Two-Loop QCD-EW Master Integrals for Z Plus Jet Production at Large Transverse Momentum

Abstract

The production of electroweak $Z$ bosons that decay to neutrinos and recoil against jets with large transverse momentum $p_{\perp }$ 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 $pp\to Z+j$ 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 $q\bar{q}\to Z+g$ 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 $m_Z/p_{\perp }$.

23 pages, 5 figures, analytical results included as ancillary files