Two-loop amplitude for $t\bar{t}W$ production at hadron colliders in the leading colour approximation

Abstract

In this contribution I present the first exact calculation of the leading-colour two-loop QCD amplitude for the associated production of a top-anti-top pair and a W boson. I discuss strategies to address the complexity of the computation, which involves complicated analytic structures, such as nested square roots, elliptic functions, and expressions with a high degree of algebraic complexity. The final result is expressed in terms of a set of special functions, which are evaluated using the method of differential equations, and rational coefficients, evaluated via finite field techniques.

11 pages, 2 figures, 2 tables; contribution to the proceedings of the Loops and Legs in Quantum Field Theory conference (LL2026), April 12-17, 2026, Bayreuth, Germany