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 $m_Z/p_{\perp }$.

arXiv comment23 pages, 5 figures, analytical results included as ancillary files

References in corpus (57)

• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• Asymptotic expansion of Feynman integrals near threshold
• Differential Equations for Two-Loop Four-Point Functions
• Differential Equations for Feynman Graph Amplitudes
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• Connection between Feynman integrals having different values of the space-time dimension
• Numerical evaluation of multiple polylogarithms
• Kira - A Feynman Integral Reduction Program
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Dimensionally Regulated One-Loop Integrals
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• FIESTA 4: optimized Feynman integral calculations with GPU support
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• Feynman Diagrams and Differential Equations
• Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• Soft triple-real radiation for Higgs production at N3LO
• New results for the epsilon-expansion of certain one-, two- and three-loop Feynman diagrams
• Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
• Magnus and Dyson Series for Master Integrals
• NLO QCD+EW predictions for V+jets including off-shell vector-boson decays and multijet merging
• Precise predictions for V+jets dark matter backgrounds
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• SecDec: A general program for sector decomposition
• - XSummer - Transcendental Functions and Symbolic Summation in Form
• Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• Electroweak corrections to W + jet hadroproduction including leptonic W-boson decays
• Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
• A quasi-finite basis for multi-loop Feynman integrals
• Electroweak corrections to dilepton + jet production at hadron colliders
• Electroweak corrections to hadronic production of W bosons at large transverse momenta
• The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
• W-boson plus jet differential distributions at NNLO in QCD
• Double Higgs boson production at NLO in the high-energy limit: complete analytic results
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the non-planar graphs
• Combination of electroweak and QCD corrections to single W production at the Fermilab Tevatron and the CERN LHC
• Phenomenology of the Z-boson plus jet process at NNLO
• QCD$\oplus$QED NNLO corrections to Drell Yan production
• One-loop weak corrections to hadronic production of Z bosons at large transverse momenta
• Logarithmic electroweak corrections to hadronic Z+1 jet production at large transverse momentum
• Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering
• Combining QED and QCD transverse-momentum resummation for Z boson production at hadron colliders
• Single mass scale diagrams: construction of a basis for the $\epsilon$-expansion
• Electroweak corrections to large transverse momentum production of W bosons at the LHC
• Double-Higgs boson production in the high-energy limit: planar master integrals
• Two-loop $gg\to Hg$ amplitude mediated by a nearly massless quark
• Mixed QCD$\otimes$QED corrections to on-shell $Z$ boson production at the LHC
• Some remarks on the epsilon-expansion of dimensionally regulated Feynman diagrams
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• LSJK - a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions
• Ratios of $W$ and $Z$ cross sections at large boson $p_T$ as a constraint on PDFs and background to new physics
• Two-loop amplitudes for processes $gg\to Hg,qg\to Hq$ and $q\bar{q}\to Hg$ at large Higgs transverse momentum
• Resummation of High Order Corrections in $Z$ Boson Plus Jet Production at the LHC
• On the computation of finite bottom-quark mass effects in Higgs boson production

Cited by in corpus (2)

• On $\epsilon$-factorised bases and pure Feynman integrals
• Two-loop mixed QCD-electroweak amplitudes for $Z+$jet production at the LHC: bosonic corrections