Fragmentation in a φ³-theory Ladder model

Abstract

We study the inclusive reaction a+b→c + (anything), where all the particles belong to a single scalar field φ(x) interacting through a gφ³(x) term. We do this in a ladder model for the forward abc̅ →abc̅ process, whose amplitude is intimately related to the inclusive distribution. The choice of the infinite sequence of ladder diagrams as well as the assumptions involved are natural extensions of analogous work in the literature for four-point functions. In the fragmentation limit, the model yields the expected Regge behavior as the initial energy tends to infinity. An expression is derived for the limiting distribution function E_cdσ/dp^→_c for fixed p^→_c as s→∞. The results are derived both in the "leading-term approximation" as well as by an exact Mellin-transform method.