QCD Corrections to Higgs Boson Production: Non- Leading Terms in the Heavy Quark Limit

TL;DR

This paper develops analytic QCD corrections to Higgs boson production via gluon fusion in hadronic collisions within the heavy-top limit, retaining the first non-leading terms ${\cal O}(\alpha_s^3 r)$ with $r=M_H^2/m_t^2$. Using a two-loop calculation with dimensional regularization and a careful expansion in external momenta, the authors derive partonic cross sections for $gg\to H$, $q\bar q\to gH$, and $qg\to qH$, including virtual, real, and counterterm contributions, and show that the dominant corrections scale with the Born cross section as $1+7r/60$ and that the $gg$ channel largely controls the hadronic rate. Numerical results for $pp$ collisions at the LHC and SSC indicate a K-factor of about 1.5–2, dominated by gluon fusion, with the heavy-quark non-leading terms providing a modest but important refinement to the standard infinite-$m_t$ predictions. The work validates the use of the $m_t\to\infty$ limit for the gluon-fusion subprocess and provides a framework to improve predictions and inform resummation approaches for Higgs phenomenology at high-energy colliders.

Abstract

We compute analytic results for the QCD corrections to Higgs boson production via gluon fusion in hadronic collisions in the limit in which the top quark is much heavier than the Higgs boson. The first non-leading corrections of $Ø(α_s^3 \mh^2/m_t^2)$ are given and numerical results presented for both LHC and SSC energies. We confirm earlier numerical results showing that the dominant corrections have the same mass dependence as the Born cross section.