NNLO QCD corrections to associated $WH$ production and $H \to b \bar b$ decay

TL;DR

The paper delivers fully differential NNLO QCD corrections to Higgs production in association with a W boson and the subsequent H → bb decay in the massless b-quark limit, using a nested soft-collinear subtraction framework. It includes top-quark-loop Higgs emission contributions and a previously neglected NNLO decay term, and examines the impact of experimental cuts on kinematic distributions. The study demonstrates substantial corrections in certain observables and validates fixed-order results against parton-shower simulations, emphasizing the importance of precise NNLO predictions for WH(b b) phenomenology. It also highlights the need for fully massive-bottom calculations to address interference effects that arise at NNLO in the decay stage.

Abstract

We present a computation of the next-to-next-to-leading order (NNLO) QCD corrections to the production of a Higgs boson in association with a W boson at the LHC and the subsequent decay of the Higgs boson into a b-bbar pair, treating the b-quarks as massless. We consider various kinematic distributions and find significant corrections to observables that resolve the Higgs decay products. We also find that a cut on the transverse momentum of the W boson, important for experimental analyses, may have a significant impact on kinematic distributions and radiative corrections. We show that some of these effects can be adequately described by simulating QCD radiation in Higgs boson decays to b-quarks using parton showers. We also describe contributions to Higgs decay to a b-bbar pair that first appear at NNLO and that were not considered in previous fully-differential computations. The calculation of NNLO QCD corrections to production and decay sub-processes is carried out within the nested soft-collinear subtraction scheme presented by some of us earlier this year. We demonstrate that this subtraction scheme performs very well, allowing a computation of the coefficient of the second order QCD corrections at the level of a few per mill.

Figures (15)

• Figure 1: Results for the rapidity and the transverse momentum distributions of the Higgs boson. Upper panes -- results in consecutive orders of perturbation theory. Lower panes -- ratios of NLO to LO and NNLO to NLO. The renormalization and factorization scales are set to $\mu = M_{WH}$. In this plot, LO, NLO and NNLO results are all computed with NNLO PDFs, see text for detail.
• Figure 2: Results for rapidity and transverse momentum distributions of the charged lepton from the decay of a $W^-$ boson. Upper panes -- results in consecutive orders of perturbation theory. Lower panes -- ratios of NLO to LO and NNLO to NLO. The renormalization and factorization scales are set to $\mu = M_{WH}$. In this plot, LO, NLO and NNLO results are all computed with NNLO PDFs, see text for detail.
• Figure 3: Illustrative interference diagrams that contribute to the $H\to b \bar{b}$ decay rate for $C_1\ne 0$. See text for details.
• Figure 4: The invariant mass of a $b$-jet and a $\bar{b}$-jet that best approximates the Higgs boson mass. Left pane -- without the $p_\perp^{W}$ cut, right pane -- with the $p_{\perp}^{W} > 150~{\rm GeV}$ cut. Lower panes -- ratio of full NNLO to approximate NNLO. The renormalization and factorization scales are set to $\mu_R=\mu_F = M_{WH}$ for the production process and to $\mu_R = m_H$ for the decay process. See text for further details.
• Figure 5: The invariant mass of a $b$-jet and a $\bar{b}$-jet that best approximates the Higgs boson mass. The $p_{\perp}^{W} > 150~{\rm GeV}$ cut is applied. Left pane: only NNLO corrections to decay are included. Right pane: NLO corrections to the production and NLO corrections to the decay are included. Lower panes -- ratio to approximate NNLO. See text for further details.