# Weyl Consistency Conditions and $\gamma_{5}$

## TL;DR

This paper uses Weyl Consistency Conditions to resolve ambiguities in the treatment of $ ext{γ}_5$ in dimensional regularization, establishing scheme-independent relations in gauge and Yukawa beta functions of the Standard Model.

## Contribution

It introduces a scheme-independent method to fix $ ext{γ}_5$ ambiguities in higher-order calculations using Weyl Consistency Conditions.

## Key findings

- Established a relation between four-loop gauge and three-loop Yukawa beta functions.
- Resolved $ ext{γ}_5$ ambiguities in Standard Model calculations.
- Proposed a method applicable to higher-order ambiguities.

## Abstract

The treatment of $\gamma_{5}$ in Dimensional Regularization leads to ambiguities in field-theoretic calculations, of which one example is the coefficient of a particular term in the four-loop gauge $\beta$-functions of the Standard Model. Using Weyl Consistency Conditions, we present a scheme-independent relation between the coefficient of this term and a corresponding term in the three-loop Yukawa $\beta$-functions, where a semi-na\"ive treatment of $\gamma_{5}$ is sufficient, thereby fixing this ambiguity. We briefly outline an argument by which the same method fixes similar ambiguities at higher orders.