Two-loop QCD helicity amplitudes for massless quark-massless gauge boson scattering
E. W. N. Glover, M. E. Tejeda-Yeomans
TL;DR
This paper develops a complete framework to compute two-loop QCD helicity amplitudes for massless quark–massless gauge boson scattering by projecting a general d-dimensional tensor onto a minimal gauge-invariant basis, renormalizing in MSbar, and obtaining finite HV-scheme helicity amplitudes. It explicitly derives the perturbative expansion of tensor coefficients, analyzes ultraviolet and infrared structures via Catani's formalism, and constructs the corresponding helicity amplitudes for all physical processes, including detailed two-loop finite remainders. Cross-checks show agreement with independent results for related processes, strengthening the reliability of the HV approach and enabling NNLO phenomenology for dijet and photon-jet production. The work provides analytic expressions (and supplementary FORM outputs) that map tensor coefficients to helicity amplitudes, facilitating precise, scheme-consistent predictions at two loops in QCD.
Abstract
We present the two-loop helicity amplitudes for the scattering of massless quarks and massless gauge bosons in QCD. We use projector techniques to compute the coefficients of the general tensor describing the two-quark two-boson amplitude in conventional dimensional regularisation and use these coefficients to derive the helicity amplitudes in the 't Hooft-Veltman scheme. The structure of the infrared divergences agrees with that predicted by Catani while expressions for the finite remainders for q qbar -> gluon gluon, q qbar -> gluon gamma, q qbar -> gamma gamma and the processes related by crossing symmetry are given in terms of logarithms and polylogarithms that are real in the physical region. We have checked that the interference of tree and two-loop helicity amplitudes, summed over helicities and colours, reproduces the previous results for the finite remainders for interference of tree and two-loop amplitudes given in Refs. [1,2]. We also find agreement with the two-loop helicity amplitudes for quark-gluon scattering presented in Ref. [3].