NLO QCD predictions for $Wb\overline{b}$ production in association with up to three light jets at the LHC

In this article we present the next-to-leading order QCD predictions for $Wb\overline{b}+n\text{−}\mathrm{jet}$ ($n=0$, 1, 2, 3) production at the Large Hadron Collider with $\sqrt{s}=13\mathrm{TeV}$. We work in the four-flavor number scheme with a nonvanishing 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 $Wb\overline{b}$ production viewed as an irreducible background to $H(\to b\overline{b})W$ 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.

Figure 1

Representative diagrams for two subprocesses contributing to $pp\to Wb\overline{b}+3\text{−}\mathrm{jet}$ production. The diagram (b) 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 $Wb\overline{b}+2\text{−}\mathrm{jet}$ 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 $\sqrt{s}=13\mathrm{TeV}$, in the same way as the phenomenological study presented in this paper, and we 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 represents the precision of the finite piece of the calculation.

Figure 3

As in Fig. 2 but for $Wb\overline{b}+3\text{−}\mathrm{jet}$ production, considering only the leading-color contributions to the one-loop matrix elements. On the left we show results associated with the six-quark and on the right the ones associated with four-quark matrix elements.

Figure 4

Ratio of the invariant mass spectrum of the $b\overline{b}$ system for the 4FNS result to the 5FNS ones, for $W^{-}b\overline{b}$ (top) and $W^{-}b\overline{b}+1\text{−}\mathrm{jet}$ (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 $W^{-}b\overline{b}+0,1,2,3\text{−}\mathrm{jet}+X$ production in the left and $W^{+}b\overline{b}+0,1,2,3\text{−}\mathrm{jet}+X$ production in the right, with ${\mu }_0={\mu }_{\mathrm{r}}={\mu }_{\mathrm{f}}={{\widehat{H}}_{\mathrm{T}}}^{\prime }/2$. 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).

Figure 6

The $p_T$ distributions of the leading $b$ jet (ordered by $p_T$) in inclusive $W^{-}b\overline{b}+n\text{−}\mathrm{jet}$ production at the LHC with $\sqrt{s}=13\mathrm{TeV}$. The light-jet multiplicity increases from $n=0$ to $n=3$ from left to right. In the upper panels the dashed (blue) lines show the LO results and the solid (black) lines the NLO results. Vertical thin lines show the statistical error from the numerical integration. In the bottom panels we show the scale-dependence bands normalized to the NLO result, in blue for LO and dark gray for NLO.

Figure 7

The $p_T$ distributions of the subleading $b$ jet (ordered by $p_T$) in inclusive $W^{-}b\overline{b}+n\text{−}\mathrm{jet}$ production at the LHC with $\sqrt{s}=13\mathrm{TeV}$. Format as in Fig. 6.

Figure 8

The $p_T$ distributions of the softest light jet in inclusive $W^{+}b\overline{b}+n\text{−}\mathrm{jet}$ production. Format as in Fig. 6.

Figure 9

Distribution in the total transverse jet energy $H_T^{\text{jets}}$ of light and $b$ jets for inclusive $W^{-}b\overline{b}+n\text{−}\mathrm{jet}$ production at the LHC with $\sqrt{s}=13\mathrm{TeV}$. Format as in Fig. 6.

Figure 10

Distribution in the $\mathrm{\Delta }{R}_{b{l}^{-}}$ separation between the first $b$ jet (ordered in $p_T$) and the charged lepton for inclusive $W^{-}b\overline{b}+n$ jets production. Format as in Fig. 6.

Figure 11

The $p_T$ distribution of the $b\overline{b}$ system in inclusive $W^{-}b\overline{b}$ production, computed at LO (dashed blue line) and NLO (solid black line) as well as by employing the exclusive sums NLO+ (dash-dotted magenta line) and NLO++ (dotted green line). The second panel shows scale dependence bands normalized by NLO+, and in the third panel they are normalized by the corresponding central value. The bottom panel shows the associated PDF uncertainties normalized with our NLO results.

Figure 12

The $p_T$ of the $W$ boson in inclusive $W^{-}b\overline{b}$ production. Format as in Fig. 11.

Figure 13

The invariant mass of the $b\overline{b}$ system in inclusive $W^{-}b\overline{b}$ production. Format as in Fig. 11.