NLO QCD corrections to Z b anti-b production with massive bottom quarks at the Fermilab Tevatron

TL;DR

This study delivers a complete NLO QCD analysis of Z b bbar production in hadronic collisions with full bottom-quark mass effects, assessing both total cross sections and the b bbar invariant-mass distribution at the Tevatron. The calculation retains mb throughout the amplitude and phase space and includes all relevant partonic channels, with meticulous checks against independent codes and unitarity-based methods. The results show that including mb reduces the NLO cross section by about 7% and significantly influences the low-mass region of the m_bb spectrum, while the NLO corrections substantially reduce renormalization/factorization scale uncertainties (to ~20% inclusive, ~11% exclusive). These findings improve background modeling for Higgs searches in ZH and MSSM hb b production and establish a framework for extending the approach to other processes like Zt tbar and gamma t tbar.

Abstract

We calculate the Next-to-Leading Order (NLO) QCD corrections to Z b anti-b production in hadronic collisions including full bottom-quark mass effects. We present results for the total cross section and the invariant mass distribution of the bottom-quark jet pair at the Fermilab Tevatron p anti-p collider. We perform a detailed comparison with a calculation that considers massless bottom quarks, as implemented in the Monte Carlo program MCFM. We find that neglecting bottom-quark mass effects overestimates the total NLO QCD cross section for Z b anti-b production at the Tevatron by about 7%, independent of the choice of the renormalization and factorization scales. Moreover, bottom-quark mass effects can impact the shape of the bottom-quark pair invariant mass distribution, in particular in the low invariant mass region.

Figures (12)

• Figure 1: Tree-level Feynman diagrams for $q\bar{q}\to Z b{\bar{b}}$. The circled crosses indicate all possible insertions of the final-state $Z$ boson leg, each insertion corresponding to a different diagram.
• Figure 2: Tree-level Feynman diagrams for $gg\to Z b{\bar{b}}$. The circled crosses indicate all possible insertions of the final-state $Z$ boson leg, each insertion corresponding to a different diagram.
• Figure 3: Quadruple cut Britto:2004nc check of the calculation of a box diagram involving a top-quark loop. It corresponds to two Feynman diagrams given by the two possible orientations of the fermion line.
• Figure 4: Dependence of $\sigma^{\rm NLO}(p\bar{p}\to Z b{\bar{b}})$ on the soft cutoff $\delta_s$ of the two-cutoff PSS method for $\mu\!=\!2m_b+M_{ Z}$, and $\delta_c\!=\!10^{-5}$. The upper plot shows the cancellation of the $\delta_s$-dependence between $\sigma^{soft}+\sigma^{hard/coll}$ and $\sigma^{hard/non-coll}$. The lower plot shows, on an enlarged scale, the dependence of the full $\sigma^{\rm NLO}=\sigma^{\rm NLO}_{gg}+\sigma^{\rm NLO}_{q\bar{q}}+\sigma^{\rm NLO}_{qg}$ on $\delta_s$ with the corresponding statistical errors of the MC integration.
• Figure 5: Dependence of $\sigma^{\rm NLO}(p\bar{p}\to Z b{\bar{b}})$ on the collinear cutoff $\delta_c$ of the two-cutoff PSS method, for $\mu\!=\!2m_b+M_{ Z}$, and $\delta_s\!=\!10^{-3}$. The upper plot shows the cancellation of the $\delta_s$-dependence between $\sigma^{soft}+\sigma^{hard/coll}$, and $\sigma^{hard/non-coll}$. The lower plot shows, on an enlarged scale, the dependence of the full $\sigma^{\rm NLO}=\sigma^{\rm NLO}_{gg}+\sigma^{\rm NLO}_{q\bar{q}}+\sigma^{\rm NLO}_{qg}$ on $\delta_c$ with the corresponding statistical errors of the MC integration.