Infrared Factorization, Wilson Lines and the Heavy Quark Limit

TL;DR

This paper demonstrates that the cusp anomalous dimension $Γ_{cusp}(θ, α_s)$ is the universal quantity governing infrared behavior across three QCD frameworks: on-shell quark form factors, velocity-dependent HQET currents, and Wilson lines with a cusp. By unifying IR factorization with the Wilson-line formalism and applying the non-abelian exponentiation theorem, the authors show these seemingly distinct quantities are identical and computable to all orders. They establish the large-$θ$ linear growth with a positive slope $K(α_s)$, the small-$θ$ quadratic behavior, and the absence of $C_F^2$ terms at two loops, aligning HQET results with Wilson-line renormalization. The work provides a coherent, cross-validated framework for infrared structure in QCD and offers practical tools for heavy-quark phenomenology.

Abstract

It is shown that, in QCD, the same universal function $Γ_{cusp}(\vartheta, α_\s)$ determines the infrared behaviour of the on-shell quark form factor, the velocity-dependent anomalous dimension in the heavy quark effective field theory (HQET) and the renormalization properties of the vacuum averaged Wilson lines with a cusp. It is demonstrated that a combined use of the methods developed in the relevant different branches of quantum field theory essentially facilitates the all-order study of the asymptotic and analytic properties of this function.