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^3right) 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^3right) 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.
Highlights
JHEP02(2022)170 amplitudes and in a breakdown of a formal power counting [23, 27, 28]
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 highenergy limit
The asymptotic behavior of the quark form factors is obtained in the doublelogarithmic approximation to all orders in strong coupling constant through O(m3q) in the small quark mass expansion and the asymptotic formula is given in a closed analytic form
Summary
At the same time as in the case of the Dirac form factor at O(m2q) [23] starting with two loops the double-logarithmic contribution to this coefficient is generated through the soft virtual quark pair exchange, figure 2(a), where the mass suppression factor comes from the numerators of the soft propagators, i.e. is associated with the chirality flip. The Pauli form factor structure requires an additional chirality flip on an eikonal quark line, which is provided either by the mass term of the propagator or by an external momentum p/i acting on the corresponding on-shell quark field Such terms cancel in the diagrams with the soft gluon exchange but give a contribution which is not suppressed by the soft momentum, where due to the topology of the fermion flow the operators p/i should be commuted with the photon vertex before the equation of motion for the initial and final quark states can be applied. At the same time in QCD it scales with the double-logarithmic variable as ln x
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