Two-loop QCD helicity amplitudes for massless quark-quark scattering

TL;DR

This paper delivers analytic two-loop QCD helicity amplitudes for massless quark-quark scattering, covering q q̄ → Q Q̄ and crossing-related processes, by constructing a comprehensive d-dimensional tensor basis and extracting coefficients with projection operators.Renormalisation is performed in the MS-bar scheme and the infrared pole structure is shown to match Catani’s predictions, while the finite remainders are expressed in terms of logarithms and polylogarithms within the t'Hooft-Veltman scheme, ensuring real-valued results in the physical region.The main contributions are the explicit finite two-loop helicity amplitudes, their organization by color and flavor, and the validation against previous interference results, which collectively enable a viable route to NNLO jet phenomenology at hadron colliders.

Abstract

We present the two-loop helicity amplitudes for the scattering of massless quarks in QCD. We use projector techniques to compute the coefficients of the general four-quark amplitude at up to two-loops 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 $q \bar q \to Q\bar Q$ 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].