One-Loop QCD Corrections to $\bar{u}d\to t\bar{t}W$ at $\mathcal{O}({\epsilon }^2)$

Abstract

We present a computation of the one-loop QCD corrections to top-quark pair production in association with a $W$ boson, including terms up to order ${\epsilon }^2$ in dimensional regularization. Providing a first glimpse into the complexity of the corresponding two-loop amplitude, this result is a first step towards a description of this process at next-to-next-to-leading order (NNLO) in QCD. We perform a tensor decomposition and express the corresponding form factors in terms of a basis of independent special functions with compact rational coefficients, providing a structured framework for future developments. In addition, we derive an explicit analytic representation of the form factors, valid up to order ${\epsilon }^0$, expressed in terms of logarithms and dilogarithms. For the complete set of special functions required, we obtain a semi-numerical solution based on generalized power series expansion.

37 pages, 1 figure, 2 tables. The paper is complemented by a Zenodo repository found at https://zenodo.org/records/14810498. v2 is published in JHEP. Added paragraphs on pages 3, 24 and 27 to stress which points of the computation will be useful for the two-loop amplitude. Corrected minor typos and added citation to the two-loop integrals paper

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• One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}({\epsilon }^2)$