quite different in general, but are simply related in the weak-coupling limit.