This presentation is based on Ref. [1]
where the amplitude of the light quark mediated Higgs boson
production via gluon fusion in the high-energy limit is
analysed at the next-to-next-to leading power in the quark mass
$m_q$. For the two-gluon Higgs boson form factor we obtain a
complete analytic result for the three-loop ${\cal O}(m_q^3)$
double-logarithmic term while the all-order analysis is
performed in the large-$N_c$ limit of QCD and for the abelian
gauge group. An estimate of the high-order high-power light
quark mass effect in the Higgs boson production and decay is
given.