Master integrals for mixed QCD-QED corrections to charged-current Drell-Yan production of a massive charged lepton

TL;DR

This paper analytically computes master integrals for mixed QCD-QED two-loop corrections to the charged-current Drell-Yan process, including lepton mass effects and expressing results in Goncharov polylogarithms.

Contribution

It introduces a method to derive canonical form differential equations for these integrals, incorporating lepton mass dependence and expanding around four dimensions.

Findings

Master integrals expressed as Taylor series up to order four in (d-4).

Results include large logarithms of lepton mass over W-boson mass.

Analytic solutions in Goncharov polylogarithms up to weight four.

Abstract

The master integrals for the mixed QCD-QED two-loop virtual corrections to the charged-current Drell-Yan process $q\bar{q}^{\prime} \rightarrow \ell \nu$ are computed analytically by using the differential equation method. A suitable choice of master integrals makes it successful to cast the differential equation system into the canonical form. We keep the dependence on charged lepton mass in the building of differential equations and then expand the system against the ratio of small charged lepton mass to large $W$-boson mass. In such a way the final results will contain large logarithms of the form $\log(m_{\ell}^2/m_W^2)$. Finally, all the canonical master integrals are given as Taylor series around $d = 4$ spacetime dimensions up to order four, with coefficients expressed in terms of Goncharov polylogarithms up to weight four.