Towards Realistic SUSY Grand Unification for Extended MSSM

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.