Higgs-Boson Production in Association with Bottom Quarks at Next-to-Leading Order

TL;DR

This paper resolves the proper leading-subprocess identification for Higgs-boson production in association with bottom quarks by employing heavy-quark parton distributions, recasting the leading process as $Q\bar Q\to H$ and treating gluon-initiated channels as $1/\ln(m_H/m_b)$ and $1/\ln^2(m_H/m_b)$ corrections. It provides analytic and numerical next-to-leading corrections in both $1/\ln(m_H/m_b)$ and $\alpha_s$, plus a next-to-next-to-leading correction in $1/\ln(m_H/m_b)$, valid for scalar and pseudoscalar Higgs bosons. Key contributions include the explicit derivation of the $1/\ln$ and $\alpha_s$ terms, the renormalization treatment of the Yukawa coupling, and comprehensive Tevatron and LHC predictions with quantified uncertainties. The results show large but partially canceling higher-order effects, leading to more reliable cross sections that can be used to normalize shower Monte Carlo programs and inform collider phenomenology.

Abstract

We argue that the leading-order subprocess for Higgs-boson production in association with bottom quarks is (b\bar{b} -> H). This process is an important source of Higgs bosons with enhanced Yukawa coupling to bottom quarks. We calculate the corrections to this cross section at next-to-leading-order in 1/ln(m_H/m_b) and alpha_s and at next-to-next-to-leading order in 1/ln(m_H/m_b).

Figures (8)

• Figure 1: Feynman diagrams for $gg \to Q\overline QH$.
• Figure 2: Feynman diagrams for (a) the leading-order subprocess $Q\overline Q \to H$; (b) $g\overline Q \to H\overline Q$ (there is also an $s$-channel diagram, not shown); and (c) $\widetilde{Q}\overline Q \to H$, where the heavy-quark distribution function $\widetilde{Q}$ is given by the perturbative solution to the DGLAP equations. Figs. (b) and (c) together constitute the $1/\ln (m_H/m_Q)$ correction to the leading-order subprocess in (a).
• Figure 3: Feynman diagrams for (a) $gg\to Q\overline QH$ (the complete set of diagrams is shown in Fig. 1); (b),(c) $\widetilde{Q}g \to QH$ and $g\widetilde{\overline Q} \to H\overline Q$ (there are also $s$-channel diagrams, not shown); and (d) $\widetilde{Q}\widetilde{\overline Q} \to H$, where the heavy-quark distribution function $\widetilde{Q}$ is given by the perturbative solution to the DGLAP equations. These diagrams together constitute the $1/\ln^2 (m_H/m_Q)$ correction to the leading-order subprocess $Q\overline Q \to H$.
• Figure 4: Feynman diagrams for (a) the virtual-gluon correction to $Q\overline Q \to H$; (b) $Q\overline Q \to Hg$; and (c) $\widetilde{Q} \overline Q \to H$, where the heavy-quark distribution function $\widetilde{Q}$ is given by the perturbative solution to the DGLAP equations. These diagrams together constitute the $\alpha_s$ correction to the leading-order subprocess $Q\overline Q \to H$.
• Figure 5: Percentage change in the cross section for Higgs-boson production in association with bottom quarks from the corrections of order $1/\ln (m_H/m_b)$, $1/\ln^2 (m_H/m_b)$, and $\alpha_s$, as a function of the Higgs-boson mass, at the Tevatron. The next-to-leading-order (NLO) cross section is the sum of the leading-order cross section and the corrections of order $1/\ln (m_H/m_b)$ and $\alpha_s$.