Abstract
We present a detailed analysis of the factorization and all-order resummation of the double-logarithmic radiative corrections which determine the asymptotic behavior of the gauge theory amplitudes suppressed by the leading power of the fermion mass in the limit of high-energy fixed-angle scattering. The result is applied to estimate the bottom quark mediated contribution to the Higgs boson production in gluon fusion.
Highlights
We present a detailed analysis of the factorization and all-order resummation of the double-logarithmic radiative corrections which determine the asymptotic behavior of the gauge theory amplitudes suppressed by the leading power of the fermion mass in the limit of high-energy fixed-angle scattering
In contrast to the Sudakov logarithms, the mass-suppressed double-logarithmic corrections are induced by a soft quark exchange
The structure of the corrections and the asymptotic behavior of the amplitudes in this case crucially depend on the color flow in a given process and are determined by the eikonal color charge nonconservation
Summary
Throughout this paper we deal with a massive quark scattering by various external currents. To introduce the main idea of our approach we start with an amplitude G for the scattering of a quark of mass mq, initial momentum p1 and final momentum p2, by a local operator (Gaμν) of the gauge field strength tensor. The origin of such a vertex is not relevant for our discussion and one may suggest that it describes the gluon field interaction to the Higgs boson mediated by an infinitely heavy quark loop This rather artificial amplitude is a perfect example to reveal the main features of the general problem in the most illustrative way and with minimal technical complications
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