Differential cross section for Higgs boson production including all-orders soft gluon resummation

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 nonperturbative input at low ${Q}_{T}.$ We provide distributions $d\ensuremath{\sigma}{/dydQ}_{T}$ 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 ${M}_{Z}l{m}_{h}l200\mathrm{GeV},$ $〈{Q}_{T}〉\ensuremath{\simeq}{0.18m}_{h}+18\mathrm{GeV}.$ We provide analogous results for Z boson production, for which we compute $〈{Q}_{T}〉\ensuremath{\simeq}25\mathrm{GeV}.$ 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.