We present the first calculation for the hadroproduction of a $W$ boson in association with a massive bottom ($b$) quark-antiquark pair at next-to-next-to-leading order (NNLO) in QCD perturbation theory. We exploit the hierarchy between the $b$-quark mass and the characteristic energy scale of the process to obtain a reliable analytic expression for the two-loop virtual amplitude with three massive legs, starting from the corresponding result available for massless $b$ quarks. The use of massive $b$ quarks avoids the ambiguities associated with the correct flavor assignment in massless calculations, paving the way to a more realistic comparison with experimental data. We present phenomenological results considering proton-proton collisions at center-of-mass energy $\sqrt{s}=13.6\mathrm{TeV}$ for inclusive $Wb\overline{b}$ production and within a fiducial region relevant for the associated production of a $W$ boson and a Higgs boson decaying into a $b\overline{b}$ pair, for which $Wb\overline{b}$ production represents one of the most relevant backgrounds. We find that the NNLO corrections are substantial and that their inclusion is mandatory to obtain reliable predictions.

• Received 16 December 2022
• Accepted 30 March 2023
• Corrected 29 November 2023

DOI:https://doi.org/10.1103/PhysRevD.107.074032

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Published by the American Physical Society