Two Feynman integral families for vector boson fusion at NNLO QCD

Abstract: We consider a planar and a non-planar two-loop Feynman integral family arising in non-factorisable quantum chromodynamics corrections to Higgs-boson production via vector boson fusion. We construct basis integrals which fulfil canonical differential equations with respect to seven variables for the external kinematics and an internal mass. One of the integral families involves nested square roots. We present strategies for deriving canonical master integrals, $\mathrm{d}\log$ forms and analytic continuation for such cases. Including also families with crossed massless legs, we express the $\varepsilon$-expanded integrals in terms of an algebraically independent function basis. For their evaluation, we employ numerical integration of the differential equations.