Towards two-loop QCD corrections to $\mathbf{pp}\to \mathbf{t}\bar{\mathbf{t}}\mathbf{j}$

Abstract

I discuss the status of the computation of the two-loop QCD corrections to top-quark pair production associated with a jet at hadron colliders. This amplitude is a missing ingredient for next-to-next-to-leading order (NNLO) QCD predictions. I briefly present computational techniques to tackle the algebraic and analytic complexities of two-loop multi-scale amplitudes, in particular where massive propagators give rise to elliptic Feynman integrals. I then describe how a special function basis for the helicity amplitudes is obtained and present first numerical evaluations for the finite remainders of the $gg\to t\bar{t}g$ channel, after the infrared and ultraviolet poles have been identified analytically.

Comments: Talk at the 17th International Workshop on Top Quark Physics (Top2024), 22-27 September 2024