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

TL;DR

This paper calculates two-loop QCD corrections to helicity amplitudes involving a massive vector boson coupling to quarks and gluons, including axial-vector effects, crucial for precise collider predictions.

Contribution

It introduces a new four-dimensional basis for amplitude decomposition and provides the complete two-loop form factors for vector and axial-vector couplings, including singlet contributions.

Findings

Finite parts of non-singlet form factors agree with previous results.

Singlet axial-vector amplitude includes axial anomaly contributions.

Results complete the two-loop amplitudes needed for NNLO vector-boson-plus-jet predictions.

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.