Gauge coupling beta functions to four-loop order in the Standard Model

TL;DR

This paper calculates the four-loop beta functions for the Standard Model gauge couplings, improving precision in understanding their energy dependence, by addressing the complexities of defining gamma_5 in dimensional regularization.

Contribution

It provides the first four-loop order beta functions for the Standard Model gauge couplings, using a novel approach to handle gamma_5 ambiguities in dimensional regularization.

Findings

Beta functions computed to four-loop order.

Enhanced understanding of gauge coupling evolution.

Method to handle gamma_5 in high-loop calculations.

Abstract

We compute the beta functions of the three Standard Model gauge couplings to four-loop order in the modified minimal subtraction scheme. At this order a proper definition of $\gamma_5$ in $D=4-2\epsilon$ space-time dimensions is required; however, in our calculation we determine the $\gamma_5$-dependent terms by exploiting relations with beta function coefficients at lower loop orders.