A step towards a consistent treatment of chiral theories at higher loop order: the abelian case

TL;DR

This paper investigates the challenges of maintaining consistency in regularization schemes for chiral theories at two-loop order, proposing improvements within the implicit regularization framework using an abelian chiral model as a case study.

Contribution

It extends the analysis of regularization inconsistencies in chiral theories to two-loop order and discusses how to adapt implicit regularization for consistency.

Findings

Identifies subtleties in two-loop regularization of chiral theories.

Proposes modifications to implicit regularization for higher-loop consistency.

Provides detailed analysis using an abelian chiral model.

Abstract

As recently pointed out, regularization schemes defined in four-dimensions may also face inconsistencies in the presence of chiral fermions. In this work, we extend this analysis to two-loop order. Adopting the implicit regularization as working arena, we discuss in detail how a consistent version of the method can be envisaged, and present many of the subtleties that appear at two-loop order using an abelian chiral model as working example.