Towards Realistic SUSY Grand Unification for Extended MSSM

TL;DR

This paper investigates the constraints on low-energy supersymmetric models like MSSM, NMSSM, and their extensions when embedded into grand unified theories such as SU(5) and SO(10), highlighting challenges and potential solutions.

Contribution

It analyzes the ultraviolet constraints of extended MSSM models within GUT frameworks, revealing embedding difficulties and proposing viable scenarios with vectorlike fermions.

Findings

Embedding NMSSM into SU(5) is unviable due to singlet S issues.

Embedding NMSSM into SO(10) faces similar problems.

Embedding MSSM with vectorlike fermions into SO(10) can evade these issues via intermediate scales.

Abstract

Low-energy supersymmetric models such as MSSM, NMSSM and MSSM with vectorlike fermion are consistent with perturbative unification. While the non-minimal extensions naturally explain Higgs mass and dark matter in the low energy region, it is unclear how seriously they are constrained in the ultraviolet region. Our study shows that $i)$, In the case of embedding MSSM into $\rm{SU}(5)$, the fit to SM fermion masses requires a singlet $S$, which leads to unviable embedding of NMSSM into $\rm{SU}(5)$ because such $S$ feeds singlet $N$ a mass of order unification scale as well. $ii)$, Similar result holds in the case of embedding NMSSM into $\rm{SO}(10)$, where $S$ is replaced by some Higgs fields responsible for $\rm{SO}(10)$ breaking. $iii)$, On the contrary, for the embedding of MSSM with $16$-dimensional vectorlike fermions into $\rm{SO}(10)$, the Higgs field responsible for the vectorlike mass of order TeV scale can evade those problems the singlet $N$ encounters because of an intermediate mass scale in the $126$-dimensional Higgs field.