Weyl Consistency Conditions and ${\hat{I}}_5^3$

Abstract

The treatment of ${\hat{I}}_5^3$ 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 ${\hat{I}}^2$-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 ${\hat{I}}^2$-functions, where a semi-naïve treatment of ${\hat{I}}_5^3$ is sufficient, thereby fixing this ambiguity. We briefly outline an argument by which the same method fixes similar ambiguities at higher orders.

9 pages, 3 figures. Version 2 notation updated to match Ref. [16], text expanded, calculation details clarified, conclusions unaffected