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

TL;DR

This paper analyzes high-energy quark scattering and Higgs production amplitudes considering quark mass effects up to third order, providing analytic formulas and estimates for high-order contributions in QCD and abelian gauge theories.

Contribution

It presents the first all-order asymptotic analysis of quark form factors with quark mass effects up to ${ m O}(m_q^3)$ in the double-logarithmic approximation, including explicit three-loop results.

Findings

Derived all-order asymptotic behavior of quark form factors.

Obtained explicit three-loop double-logarithmic terms for Higgs form factors.

Estimated high-order quark mass effects in Higgs production and decay.

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 ${\cal O}(m_q^3)$ 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.