Higher-order $\beta$-functions in the Standard Model and beyond

TL;DR

This paper reviews recent high-order calculations of gauge and Yukawa beta-functions in general quantum field theories, addressing ambiguities and divergences encountered in these computations.

Contribution

It presents the latest four-loop gauge and three-loop Yukawa beta-function calculations in the most general renormalizable quantum field theory, highlighting issues with ambiguities and divergences.

Findings

Computed four-loop gauge beta-functions.

Calculated three-loop Yukawa beta-functions.

Discussed ambiguities and divergences in Yukawa beta-functions.

Abstract

In this contribution we consider the recent computation of the gauge coupling $\beta$-function at four loops and the Yukawa matrix $\beta$-function at three loops in the most general, renormalizable and four-dimensional quantum field theory. Furthermore, we discuss ambiguities and divergences arising in Yukawa matrix $\beta$-functions.