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We study a recently-proposed approach to the numerical evaluation ofmulti-loop Feynman integrals using available sector decomposition programs. Asour main example, we consider the two-loop integrals for the $\alpha \alpha_s$corrections to Drell-Yan lepton production with up to one massive vector bosonin physical kinematics. As a reference, we evaluate these planar and non-planarintegrals by the method of differential equations through to weight five.Choosing a basis of finite integrals for the numerical evaluation with SecDec3leads to tremendous performance improvements and renders the otherwiseproblematic seven-line topologies numerically accessible. As another example,basis integrals for massless QCD three loop form factors are evaluated withFIESTA4. Here, employing a basis of finite integrals results in an overallspeedup of more than an order of magnitude.

Numerical Multi-Loop Calculations via Finite Integrals and One-Mass EW-QCD Drell-Yan Master Integrals