Production of Higgs bosons at the LHC is affected by the contribution of
light quarks, that mediate the gg \to 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 \to Hg amplitudes of the form (C_F alphas L^{2})^n, where $L \in {
ln(s/mb^2), ln(p_\perp^2/mb^2) }. 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.Comment: 18 pages, 2 figure
