Soft gluon evolution and non-global logarithms

TL;DR

This paper develops a comprehensive framework for soft-gluon evolution at the amplitude level, incorporating Coulomb exchanges and a Lorentz-invariant variable, with methods to handle large colour matrices for practical computations.

Contribution

It introduces a general evolution algorithm for soft gluons applicable to any number of coloured partons, connecting it to renormalization group equations and addressing large colour matrix challenges.

Findings

Evolution algorithm includes Coulomb exchanges and Lorentz-invariant variable.

Systematic expansion method for large colour matrices.

Relation established between evolution algorithm and renormalization group equations.

Abstract

We consider soft-gluon evolution at the amplitude level. Our evolution includes Coulomb exchanges and applies to generic hard-scattering processes involving any number of coloured partons. We emphasise the special role played by a Lorentz-invariant evolution variable, which coincides with the transverse momentum of the latest emission in a suitably defined dipole zero-momentum frame. We also relate the evolution algorithm, which was used originally in the derivation of super-leading logarithms, to renormalization group evolution equations that have been encountered recently. Handling large colour matrices presents the most significant challenge to numerical implementations and we present a means to expand systematically about the leading colour approximation.