Differential Cross Section for Higgs Boson Production Including All-Orders Soft Gluon Resummation

TL;DR

This work develops and applies an all-orders soft-gluon resummation framework in impact-parameter space (CSS) to predict the Higgs boson transverse-momentum distribution at the LHC, focusing on gg fusion with subleading channels and ensuring a smooth match to fixed-order results without explicit matching. It demonstrates that at LHC energies the dominant perturbative region governs the Q_T spectrum, with large-b contributions being suppressed, and provides predictions for mh from M_Z up to 200 GeV, showing a nearly linear rise of the mean Q_T with mh. The study also compares Higgs and Z production, highlighting the harder Higgs Q_T spectrum due to larger gluon color factors and showering, and assesses theoretical uncertainties from scale choices and non-perturbative inputs. Overall, the resummed predictions are stable, perturbatively driven, and potentially useful for enhancing Higgs signal discrimination via high-Q_T selection.

Abstract

The transverse momentum $Q_T$ distribution is computed for inclusive Higgs boson production at the energy of the CERN Large Hadron Collider. We focus on the dominant gluon-gluon subprocess in perturbative quantum chromodynamics and incorporate contributions from the quark-gluon and quark-antiquark channels. Using an impact-parameter $b$-space formalism, we include all-orders resummation of large logarithms associated with emission of soft gluons. Our resummed results merge smoothly at large $Q_T$ with the fixed-order expectations in perturbative quantum chromodynamics, as they should, with no need for a matching procedure. They show a high degree of stability with respect to variation of parameters associated with the non-perturbative input at low $Q_T$. We provide distributions $dσ/dy dQ_T$ for Higgs boson masses from $M_Z$ to 200 GeV. The average transverse momentum at zero rapidity $y$ grows approximately linearly with mass of the Higgs boson over the range $M_Z < m_h <200$ GeV, $<Q_T> \simeq 0.18 m_h + 18 $~GeV. We provide analogous results for $Z$ boson production, for which we compute $<Q_T> \simeq 25$ GeV. The harder transverse momentum distribution for the Higgs boson arises because there is more soft gluon radiation in Higgs boson production than in $Z$ production.

Figures (13)

• Figure 1: The function $S(b,Q)$ for Higgs boson production in gluon-gluon fusion at (a) $Q=m_h=125$ GeV and (b) $m_h = M_Z$ as a function of impact parameter $b$. We show results for different orders of accuracy in the perturbative expansions of the functions $A_g$ and $B_g$. The dotted curve is obtained with only the first order contributions $A^{(1)}_g$ and $B^{(1)}_g$ retained. For the dashed curve, we include $A^{(2)}_g$ in addition, and for the solid curve, we keep all terms through $A^{(2)}_g$ and $B^{(2)}_g$ in Eq. (\ref{['css-AB']}).
• Figure 2: The function $S(b,Q)$ for $Z$ boson production in as a function of impact parameter $b$. We show results for different orders of accuracy in the perturbative expansions of the functions $A_g$ and $B_g$.
• Figure 3: The all-orders $b$-space resummed function $bW(b,Q)$ for Higgs boson production in gluon-gluon fusion at $\sqrt{S} = 14$ TeV for (a) $Q=m_h=125$ GeV and (b) $m_h = M_Z$ as a function of impact parameter $b$.
• Figure 4: The all-orders $b$-space resummed function $bW(b,Q)$ for $Z$ boson production at $\sqrt{S} = 14$ TeV as a function of impact parameter $b$.
• Figure 5: Ratios of the functions $bW(b,Q)$. Comparisons are shown of (a) the DS parametrization and (b) the LY choice with respect to the function we use in this paper. The solid lines show the comparisons for $Z$ production at the energy of the Fermilab Tevatron, $\sqrt S = 1.8$ TeV. The dashed and dotted lines show the ratios for Higgs boson production at the LHC.