On the Consistency of Perturbativity and Gauge Coupling Unification

TL;DR

This paper examines how the demands of perturbativity and gauge coupling unification restrict extensions of the Standard Model and MSSM, highlighting challenges in achieving unification at high scales without violating proton decay constraints.

Contribution

It provides a detailed analysis of the renormalization group running in various SUSY models, showing the typical unification scales and the limitations on particle content to maintain perturbativity.

Findings

Unification often occurs below 10^16 GeV, risking proton decay conflicts.

Extending particle content to raise unification scales often leads to non-perturbative behavior.

Certain extra dimensional models can circumvent perturbativity and proton decay issues.

Abstract

We investigate constraints that the requirements of perturbativity and gauge coupling unification impose on extensions of the Standard Model and of the MSSM. In particular, we discuss the renormalization group running in several SUSY left-right symmetric and Pati-Salam models and show how the various scales appearing in these models have to be chosen in order to achieve unification. We find that unification in the considered models occurs typically at scales below M^{min}_{B violation} = 10^16 GeV, implying potential conflicts with the non-observation of proton decay. We emphasize that extending the particle content of a model in order to push the GUT scale higher or to achieve unification in the first place will very often lead to non-perturbative evolution. We generalize this observation to arbitrary extensions of the Standard Model and of the MSSM and show that the requirement of perturbativity up to M^{min}_{B violation}, if considered a valid guideline for model building, severely limits the particle content of any such model, especially in the supersymmetric case. However, we also discuss several mechanisms to circumvent perturbativity and proton decay issues, for example in certain classes of extra dimensional models.