Higgs-Boson Production Induced by Bottom Quarks

TL;DR

The paper analyzes bottom-quark induced Higgs production to resolve the mismatch between inclusive and exclusive rates by deriving an appropriately small bottom-factorization scale from exclusive-process kinematics. It shows that the relevant scale is set by the upper limit of the bottom-quark's collinear plateau, roughly mu_F,b ~ M/4 (often M/5), rather than the heavy-system mass M, and that the associated logarithms are smaller than naive expectations. This framework explains why higher-order calculations favor low bottom scales and extends to both charged and neutral Higgs production at the LHC and Tevatron, with single-top production following different kinematic behavior. The work thus justifies the bottom-parton approach for heavy Higgs channels and clarifies the role of phase-space effects and gluon luminosities in determining resummation needs.

Abstract

Bottom quark-induced processes are responsible for a large fraction of the LHC discovery potential, in particular for supersymmetric Higgs bosons. Recently, the discrepancy between exclusive and inclusive Higgs boson production rates has been linked to the choice of an appropriate bottom factorization scale. We investigate the process kinematics at hadron colliders and show that it leads to a considerable decrease in the bottom factorization scale. This effect is the missing piece needed to understand the corresponding higher order results. Our results hold generally for charged and for neutral Higgs boson production at the LHC as well as at the Tevatron. The situation is different for single top quark production, where we find no sizeable suppression of the factorization scale. Turning the argument around, we can specify how large the collinear logarithms are, which can be resummed using the bottom parton picture.

Figures (8)

• Figure 1: Normalized distributions for the hadronic charged Higgs boson production $gg \to \bar{b}tH^-$. Left: difference between the invariant mass of the $tH^-$ system and its threshold mass $M=m_t+m_H$. Right: ratio of the longitudinal and transverse momentum of the bottom jet $\rho = p_{z,b}/p_{T,b}$ in the parton center-of-mass system. The steeper set of curves is after a cut $Q_b>M/5$.
• Figure 2: Ratio of parton distributions in the proton and the function $x^{-n}$ for two different values of the factorization scale. All curves are normalized to their values at $x=0.1$. The different lines correspond to the gluon (solid, $n=2$), down-quark (dashed, $n=1.1$), anti-up-quark (dotted, $n=1.7$), and bottom quark(dash--dotted, $n=2$) content. We use CTEQ6L parton densities cteq6.
• Figure 3: The normalized function $F(\tau)$, defined in eq.(\ref{['eq:cxn3']}). The hadronic center-of-mass energy is set to $\sqrt{S}=14\;{\rm TeV}$ and the threshold mass to $675\;{\rm GeV}$, corresponding to a $500\;{\rm GeV}$ charged Higgs boson. We display the behavior of the plateau in $Q_b$ for different values of $j$, which arise from the $x_1 x_2$ behavior of the partonic cross section.
• Figure 4: Normalized distributions for the hadronic charged Higgs boson production process, for the complete gluon density (first row), for a constant gluon density (second row), and for the approximate gluon density $P(x)=1/x^2$ (third row). The left column shows the bottom quark virtuality distribution, the right column the bottom quark transverse momentum. The normalization for the largest Higgs boson mass is by the total rate; for all other masses the curves are normalized such that their maxima coincide. The normalization factors for the virtuality and the transverse momentum are identical. We note that for a comparison with the approximate form $F(\tau)$ we have to identify $M=m_t+m_H$.
• Figure 5: The numerical solution of eq.(\ref{['eq:qpt']}) for two different values of $C_Q=Q_b/M$, giving $C_p=p_{T,b}/Q_b$ as a function of $\rho=p_{z,b}/p_{T,b}$. The longitudinal momentum of the bottom quarks is defined in the parton center-of-mass system.