Collision integral for multigluon production in a scalar quark and gluon model

TL;DR

This paper develops a scalar gluon and quark model to derive transport equations and a collision integral for high-energy quark-gluon interactions, highlighting the dominance of gluon production diagrams and initial/final state interactions.

Contribution

It introduces a generalized collision integral for quark transport involving multiple gluon exchanges within a scalar model, emphasizing the role of gluon production and state interactions.

Findings

Explicit derivation of two-body scattering cross sections in the Boltzmann equation.

Identification of gluon production diagrams as dominant in the large color number limit.

Development of a generalized Boltzmann-like equation with multiple gluon exchanges.

Abstract

A model of scalar gluons and scalar quarks that successfully gives a ln s behavior in high energy qq scattering and which contains a three gluon vertex is used to derive transport equations for the quarks and gluons. Quasiparticle and semiclassical approximations are utilized. In particular, the collision integral is studied. At first the terms are organized according to the number of gluon exchange interactions, and it is shown explicitly that the occurrence of all two body differential scattering cross sections in the Boltzmann equation requires an evaluation of all terms to this order. One obtains qg-> qg, q bar q->gg, qq->qq, and q bar q -> q bar q. An additional ordering according to the inverse number of colors reveals that the quark loop diagrams are suppressed, and diagrams that lead to gluon production or scattering dominate. The self energy with three gluons exchanged is then examined. From this, it is evident that initial as well as final state interactions enter into a generalized collision integral. The generalized Boltzmann-like equation involving n gluon exchange for quark transport is given.