The asymptotic behavior of the heavy quark form factors at higher order

TL;DR

This paper analyzes the high-energy behavior of heavy quark form factors in QCD, deriving higher-order logarithmic contributions and elucidating their infrared divergence structure in the asymptotic limit.

Contribution

It provides the complete three-loop and partial four-loop logarithmic corrections to heavy quark form factors, advancing precision in perturbative QCD calculations.

Findings

Derived three-loop logarithmic contributions

Obtained partial four-loop corrections

Clarified infrared divergence structure

Abstract

In the asymptotic limit $Q^2 \gg m^2$, the heavy quark form factors exhibit Sudakov behavior. We study the corresponding renormalization group equations of the heavy quark form factors which do not only govern the structure of infrared divergences, but also control the high energy logarithms. This enables us to obtain the complete logarithmic three--loop and partial four--loop contributions to the heavy quark form factors in perturbative Quantum Chromodynamics.