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We compute the full set of two-loop Feynman integrals appearing in masslesstwo-loop four-point functions with two off-shell legs with the same invariantmass. These integrals allow to determine the two-loop corrections to theamplitudes for vector boson pair production at hadron colliders, $q \bar{q} \toV V$, and thus to compute this process to next-to-next-to-leading orderaccuracy in QCD. The master integrals are derived using the method ofdifferential equations, employing a canonical basis for the integrals. Weobtain analytical results for all integrals, expressed in terms of multiplepolylogarithms. We optimize our results for numerical evaluation by employingfunctions which are real valued for physical scattering kinematics and allowfor an immediate power series expansion.

The Two-Loop Master Integrals for $q \bar{q} \to V V$