Consistency of perturbativity and gauge coupling unification

Abstract

We investigate constraints that the requirements of perturbativity and gauge coupling unification impose on extensions of the standard model and of the minimal supersymmetric standard model. In particular, we discuss the renormalization group running in several supersymmetric 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 ${M}_{\mathrm{B\ensuremath{\llap{\not\;}}}}^{\mathrm{min}}={10}^{16}\text{ }\text{ }\mathrm{GeV}$, implying potential conflicts with the nonobservation of proton decay. We emphasize that extending the particle content of a model in order to push the grand unified theory scale higher or to achieve unification in the first place will very often lead to nonperturbative evolution. We generalize this observation to arbitrary extensions of the standard model and of the minimal supersymmetric standard model and show that the requirement of perturbativity up to ${M}_{\mathrm{B\ensuremath{\llap{\not\;}}}}^{\mathrm{min}}$, 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.