Two-loop QCD-EW master integrals for Z plus jet production at large transverse momentum

The production of electroweak Z bosons that decay to neutrinos and recoil against jets with large transverse momentum p(perpendicular to) is an important background process to searches for dark matter at the Large Hadron Collider (LHC). To fully benefit from opportunities offered by the future high-luminosity LHC, the theoretical description of the pp -> Z + j process should be extended to include mixed QCD-electroweak corrections. The goal of this paper is to initiate the computation of such corrections starting with the calculation of the Feynman integrals needed to describe two-loop QCD-electroweak contributions to qq over bar -> Z + g scattering amplitudes. Making use of the hierarchy between the large transverse momenta of the recoiling jet, relevant for heavy dark matter searches, and the Z boson mass mZ , we present the relevant master integrals as a series expansion in m(Z)/p(perpendicular to).