W- and Z-boson production with a massive bottom-quark pair at the Large Hadron Collider

TL;DR

This study provides NLO QCD predictions for $Wb\bar{b}$ and $Zb\bar{b}$ production at the LHC, including full bottom-quark mass effects, and compares to massless-$b$ results from MCFM. It shows that $\mathrm{Z}b\bar{b}$ cross sections have well-behaved scale dependence, while $Wb\bar{b}$ exhibits large inclusive scale uncertainties due to the new tree-level $qg$-initiated channel, with bottom-m-quark mass effects most pronounced in regions where kinematic observables are near $m_b$. NLO corrections significantly reshape differential distributions beyond simple K-factors, and massless approximations can overestimate cross sections by up to about 10% in some cases. The findings underscore the need for resummation or NLO-showered approaches for precise Higgs-background predictions and highlight the relative viability of massless versus massive treatments across different jet-inclusive scenarios.

Abstract

We present total and differential cross sections for W b anti-b and Z b anti-b production at the CERN Large Hadron Collider with a center-of-mass energy of 14 TeV, including Next-to-Leading Order (NLO) QCD corrections and full bottom-quark mass effects. We also provide numerical results obtained with a center-of-mass energy of 10 TeV. We study the scale uncertainty of the total cross sections due to the residual renormalization- and factorization-scale dependence of the truncated perturbative series. While in the case of Z b anti-b production the scale uncertainty of the total cross section is reduced by NLO QCD corrections, the W b anti-b production process at NLO in QCD still suffers from large scale uncertainties, in particular in the inclusive case. We also perform a detailed comparison with a calculation that considers massless bottom quarks, as implemented in the Monte Carlo program MCFM. The effects of a non-zero bottom-quark mass (m_b) cannot be neglected in phase-space regions where the relevant kinematic observable, such as the transverse momentum of the bottom quarks or the invariant mass of the bottom-quark pair, are of the order of m_b. The effects on the total production cross sections are usually smaller than the residual scale uncertainty at NLO in QCD.

Figures (16)

• Figure 1: Dependence of the LO (black, solid), NLO exclusive (blue, solid), and NLO inclusive (red, solid) total cross sections for $W^+b\bar{b}$ and $W^-b\bar{b}$ production on the renormalization/factorization scales, including full $b$-quark mass effects, when $\mu=\mu_r=\mu_f$ is varied between $\mu_0/2$ and $2\mu_0$ (with $\mu_0=M_W+2m_b$). We also show the individual channels, $q\bar{q}^\prime$ (dash-dotted) and $qg+\bar{q}g$ (dotted), for the inclusive (red) and exclusive (blue) cases.
• Figure 2: LO (black, dashed), NLO inclusive (red, solid) and NLO exclusive (blue, dot-dashed) transverse momentum distributions for the $b$ jet with the leading (left hand side) and subleading (right hand side) transverse momentum in $W^+b\bar{b}$ (upper plots) and $W^-b\bar{b}$ (lower plots) production. The lower window shows a bin-by-bin K factor, for the inclusive (red, solid) and exclusive (blue, dot-dashed) cases.
• Figure 3: LO (black, dashed), NLO inclusive (red, solid) and NLO exclusive (blue, dot-dashed) transverse momentum distributions for the $W^+$ (left hand side) and $W^-$ (right hand side) bosons in $W^+b\bar{b}$ and $W^-b\bar{b}$ production respectively. The lower window shows a bin-by-bin K factor, for the inclusive (red, solid) and exclusive (blue, dot-dashed) cases.
• Figure 4: LO (black, dashed), NLO inclusive (red, solid) and NLO exclusive (blue, dot-dashed) pseudorapidity distributions for the $b$ jet with the leading (left hand side) and subleading (right hand side) transverse momentum in $W^+b\bar{b}$ (upper plots) and $W^-b\bar{b}$ (lower plots) production. The lower window shows a bin-by-bin K factor, for the inclusive (red, solid) and exclusive (blue, dot-dashed) cases.
• Figure 5: LO (black, dashed), NLO inclusive (red, solid) and NLO exclusive (blue, dot-dashed) pseudorapidity distributions for the $W^+$ (left hand side) and $W^-$ (right hand side) bosons in $W^+b\bar{b}$ and $W^-b\bar{b}$ production respectively. The lower window shows a bin-by-bin K factor, for the inclusive (red, solid) and exclusive (blue, dot-dashed) cases.