Higgs-Boson Production via Bottom-Quark Fusion

TL;DR

This work addresses inconsistencies in Higgs production via bottom-quark fusion by reexamining the NLO calculation and identifying the appropriate factorization scale. Through an analysis of collinear logarithms within the ACOT framework, the authors argue that mu_F ≈ m_h/4, not m_h, yields better perturbative convergence and weaker scale dependence, bringing the bb -> h result into better agreement with the gg -> bb h channel when scales are chosen accordingly. They demonstrate that at this scale the mixed corrections are modest and the NNLO piece from gg -> bb h is small, enhancing the reliability of the inclusive bbbar -> h cross section for large tan beta. The study thus provides a more accurate and stable prediction for Higgs production in bottom-quark–enhanced scenarios and outlines paths for full NNLO validation.

Abstract

Higgs bosons with enhanced coupling to bottom quarks are copiously produced at hadron colliders via b\bar{b} -> h, where the initial b quarks reside in the proton sea. We revisit the calculation of the next-to-leading-order cross section for this process and argue that the appropriate factorization scale for the b distribution functions is approximately m_h/4, rather than m_h, as had been previously assumed. This greatly improves the convergence of the perturbation series, and yields a result with mild factorization-scale dependence. We also show that the leading-order calculation of gg -> b\bar{b}h, integrated over the momenta of the final-state particles, is very sensitive to the factorization and renormalization scales. For scales of order m_h/4 the gg -> b\bar{b}h cross section is comparable to that of b\bar{b} -> h, in contrast to the order-of-magnitude discrepancy between these two calculations for the scale m_h. The result we obtain improves the prospects for Higgs-boson discovery at hadron colliders for large values of tan(β).

Figures (7)

• Figure 1: Leading-order diagram for the production of the Higgs boson via bottom-quark fusion.
• Figure 2: Representative diagrams for associated production of the Higgs boson and two high-$p_T$ bottom quarks: (a) $gg\to b\bar{b}h$ (8 diagrams); (b) $q\bar{q}\to b\bar{b}h$ (2 diagrams).
• Figure 3: Diagrams for the next-to-leading-order correction to $b\bar{b}\to h$ from initial gluons. This correction is of order $1/\ln(m_h/m_b)$.
• Figure 4: Diagrams for the next-to-leading-order correction to $b\bar{b}\to h$ from real and virtual gluon emission. This correction is of order $\alpha_S$.
• Figure 5: Hadronic differential cross section times the squared virtuality for the subprocess $bg\to bh$vs. the virtuality (scaled to the Higgs-boson mass) at both the Tevatron (upper plot) and the LHC (lower plot). Curves are shown for a variety of Higgs-boson masses, scaled such that they overlap at small virtuality.