Soft radiation in heavy-particle pair production: all-order colour structure and two-loop anomalous dimension

TL;DR

This paper develops a comprehensive theoretical framework for understanding soft gluon effects in heavy-particle pair production near threshold, including a new basis for colour space and an analytic two-loop anomalous dimension expression.

Contribution

It introduces a diagonalizing colour basis and derives an all-order soft function structure, extending previous results to all relevant production processes.

Findings

Derived an analytic two-loop soft anomalous dimension at threshold.

Constructed a basis in colour space that diagonalizes the soft function.

Extended the understanding of soft anomalous dimensions to all orders.

Abstract

We present a factorization formula for the production of pairs of heavy coloured particles in hadronic collisions at the production threshold, which forms the basis for the resummation of soft gluons and Coulomb gluons. We construct a basis in colour space that diagonalizes the soft function appearing in the factorization formula to all orders in perturbation theory. This extends recent results on the structure of soft anomalous dimensions and allows us to determine an analytic expression for the two-loop soft anomalous dimension at threshold for all production processes of interest.