Gauge-Yukawa Unification in Asymptotically Non-free Theories

TL;DR

This paper investigates gauge-Yukawa unification in asymptotically non-free supersymmetric theories, deriving RG-invariant relations among couplings that align with experimental data within certain supersymmetry breaking scales.

Contribution

It identifies RG-invariant relations in a specific supersymmetric model that unify gauge and Yukawa couplings, extending understanding of coupling behavior in non-free theories.

Findings

Relations among couplings are RG-invariant and predictive.

Predictions agree with LEP and Tevatron measurements.

Results are consistent for a specific supersymmetry breaking scale.

Abstract

We study asymptotically non-free gauge theories and search for renormalization group invariant (i.e. technically natural) relations among the couplings which lead to successful gauge-Yukawa unification. To be definite, we consider a supersymmetric model based on $SU(4)\times SU(2)_{R}\times SU(2)_{L}$. It is found that among the couplings of the model, which can be expressed in this way by a single one in the lowest order approximation, are the tree gauge couplings and the Yukawa coupling of the third generation. The corrections to the lowest order results are computed, and we find that the predictions on the low energy parameters resulting from those relations are in agreement with the measurements at LEP and Tevatron for a certain range of supersymmetry breaking scale.