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We present the calculation of the master integrals needed for the two-loopQCDxEW corrections to $ q + \bar{q} \to l^- + l^+$ and $ q + \bar{q}' \to l^- +\overline{\nu} \, , $ for massless external particles. We treat W and Z bosonsas degenerate in mass. We identify three types of diagrams, according to thepresence of massive internal lines: the no-mass type, the one-mass type, andthe two-mass type, where all massive propagators, when occurring, contain thesame mass value. We find a basis of 49 master integrals and evaluate them withthe method of the differential equations. The Magnus exponential is employed tochoose a set of master integrals that obeys a canonical system of differentialequations. Boundary conditions are found either by matching the solutions ontosimpler integrals in special kinematic configurations, or by requiring theregularity of the solution at pseudo-thresholds. The canonical master integralsare finally given as Taylor series around d=4 space-time dimensions, up toorder four, with coefficients given in terms of iterated integrals,respectively up to weight four.

Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering