Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production

TL;DR

This paper calculates two-loop soft anomalous dimensions for heavy quark production, enabling precise NNLL resummation, with explicit formulas, numerical analysis, and extensions to collider processes.

Contribution

It provides the first explicit two-loop soft anomalous dimensions for heavy quark production, including a simple accurate approximation and extension to collider scenarios.

Findings

Derived explicit two-loop soft anomalous dimensions for heavy quarks.

Found a proportionality relation to one-loop results in massless limit.

Extended calculations to collider processes like single top and top pair production.

Abstract

I present results for two-loop soft anomalous dimensions for heavy quark production which control soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. I derive an explicit expression for the exact result and study it numerically for top quark production via e+ e- -> t tbar, and I construct a surprisingly simple but very accurate approximation. I show that the two-loop soft anomalous dimensions with massive quarks display a simple proportionality relation to the one-loop result only in the limit of vanishing quark mass. I also discuss the extension of the calculation to single top and top pair production in hadron colliders.