New Features of the Mandelstam-Leibbrandt Lightcone Gauge

TL;DR

This paper investigates the Mandelstam-Leibbrandt prescription in the lightcone gauge, revealing new features and regularization issues, including ambiguous terms and a double pole in the self-energy calculation.

Contribution

It uncovers unexpected regularization-dependent features of the Mandelstam-Leibbrandt prescription when applied to spacelike Wilson lines, highlighting subtle issues in the gauge's consistency.

Findings

Ambiguous terms cancel out in the final result, ensuring gauge independence.

A double pole appears in the self-energy calculation at epsilon=0.

The regularization parameter omega must be kept throughout calculations for consistency.

Abstract

This is about new unexpected features of the Mandestam-Leibbrandt prescription found as applied to spacelike Wilson lines. The regularization parameter $ \omega $ in the M-L denominator for the spurious poles has to be kept throughout the calculation till the very end or else the integrals do not make sense. We get various `ambiguous' terms of the form $ \omega ^{-{\epsilon\over2}} \epsilon^{-2} $ which are not controlled by any sort of Ward identity. These terms cancel out in the sum and the final result is independent of $ \omega $. However, for the self energy on the spacelike Wilson line we obtain an unexpected double pole at $ \epsilon=0 $, using dimensional regularization in $ 4-\epsilon $ dimensions.