Anomalous dimensions of gauge fields and gauge coupling beta-functions in the Standard Model at three loops

TL;DR

This paper calculates three-loop anomalous dimensions and gauge coupling beta-functions in the Standard Model using background field gauge, providing precise theoretical results crucial for high-energy physics research.

Contribution

It presents the first three-loop calculations of gauge field anomalous dimensions and beta-functions in the Standard Model within a general background gauge framework.

Findings

Validated gauge-fixing independence of beta-functions

Provided explicit three-loop anomalous dimensions for gauge fields

Enhanced precision of Standard Model renormalization group analysis

Abstract

We present the results for three-loop gauge field anomalous dimensions in the SM calculated in the background field gauge within the unbroken phase of the model. The results are valid for the general background field gauge parameterized by three independent parameters. Both quantum and background fields are considered. The former are used to find three-loop anomalous dimensions for the gauge-fixing parameters, and the latter allow one to obtain the three-loop SM gauge beta-functions. Independence of beta-functions of gauge-fixing parameters serves as a validity check of our final results.