Weyl Consistency Conditions and $gamma_{5}$

Preprint number: CP3-Origins-2019-1 DNRF90
Authors: Colin Poole (CP3-Origins) and Anders Eller Thomsen (CP3-Origins)

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.