Analytic two-loop master integrals for $tW$ production at hadron colliders. Part II

TL;DR

This paper provides analytic two-loop master integrals for hadronic tW production, employing canonical bases and series expansions, facilitating precise amplitude calculations for collider physics.

Contribution

It introduces new analytic solutions for two-loop integrals with massive propagators, including non-planar cases, using polylogarithms and series expansion techniques.

Findings

Master integrals expressed in terms of multiple polylogarithms.

Series expansion approach for non-planar integrals with square root complexities.

Results enable more accurate two-loop amplitude computations for tW production.

Abstract

We present analytic results of the two-loop master integrals for hadronic $tW$ production that contain two massive propagators. For the planar integral family, we succeed in constructing the canonical basis, so the results are written in terms of multiple polylogarithms. The master integrals in the non-planar integral families have been calculated by Taylor series expansion around $m_W^2=0$. Even with this simplification, there are multiple square roots involved in the differential equations, which can not be rationalized simultaneously. We find that a proper linear combination of the integral basis alleviates the problem so that the results are expressed by multiple polylogarithms or single integrals over multiple polylogarithms up to weight four. These single integrals can be evaluated using the classic Newton-Cotes formulas. Our analytic results of master integrals would be used in the computation of the two-loop amplitudes for $tW$ production.