Analytical Soft Functions for Heavy-Quark Final States at Hadron Colliders

TL;DR

This paper computes a complex two-loop soft function for heavy-quark pair production with a color-singlet at hadron colliders, enabling more precise theoretical predictions for heavy-quark physics at the LHC.

Contribution

It provides the first complete analytic two-loop soft function for heavy-quark pair production with generic kinematics, including a decomposition into color correlators.

Findings

Analytic two-loop soft function in closed form.

Decomposition into dipole and tripole color correlators.

Enhanced precision for heavy-quark process predictions at the LHC.

Abstract

We present the first computation of the complete two-loop, fully-differential soft function describing the production of a heavy-quark pair in association with a color-singlet system at hadron colliders. This result constitutes one of the most complex soft functions known to date and it is obtained in closed analytic form for generic multi-dimensional kinematics. This allows us to obtain novel analytic results for the transverse-momentum-dependent and threshold soft functions in this class of processes. We further obtain a decomposition of the soft function into dipole and tripole color correlators, thereby supplying essential building blocks for processes involving a heavy-quark pair produced together with additional light jets at both hadron and lepton colliders. These results represent a key ingredient for advancing precision predictions for heavy-quark physics at the LHC.