Towards realistic SUSY grand unification for extended MSSM models

Abstract

Low-energy supersymmetric models such as the minimal supersymmetric standard model (MSSM), next-to-minimal supersymmetric standard model (NMSSM), and MSSM with vectorlike fermion are consistent with perturbative unification. While the nonminimal 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 the following. First, in the case of embedding the MSSM into SU(5) the fit to standard model fermion masses requires a singlet $S$, which leads to unviable embedding of the NMSSM into SU(5) because such $S$ feeds singlet $N$ a mass of order unification scale as well. Second, a similar result holds in the case of embedding the NMSSM into SO(10), where $S$ is replaced by some Higgs fields responsible for SO(10) breaking. Third, on the contrary, for the embedding of the MSSM with 16-dimensional vectorlike fermions into SO(10), the Higgs field responsible for the vectorlike mass of order tera-electron-volts scale can evade those problems the singlet $N$ encounters because of an intermediate mass scale in the 126-dimensional Higgs field.