NLO QCD Predictions for $Wb\bar b$ Production in Association with up to Three Light Jets at the LHC

TL;DR

This work delivers the first NLO QCD predictions for $W\bar{b}b$ production in association with up to three light jets, using a 4-flavor scheme with massive bottom quarks. Employing an upgraded BlackHatII+SHERPA framework, it provides fixed-order parton-level results and introduces exclusive sums to stabilize large NLO corrections, particularly relevant for Higgs studies with $H\rightarrow b\bar{b}$ in associated $HW$ production. The study shows that NLO corrections are milder for higher jet multiplicities and that exclusive-sum predictions reduce uncertainties to the 10–17% level, with PDFs contributing only a few percent. The results, including $n$-tuple outputs, offer a valuable, publicly accessible resource for precision background modeling and for informing future NNLO or resummation efforts in multi-jet final states.

Abstract

In this article we present the next-to-leading order QCD predictions for $Wb\bar{b}+n$-jet ($n=0,1,2,3$) production at the Large Hadron Collider with $\sqrt{s}=13$ TeV. We work in the four-flavor number scheme with a non-vanishing bottom-quark mass and include all subprocesses at leading electroweak order as well as all heavy-fermion-loop effects. We show the impact of QCD corrections for total as well as differential cross sections and make an assessment of theoretical uncertainties of $Wb\bar{b}$ production viewed as an irreducible background to $H(\rightarrow b{\bar b})W$ studies. For the calculations we have employed an upgraded version of the BlackHat library which can handle massive fermions in combination with SHERPA. Our results can be explored through publicly available $n$-tuple sets.

Figures (13)

• Figure 1: Representative diagrams for two subprocesses contributing to $pp\rightarrow$$Wb\bar{b}+3$-jet production. The diagram \ref{['subfloat:nf']} displays a contribution from closed loops of top and bottom quarks.
• Figure 2: The logarithmic relative error of the full-color matrix elements for two types of subprocesses contributing to the $Wb\bar{b}+2$-jet production calculation. On the left we show results for the six-quark and on the right for four-quark matrix elements, respectively. We use a set of $10^5$ phase-space points sampled for the LHC setup with $\sqrt{s}=13$ TeV, in the same way as the phenomenological study presented in this paper, and use a dedicated calculation in quadruple precision for computing reference results. The dashed (blue) line represents the precision of the double pole, the dotted (green) line represents the single pole and the solid (black) line the precision of the finite piece of the calculation.
• Figure 3: As in fig. \ref{['fig:stabilityWbb2j']} but for $Wb\bar{b}+3$-jet production, considering only the leading-color contributions to the one-loop matrix elements. On the left we show results associated to the six-quark and on the right the ones associated to four-quark matrix elements.
• Figure 4: Ratio of the invariant mass spectrum of the $b\bar{b}$ system for 4FNS result to the 5FNS ones, for $W^-b\bar{b}$ (top) and $W^-b\bar{b}$+1-jet (bottom) production. The ratios are taken at LO (dashed blue line) and at NLO (solid black line). Statistical errors are shown as thin vertical lines. We include a dotted horizontal line at a ratio value of 1.
• Figure 5: The renormalization- and factorization-scale dependence of total cross sections for $W^-b\bar{b}$$+0,1,2,3$-jet$+X$ production in the left and $W^+b\bar{b}$$+0,1,2,3$-jet$+X$ production to the right, with $\mu_0=\mu_{\rm r}=\mu_{\rm f}={\hat{H}}_{\rm T}'/2$. The upper four panels show the dependence of LO (dashed blue line) and NLO (solid black line) predictions. The lower panel shows the K-factor (ratio of NLO/LO).