LAUSR

Abstract 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 $$ \mathcal{O}\left({m}_q^3\right) $$ 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 $$ \mathcal{O}\left({m}_q^3\right) $$ O m q 3 double-logarithmic term while the all-order analysis is performed in the large-Nc 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.