High-Energy Limit of QCD beyond Sudakov Approximation

TL;DR

The high-energy fixed-angle Sudakov limit of the scattering amplitudes suppressed by the leading power of the quark mass in perturbative quantum chromodynamics is studied and the factorization and all-order resummation of the double-logarithmic radiative corrections are proved.

Abstract

We study the high-energy limit of the scattering amplitudes suppressed by the leading power of the quark mass in perturbative quantum chromodynamics. We prove the factorization and perform all-order resummation of the double-logarithmic radiative corrections which determine the asymptotic behavior of the amplitudes. In contrast to the Sudakov logarithms, the mass-suppressed double-logarithmic corrections are induced by 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. We present explicit results for the Higgs boson production in gluon fusion mediated by a light-quark loop and for the leading power-suppressed contributions to the quark form factors, which reveal "magical" universality. Nontrivial relations between the asymptotic behavior of different amplitudes and the amplitudes in different gauge theories are found.

Figures (3)

• Figure 1: The leading order one-loop Feynman diagrams for (a) quark scattering by the $(G_{\mu\nu}^a)^2$ vertex (black circle) and (c) the Higgs boson production in gluon fusion. The diagrams (b) and (d) with the effective vertices (gray circles) defined in the text represent the non-Sudakov double-logarithmic corrections to the process (a) and (c), respectively.
• Figure 2: Diagramatic representation of the sequence of identities which move the soft gauge boson vertex from the soft quark to the eikonal gauge boson line, as explained in the text.
• Figure 3: The diagrams with an effective soft gluon exchange which incorporate the non-Sudakov double-logarithmic corrections to (a) vector and (b,c) scalar form factor of a quark. The symmetric diagrams are not shown.