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We study the amplitudes of the quark scattering by an externalelectromagnetic field and of the light quark mediated Higgs boson productionvia gluon fusion in the high-energy limit. The asymptotic behavior of the quarkform factors is obtained in the double-logarithmic approximation to all ordersin strong coupling constant through ${\cal O}(m_q^3)$ in the small quark massexpansion and the asymptotic formula is given in a closed analytic form. In thecase of the two-gluon Higgs boson form factor we obtain a complete analyticresult for the three-loop ${\cal O}(m_q^3)$ double-logarithmic term while theall-order analysis is performed in the large-$N_c$ limit of QCD and for theabelian gauge group. An estimate of the high-order high-power light quark masseffect in the Higgs boson production and decay is given.

Higgs Boson Production and Quark Scattering Amplitudes at High Energy through the Next-to-Next-to-Leading Power in Quark Mass