Renormalization of Wilson Operators in the Light-Cone Gauge

TL;DR

This paper investigates the renormalization properties of Wilson operators in the Mandelstam-Leibbrandt gauge, revealing divergence issues and their resolution through gauge invariance constraints.

Contribution

It provides a detailed analysis of divergences in Wilson operators within the M-L gauge and demonstrates how gauge invariance ensures their cancellation.

Findings

Double divergences appear in M-L gauge graphs where none exist in Feynman gauge.

Non-local functions cancel out when summing all graphs, preserving gauge invariance.

Discussion of challenges with spacelike loops in M-L gauge.

Abstract

We test the renormalization of Wilson operators and the Mandelstam- Leibbrandt gauge in the case when the sides of the loop are parallel to the n, n* vectors used in the M-L gauge. Graphs which in the Feynman gauge are free of ultra-violet divergences, in the M-L gauge show double divergences and single divergences with non-local Si and Ci functions. These non-local functions cancel out when we add all graphs together and the constraints of gauge invariance are satisfied. In Appendix C we briefly discuss the problems of the M-L gauge for loops containing spacelike lines.