Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

We present the calculation of the master integrals needed for the two-loopQCDEW corrections toq+ for massless external particles. We treat theWandZbosons as degenerate in mass. We identify three types ofdiagrams, according to the presence of massive internal lines: the no-mass type, the one-mass type, and the two-mass type, where all massive propagators, when occurring, containthe same mass value. We nd a basis of 49 master integrals and evaluate them with themethod of the di erential equations. The Magnus exponential is employed to choose aset of master integrals that obeys a canonical system of di erential equations. Boundaryconditions are found either by matching the solutions onto simpler integrals in specialkinematic con gurations, or by requiring the regularity of the solution at pseudothresholds.The canonical master integrals are nally given as Taylor series aroundd= 4 space-time dimensions, up to order four, with coecients given in terms of iterated integrals,respectively up to weight four.