Two-loop scattering amplitude for heavy-quark pair production through light-quark annihilation in QCD

TL;DR

This paper provides the first complete analytic calculation of the two-loop scattering amplitude for heavy-quark pair production via light-quark annihilation in QCD, including all form factors and both planar and non-planar diagrams.

Contribution

It delivers the full analytic evaluation of the two-loop amplitude for $q ar{q} o Q ar{Q}$ in QCD, extending previous partial results to all form factors and diagram types.

Findings

Validated numerical results with analytic expressions.

Expressed amplitudes in terms of polylogarithms and constants up to weight four.

Covered both planar and non-planar diagram contributions.

Abstract

We present the first full analytic evaluation of the scattering amplitude for the process $q {\bar q} \to Q {\bar Q}$ up-to two loops in Quantum Chromodynamics, for a massless $(q)$ and a massive $(Q)$ quark flavour. The interference terms of the one- and two-loop amplitudes with the Born amplitude, decomposed in terms of gauge invariant form factors depending on the colour and flavour structure, are analytically calculated by keeping complete dependence on the squared center-of-mass energy, the squared momentum transfer, and the heavy-quark mass. The results are expressed as Laurent series around four space-time dimensions, with coefficients given in terms of generalised polylogarithms and transcendental constants up-to weight four. Our results validate the known, purely numerical calculations of the squared amplitude, and extend the analytic knowledge, previously limited to a subset of form factors, to their whole set, coming from both planar and non-planar diagrams, up-to the second order corrections in the strong coupling constant.