Renormalization constants and beta functions for the gauge couplings of the Standard Model to three-loop order

TL;DR

This paper calculates the three-loop beta functions for the Standard Model's gauge couplings, providing precise renormalization constants crucial for high-precision theoretical predictions.

Contribution

It presents the first complete three-loop computation of the Standard Model gauge coupling beta functions, including detailed treatment of gamma_5 and automated diagram calculation setup.

Findings

Three-loop beta functions for all Standard Model gauge couplings.

Automated framework for Feynman diagram generation and calculation.

Consistent treatment of gamma_5 in multi-loop calculations.

Abstract

We compute the beta functions for the three gauge couplings of the Standard Model in the minimal subtraction scheme to three loops. We take into account contributions from all sectors of the Standard Model. The calculation is performed using both Lorenz gauge in the unbroken phase of the Standard Model and background field gauge in the spontaneously broken phase. Furthermore, we describe in detail the treatment of $\gamma_5$ and present the automated setup which we use for the calculation of the Feynman diagrams. It starts with the generation of the Feynman rules and leads to the bare result for the Green's function of a given process.