Associated production of a $W$ boson and massive bottom quarks at next-to-next-to-leading order in QCD

TL;DR

This work delivers the first next-to-next-to-leading order (NNLO) QCD calculation for hadroproduction of a $W$ boson in association with a massive $b\bar{b}$ pair, thereby avoiding flavour-assignment ambiguities inherent to massless $b$-quark treatments. Leveraging the hierarchy $m_b \ll Q$, the authors massify the known massless two-loop amplitude to construct the massive two-loop contribution, and compute the NNLO cross section using the $q_T$ subtraction formalism with a massification formula $\mathcal{M}^{m}_{2} = \mathcal{M}^{m=0}_{2} + Z_{[q]}^{1} \mathcal{M}^{m=0}_{1} + Z_{[q]}^{2} \mathcal{M}^{m=0}_{0}$. The results, at $\sqrt{s}=13.6$ TeV for inclusive and a Higgs-background-relevant fiducial region, show substantial NNLO corrections relative to NLO and reduced scale uncertainties, with the fiducial distributions (notably $m_{bb}$) shifting and stabilizing at NNLO. This work enables direct data comparisons, supports future Monte Carlo matching to parton showers, and provides a framework to extend the methodology to other heavy-quark processes such as $W$+charm and $Z+b\bar{b}$.

Abstract

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 bottom quarks. The use of massive $b$ quarks avoids the ambiguities associated with the correct flavour assignment in massless calculations, paving the way to a more realistic comparison with experimental data. We present phenomenological results considering proton-proton collisions at centre-of-mass energy $\sqrt{s}=13.6$ TeV for inclusive $Wb \bar b$ production and within a fiducial region relevant for the associated production of a $W$ boson and a Higgs boson decaying into a $b \bar b$ pair, for which $Wb \bar b$ 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.

Figures (2)

• Figure 1: Invariant-mass distribution of the $b$-jet pair in fiducial region, in bin I (left) and bin II (right), at LO (red), NLO (green) and NNLO (blue). See text for more details.
• Figure 2: Rapidity and azimuthal angle separation $\Delta R_{bb}$ between the two leading $b$ jets in the 4FS (blue) and in the 5FS with $a=0.1$ (green) calculations. For reference, the 5FS result with $a=0.2$ is also shown (orange). The 5FS results are taken from Ref. Hartanto:2022ypo.