One-loop QCD helicity amplitudes for $pp\to t\bar{t}j$ to $O({\epsilon }^2)$

Abstract

We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set of uniformly transcendental master integrals. We provide corrections up to $O({\epsilon }^2)$ in the dimensional regulator for the first time which are relevant at NNLO. Four independent pentagon integral topologies appear in the complete description of the colour structure for which we provide numerical solutions using canonical form differential equations and the method of generalised power series expansions. Analytic forms of the boundary values are obtained in all cases except one where we find a one-dimensional integral representation.

arXiv comment37 pages. ancillary files containing analytic amplitudes and integral evaluation routines. v2 references added. v3 fixing minor typos in the text and in the ancillary files

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Cited by in corpus (10)

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• Numerical evaluation of two-loop QCD helicity amplitudes for $gg\to t\bar{t}g$ at leading colour
• Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders
• Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar{t}+$jet production at leading colour
• p-adic reconstruction of rational functions in multi-loop amplitudes
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
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• One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}({\epsilon }^2)$