Higgs boson production in bottom quark fusion at next-to-next-to-leading order

TL;DR

The paper delivers a NNLO QCD calculation of Higgs production in bottom-quark fusion within the variable-flavor-number scheme, incorporating all ${ m O}(eta_s^2)$ terms and combining with MRST NNLO PDFs. It demonstrates that scale uncertainties are dramatically reduced at NNLO and that a central scale choice of $ oldsymbol{m_R}=M_{ ext{H}}$, $ oldsymbol{m_F}=M_{ ext{H}}/4$ yields particularly stable perturbative behavior, in agreement with prior scale studies. A key advance is the inclusion of the parent process $gg o bar b ext{φ}$ at NNLO, which aligns the VFS results with the full kinematic range of bottom-quark emissions. The resulting predictions for the LHC and Tevatron indicate the inclusive bottom-quark initiated Higgs cross section is now robust and under good theoretical control, with important implications for MSSM Higgs searches and phenomenology.

Abstract

The total cross section for Higgs production in bottom-quark annihilation is evaluated at next-to-next-to-leading order (NNLO) in QCD. This is the first time that all terms at order alpha_s^2 are taken into account. We find a greatly reduced scale dependence with respect to lower order results, for both the factorization and the renormalization scales. The behavior of the result is consistent with earlier determinations of the appropriate factorization scale for this process of mu_F ~ M_H/4, and supports the validity of the bottom parton density approach for computing the total inclusive rate. We present precise predictions for the cross section at the Tevatron and the LHC.

Figures (10)

• Figure 1: For large $\tan\beta$, the bottom quark contribution to the gluon fusion process can be comparable to the top quark contribution.
• Figure 2: Partonic processes for $pp\to b\bar{b} H$. Not shown are diagrams that can be obtained by crossing the initial state gluons, or radiating the Higgs off an antibottom quark.
• Figure 3: Lowest order diagrams contributing to (a) $b\bar{b}\to H$, (b) $b\bar{b}\to Hg$, and (c) $bg\to Hb$. At NNLO, these diagrams receive corrections up to two loops in case (a), and one loop in case (b) and (c).
• Figure 4: Diagrams contributing at NNLO. Note that the Higgs boson can couple to the $b$--quarks at any point; only representative diagrams are shown.
• Figure 5: The cross section $\sigma(pp\to (b\bar{b})H+X)$ (in picobarns) at (a) LO, (b) NLO, (c) NNLO for the LHC. The axes labels are $F=\log_{10}(\mu_F/M_H)$ and $R=\log_{10}(\mu_R/M_H)$. Thus, the point $\mu_R=M_H$, $\mu_F=0.25\,M_H$ corresponds to $R=0$, $F=-0.6$. The Higgs boson mass is set to $M_H=120$ GeV.