NLO QCD corrections to W boson production with a massive b-quark jet pair at the Fermilab Tevatron p-pbar collider

TL;DR

This work computes NLO QCD corrections to $q\bar{q}'\to Wb\bar{b}$ with full bottom-quark mass effects, comparing to the massless $m_b=0$ approximation at the Tevatron. The calculation includes virtual and real contributions with Phase Space Slicing and uses a $k_T$ jet algorithm under realistic cuts, assessing both inclusive and exclusive two-jet final states. The results show that finite $m_b$ effects amount to about 8% of the NLO cross-section and can reshape the $m_{b\bar{b}}$ distribution, especially at low invariant mass, with reduced scale uncertainty at NLO. These findings refine background predictions for $HW$ Higgs searches and single-top processes, highlighting the importance of retaining $m_b$ in precision QCD predictions for Tevatron analyses.

Abstract

We calculate the Next-to-Leading Order (NLO) QCD corrections to W-b-bbar production including full bottom-quark mass effects. We study the impact of NLO QCD corrections on the total cross section and invariant mass distribution of the bottom-quark jet pair at the Fermilab Tevatron p-pbar collider. We perform a detailed comparison with a calculation that considers massless bottom quarks. We find that neglecting bottom-quark mass effects overestimates the NLO total cross-section for W-b-bbar production at the Tevatron by about 8% independent of the choice of renormalization and factorization scale.

Figures (13)

• Figure 1: Tree level Feynman diagrams for $q\bar{q}^\prime\rightarrow b\bar{b}W$.
• Figure 2: Dependence of the total NLO QCD cross-section on the $\delta_s$ PSS parameter, when $\delta_c$ is fixed at $\delta_c=10^{-5}$. In the upper window we illustrate separately the cutoff dependence of the soft and hard-collinear part ($2\rightarrow 3$, red dashed curve) and of the hard non-collinear part ($2\rightarrow 4$, blue dotted curve) of the real corrections to the total cross-section. The $2\rightarrow 3$ curve also includes those parts of the $2\rightarrow 3$ NLO cross-section that do not depend on $\delta_c$ and $\delta_s$, i.e. the tree level and one-loop virtual contributions. The sum of all the contributions corresponds to the black solid line. The lower window shows a blow-up of the black solid line in the upper plot, to illustrate the stability of the result. The error bars indicate the statistical uncertainty of the Monte Carlo integration.
• Figure 3: Dependence of the total NLO QCD cross-section on the $\delta_c$ PSS parameter, when $\delta_s$ is fixed at $\delta_s=10^{-3}$. In the upper window we illustrate separately the cutoff dependence of the soft and hard-collinear part ($2\rightarrow 3$, red dashed curve) and of the hard non-collinear part ($2\rightarrow 4$, blue dotted curve) of the real corrections to the total cross-section. The $2\rightarrow 3$ curve also includes those parts of the $2\rightarrow 3$ NLO cross-section that do not depend on $\delta_c$ and $\delta_s$, i.e. the tree level and one-loop virtual contributions. The sum of all the contributions corresponds to the black solid line. The lower window shows a blow-up of the black solid line in the upper plot, to illustrate the stability of the result. The error bars indicate the statistical uncertainty of the Monte Carlo integration.
• Figure 4: Dependence of the LO (black solid band), NLO inclusive (blue dashed band), and NLO exclusive (red dotted band) total cross-sections on the renormalization/factorization scales, including full bottom-quark mass effects. The bands are obtained by varying both $\mu_R$ and $\mu_F$ between $\mu_0/2$ and $4\mu_0$ (with $\mu_0=m_b+M_W/2$).
• Figure 5: Dependence of the LO and NLO inclusive total cross-section on the renormalization/factorization scale, when $\mu_R\!=\!\mu_F$. The left hand side plot compares both LO and NLO total cross-sections for the case in which the bottom quark is treated as massless (MCFM) or massive (our calculation). The right hand side plot shows separately, for the massive case only, the scale dependence of the $q\bar{q}^\prime$ and $qg+\bar{q}g$ contributions, as well as their sum.