The complete set of two-loop master integrals for Higgs plus jet production in QCD

In this paper we complete the computation of the two-loop master integrals relevant for Higgs plus one jet production initiated in [1-3]. Specifically, we compute the remaining family of non-planar master integrals. The computation is performed by defining differential equations along contours in the kinematic space, and by solving them in terms of one-dimensional generalized power series. This method allows for the efficient evaluation of the integrals in all kinematic regions, with high numerical precision. We show the generality of our approach by considering both the top- and the bottom-quark contributions. This work along with [1-3] provides the full set of master integrals relevant for the NLO corrections to Higgs plus one jet production, and for the real-virtual contributions to the NNLO corrections to inclusive Higgs production in QCD in the full theory.