Towards a Two-Loop Matching of Gauge Couplings in Grand Unified Theories

TL;DR

This paper computes two-loop gauge coupling matching corrections at the GUT scale in a general framework, highlighting significant numerical effects and providing detailed technical methods applicable to various GUT models.

Contribution

It introduces a general two-loop matching calculation framework for gauge couplings in GUTs, applicable to models like SU(5), with detailed technical procedures for future extensions.

Findings

Numerical effects exceed current experimental uncertainties on alpha_s.

The framework is adaptable to different GUT models including supersymmetric theories.

Provides detailed methodology for two-loop matching calculations.

Abstract

We calculate the two-loop matching corrections for the gauge couplings at the Grand Unification scale in a general framework that aims at making as few assumptions on the underlying Grand Unified Theory (GUT) as possible. In this paper we present an intermediate result that is general enough to be applied to the Georgi-Glashow SU(5) as a "toy model". The numerical effects in this theory are found to be larger than the current experimental uncertainty on $alpha_s$. Furthermore, we give many technical details regarding renormalization procedure, tadpole terms, gauge fixing and the treatment of group theory factors, which is useful preparative work for the extension of the calculation to supersymmetric GUTs.