On the light quark mass effects in Higgs boson production in gluon fusion

Production of Higgs bosons at the LHC is affected by the contribution of light quarks, that mediate the gg → Hg transition. Although their impact is suppressed by small Yukawa couplings, it is enhanced by large logarithms of the ratio of the Higgs boson mass or its transverse momentum to light quark masses. We study the origin of this enhancement, focusing on the abelian corrections to gg → Hg amplitudes of the form CFαsℒ2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\left({C}_F{\alpha}_s{\mathrm{\mathcal{L}}}^2\right)}^n $$\end{document}, where ℒ∈lns/mb2,lnp⊥2/mb2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathrm{\mathcal{L}}\in \left\{ \ln \left(s/{m}_b^2\right),\kern0.5em \ln \left({p}_{\perp}^2/{m}_b^2\right)\right\} $$\end{document}. We show how these non-Sudakov double logarithmic terms can be resummed to all orders in the strong coupling constant. Interestingly, we find that the transverse momentum dependence of these corrections is very weak due to a peculiar cancellation between different logarithmic terms. Although the abelian part of QCD corrections is not expected to be dominant, it can be used to estimate missing higher-order corrections to light quark contributions to Higgs boson production at the LHC.