Two-loop QCD corrections to the $V\to q\bar{q}g$ helicity amplitudes with axial-vector couplings

Abstract

We compute the two-loop corrections to the helicity amplitudes for the coupling of a massive vector boson to a massless quark-antiquark pair and a gluon, accounting for vector and axial-vector couplings of the vector boson and distinguishing isospin non-singlet and singlet contributions. A new four-dimensional basis for the decomposition of the amplitudes into 12 invariant tensor structures is introduced. The associated form factors are then computed up to two loops in QCD using dimensional regularization. After performing renormalization and infrared subtraction, the finite parts of the renormalized non-singlet vector and axial-vector form factors are shown agree with each other, and to reproduce the previously known two-loop amplitudes. The singlet axial-vector amplitude receives a contribution from the axial anomaly from two loops onwards. This amplitude is computed for massless and massive internal quarks. Our results provide the last missing two-loop amplitudes entering the NNLO QCD corrections of vector-boson-plus-jet production at hadron colliders.

arXiv commentversion 3: added missing term in the renormalization of the pure-singlet axial contribution, eq (4.13) and updated ancillary files

References in corpus (37)

• Scattering Amplitudes with Open Loops
• Harmonic Polylogarithms
• Asymptotic expansion of Feynman integrals near threshold
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• OpenLoops 2
• The renormalization of the axial anomaly in dimensional regularization
• One-Loop Amplitudes for e^+ e^- to Four Partons
• Numerical evaluation of multiple polylogarithms
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Reduze - Feynman Integral Reduction in C++
• Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Numerical Evaluation of Harmonic Polylogarithms
• Precise QCD predictions for the production of a Z boson in association with a hadronic jet
• NNLO corrections to event shapes in $e^{+}{e}^{-}$ annihilation
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• Two-Loop QCD Helicity Amplitudes for $e^{+}{e}^{-}\to 3$~Jets
• The Two-Loop QCD Matrix Element for $e^{+}{e}^{-}\to 3$ Jets
• Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms
• Event shapes and jet rates in electron-positron annihilation at NNLO
• Jet rates in electron-positron annihilation at O(α_s^3) in QCD
• Three-jet production in electron-positron collisions using the CoLoRFulNNLO method
• On soft singularities at three loops and beyond
• Analytic Continuation of Massless Two-Loop Four-Point Functions
• Two-loop QCD helicity amplitudes for $q\bar{q}\to W^{\pm }\gamma$ and $q\bar{q}\to Z^0\gamma$
• Lepton-pair production at hadron colliders at N${}^3$LO in QCD
• NNLO QCD corrections to jet production in deep inelastic scattering
• Tensor decomposition for bosonic and fermionic scattering amplitudes
• Adaptive Integrand Decomposition in parallel and orthogonal space
• Physical projectors for multi-leg helicity amplitudes
• Next-to-Leading Order QCD Corrections to Jet Cross Sections and Jet Rates in Deeply Inelastic Electron Proton Scattering
• NNLO QCD corrections to event orientation in e+e- annihilation
• The complete singlet contribution to the massless quark form factor at three loops in QCD
• The three-loop singlet contribution to the massless axial-vector quark form factor
• Renormalization of the axial current operator in dimensional regularization at four-loop in QCD

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