One-loop QCD helicity amplitudes for $pp\to t\bar{t} j$ to $O(\epsilon^2)$

TL;DR

This paper analytically computes one-loop QCD helicity amplitudes for top-quark pair production with corrections up to $O( ext{epsilon}^2)$, providing essential ingredients for NNLO precision calculations.

Contribution

It presents the first analytical computation of helicity amplitudes including $O( ext{epsilon}^2)$ terms for NNLO accuracy in top-quark pair production.

Findings

Provides explicit expressions for master integrals with $O( ext{epsilon}^2)$ terms.

Develops numerical solutions for complex pentagon integral topologies.

Offers analytic boundary values and integral representations for key integrals.

Abstract

We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set of uniformly transcendental master integrals. We provide corrections up to $O(\epsilon^2)$ in the dimensional regulator for the first time which are relevant at NNLO. Four independent pentagon integral topologies appear in the complete description of the colour structure for which we provide numerical solutions using canonical form differential equations and the method of generalised power series expansions. Analytic forms of the boundary values are obtained in all cases except one where we find a one-dimensional integral representation.