Analytic two-loop amplitudes for $tW$ production: leading color and light fermion-loop contributions

TL;DR

This paper analytically computes two-loop amplitudes for hadronic tW production, focusing on leading color and light fermion-loop contributions, providing results crucial for precise NNLO predictions.

Contribution

It presents the first analytical calculation of two-loop amplitudes for tW production including leading color and light fermion loops, using canonical differential equations and multiple polylogarithms.

Findings

The hard function varies slowly at small top quark velocities.

It increases dramatically at very large top quark velocities.

Leading color correction adds about 5.4% to the cross section.

Abstract

We present the analytical results of the two-loop amplitudes for hadronic $tW$ production, focusing on the leading color and light fermion-loop contributions. The calculation of the two-loop integrals is performed using the method of canonical differential equations. The results have been expressed in terms of multiple polylogarithms and checked by comparing the infra-red divergences with the predictions from anomalous dimensions. Combined with the one-loop squared amplitudes we have computed previously, we obtain the hard function relevant to a NNLO Monte Carlo calculation. We find that the hard function varies slowly in the region with small top quark velocity but increases dramatically in the region with very large top quark velocity. After phase space integration, the leading color hard function gives an about $5.4\%$ correction to the leading order cross section, while the light fermion loop contributes about $-1.4\%$.