Two-loop anomalous dimension in light-cone gauge with Mandelstam-Leibbrandt prescription

TL;DR

This work reevaluates the non-singlet two-loop anomalous dimensions in light-cone gauge using the Mandelstam-Leibbrandt prescription within the Curci-Furmanski-Petronzio framework. It provides a detailed, diagrammatic calculation of CF$^2$ contributions, separating virtual and real parts and revealing the critical role of axial ghosts in ML. The authors show that ML yields a consistent ultraviolet structure and cancellations of spurious poles, while PV introduces scheme-dependent remnants that are compensated by ghost contributions in ML. The findings argue that ML is theoretically favorable for CFP-based higher-order QCD calculations and clarify how axial ghost terms reproduce the phenomenological subtraction rules used with PV.

Abstract

All the next-to-leading order results on Altarelli-Parisi splitting functions have been obtained in the literature either by using the operator product expansion method or by making use of the Curci Furmanski Petronzio (CFP) formalism in conjunction with light-like axial gauge, principal value (PV) prescription and dimensional regularization. In this paper we present the calculation of some non-singlet two-loop anomalous dimensions within the CFP formalism using light-cone axial gauge with Mandelstam-Leibbrandt (ML) prescription. We make a detailed comparison between the intermediate results given by the (PV) versus the (ML) method. We point out that the (ML) method is completely consistent and avoids the ``phenomenological rules'' used in the case of (PV) regularization.