Next-to-next-to-leading order threshold soft function for $tW$ production

TL;DR

This paper calculates the two-loop soft function for $tW$ production near threshold, enabling more precise resummation of large logarithms in collider predictions.

Contribution

It provides the first analytical computation of the two-loop soft function for $tW$ production using reverse unitarity and differential equations methods.

Findings

Analytical expression for the two-loop soft function in terms of polylogarithms.

Analysis of the soft function's behavior in low and high energy limits.

Foundation for next-to-next-to-next-to-leading logarithmic resummation in $tW$ production.

Abstract

We compute the two-loop soft function for the associated production of a top quark and a $W$ boson near the threshold, where the invariant mass of the $tW$ system approaches the collider energy. We employ the reverse unitarity technique and integration-by-parts identities to reduce soft loop integrals to a minimal basis of master integrals. These master integrals are analytically evaluated using the method of differential equations, yielding results expressed in terms of multiple polylogarithms. Additionally, we analyze the asymptotic behavior of the soft function in the low and high energy limits. Our results provide a vital component for threshold resummation at the next-to-next-to-next-to-leading logarithmic level in this process.