Gauge Invariance and Anomalous Dimensions of a Light-Cone Wilson Loop in Light-Like Axial Gauge

TL;DR

This work computes the dimensionally regularized, light-like Wilson loop at two loops in the light-like axial gauge with the Mandelstam-Leibbrandt prescription, demonstrating that the unrenormalized result exactly matches the covariant-gauge calculation. It then renormalizes the Wilson loop in the ${\overline{MS}}$ scheme within this gauge and shows that the renormalized loop obeys the renormalization-group equation with the same cusp anomalous dimension $\Gamma_{\text{cusp}}(g)$ and velocity-dependent anomalous dimension $\Gamma(g)$ as in covariant gauges, thereby confirming gauge invariance and the consistency of ML propagation for nonlocal operators. The analysis relies on explicit evaluations of the crossed, self-energy, and three-gluon diagrams, together with a careful MS-bar renormalization that subtracts light-cone and cusp divergences. The results have implications for the infrared structure of perturbative QCD and validate the use of the Mandelstam-Leibbrandt prescription in this nonlocal context.

Abstract

Complete two-loop calculation of a dimensionally regularized Wilson loop with light-like segments is performed in the light-like axial gauge with the Mandelstam-Leibbrandt prescription for the gluon propagator. We find an expression which {\it exactly} coincides with the one previously obtained for the same Wilson loop in covariant Feynman gauge. The renormalization of Wilson loop is performed in the $\MS-$scheme using a general procedure tailored to the light-like axial gauge. We find that the renormalized Wilson loop obeys a renormalization group equation with the same anomalous dimensions as in covariant gauges. Physical implications of our result for investigation of infrared asymptotics of perturbative QCD are pointed out.