Analytic two-loop QCD amplitudes for tW production: Leading color and light fermion-loop contributions

We present the analytical results of the two-loop QCD 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 infrared divergences with the predictions from anomalous dimensions. Combining these with the one-loop squared amplitudes we have computed previously, we obtain the hard function relevant to a next-to-next-to-leading order 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 large top-quark velocity. After performing phase space integration and convolution with the parton distribution function, the leading color hard function gives a correction of about 5.4% to the leading order cross section, while the light fermion-loop diagrams contribute about -1.4%.