Consistency in Regularizations of the Gauged NJL Model at One Loop Level

TL;DR

This paper addresses divergences in the gauged NJL model at one loop, proposing a regulator-independent method to obtain unambiguous, symmetry-preserving amplitudes, thereby enhancing the model's predictive reliability.

Contribution

It introduces an alternative, general prescription for handling divergences in the gauged NJL model that preserves symmetries without relying on explicit regulator forms.

Findings

Achieved symmetry-preserving amplitudes at one loop

Identified conditions for consistent regularization

Provided a regulator-independent divergence handling method

Abstract

In this work we revisit questions recently raised in the literature associated to relevant but divergent amplitudes in the gauged NJL model. The questions raised involve ambiguities and symmetry violations which concern the model's predictive power at one loop level. Our study shows by means of an alternative prescription to handle divergent amplitudes, that it is possible to obtain unambiguous and symmetry preserving amplitudes. The procedure adopted makes use solely of {\it general} properties of an eventual regulator, thus avoiding an explicit form. We find, after a thorough analysis of the problem that there are well established conditions to be fulfiled by any consistent regularization prescription in order to avoid the problems of concern at one loop level.