The two-loop soft function for heavy quark pair production at future linear colliders

TL;DR

This paper calculates the two-loop threshold soft function for heavy quark pair production in e+ e- annihilation, generalizing the Drell-Yan soft function to include non-zero quark masses, aiding precision collider physics.

Contribution

It introduces a framework based on differential equations for calculating massive soft functions at high orders, linking massive and massless soft Wilson line matrix elements.

Findings

Derived the two-loop soft function for massive quarks.

Established a method to relate massive and massless soft functions.

Provided results useful for precision collider physics.

Abstract

We report on the calculation of the threshold soft function for heavy quark pair production in e+ e- annihilation at two-loop order. Our main result is a generalization of the familiar Drell-Yan threshold soft function to the case of non-zero primary quark mass. We set up a framework based on the method of differential equations which allows for the straightforward calculation of the bare soft function to arbitrarily high orders in the dimensional regularization parameter. Remarkably, we find that we can obtain the bare two-loop Drell-Yan soft function from the heavy quark soft function to the order in epsilon required for a two-loop calculation by making simple replacements. We expect that our results will be of use, both as an important input for precision physics calculations at linear colliders and, more formally, as a first step towards a better understanding of the connection between vacuum matrix elements of massive soft Wilson lines and vacuum matrix elements of massless soft Wilson lines.