Analytic two-loop master integrals for $tW$ production at hadron colliders: I

TL;DR

This paper analytically computes two-loop master integrals for $tW$ production at hadron colliders, focusing on integrals with a single massive propagator, using differential equations and multiple polylogarithms.

Contribution

It provides the first analytic solutions for these two-loop integrals in the context of $tW$ production, employing a canonical basis and differential equations in $d$ln form.

Findings

Analytic expressions for two-loop master integrals are obtained.

Results are expressed in terms of multiple polylogarithms.

Numerical checks confirm the accuracy of the analytical solutions.

Abstract

We present the analytic calculation of two-loop master integrals that are relevant for $tW$ production at hadron colliders. We focus on the integral families with only one massive propagator. After choosing a canonical basis, the differential equations for the master integrals can be transformed into the $d$ln form. The boundaries are determined by simple direct integrations or regularity conditions at kinematic points without physical singularities. The analytical results in this work are expressed in terms of multiple polylogarithms, and have been checked with numerical computations.