Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC

TL;DR

This paper computes the complex two-loop QCD corrections for top-quark pair plus jet production at the LHC, providing analytical results and a C++ library for phenomenology.

Contribution

It introduces a novel analytical extraction of finite remainders of two-loop amplitudes and a new numerical technique for evaluating special functions in QCD calculations.

Findings

Finite remainders obtained analytically from finite field evaluations.

A C++ library for practical use in collider phenomenology.

New numerical methods for evaluating special functions across phase space.

Abstract

We present a leading colour computation of the double virtual contributions to top-quark pair production in association with a jet at a hadron collider at next-to-next-to-leading order in QCD. The finite remainders of the two-loop amplitudes, after subtraction of infrared and ultraviolet divergences, are extracted analytically from evaluations over finite fields by using a (potentially) overcomplete basis of special functions defined through their differential equations. We construct the colour- and spin-summed interference with the tree-level amplitudes and present a \texttt{C++} library suitable for immediate use in phenomenological studies. We present new techniques for the evaluation of the special functions through direct numerical integration of differential equations which perform well across the full physical phase space.