  We study the amplitudes of the quark scattering by an external
electromagnetic field and of the light quark mediated Higgs boson production
via gluon fusion in the high-energy limit. The asymptotic behavior of the quark
form factors is obtained in the double-logarithmic approximation to all orders
in strong coupling constant through ${\cal O}(m_q^3)$ in the small quark mass
expansion and the asymptotic formula is given in a closed analytic form. In the
case of 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.
