BRST-invariant Pauli-Villars regularization of QCD

TL;DR

This paper develops a BRST-invariant Pauli-Villars regularization scheme for QCD by extending the Lagrangian with PV fields, enabling nonperturbative and perturbative calculations without relying on dimensional regularization.

Contribution

It introduces a novel regularization method for QCD that maintains BRST invariance using PV fields, suitable for nonperturbative light-front calculations and applicable in gauges beyond dimensional regularization.

Findings

Constructed a BRST-invariant PV regularized QCD Lagrangian.

Demonstrated gauge parameter independence of physical quantities.

Provided a framework for nonperturbative QCD calculations.

Abstract

We extend the QCD Lagrangian to include Pauli-Villars (PV) gluons, quarks, and ghosts in such a way as to retain BRST invariance in an arbitrary covariant gauge. The extended Lagrangian can provide a starting point for nonperturbative calculations in QCD, particularly with light-front techniques, and the methods used to construct it may be useful for perturbative calculations in theories where dimensional regularization is not viable. The regularization is arranged by having all interaction terms in the Lagrangian be couplings between null fields, specific combinations of positive and negative-metric PV fields. The construction is done in steps, beginning with a gauge-invariant Lagrangian with massless PV gluons and degenerate-mass PV quarks. Auxiliary scalars are introduced to give mass to the PV gluons, and break the mass degeneracy of the PV quarks, following a method due to Stueckelberg. Gauge fixing terms for the gluon fields are a part of this construction. The ghost terms are then obtained and shown to provide the BRST invariance. A lack of dependence on the gauge parameter can be checked by the calculation of physical quantities for a range of values of the parameter.