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

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 $-1.4\%$.

20 pages, 8 figures

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• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Analytic two-loop master integrals for $tW$ production at hadron colliders. Part II
• Next-to-next-to-leading order threshold soft function for $tW$ production
• Subtraction of the $t\bar{t}$ contribution in $tW\bar{b}$ production at the one-loop level
• Constraining dimension-6 SMEFT with higher-order predictions for $pp\to tW$
• Approximate N${}^2$LO and N${}^3$LO QCD Predictions for $tW$ Production