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$_{⊥}$ is an important background process to searches for dark matter at the Large Hadron Collider (LHC). To fully benet 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 qq̅ → 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 m$_{Z}$, we present the relevant master integrals as a series expansion in m$_{Z}$/p$_{⊥}$.