Unification of Gauge Couplings and the Higgs Mass in Vector-Like Particle Theories Extended into NMSSM

The minimal supersymmetry standard model (MSSM) extended with vector-like theories have long been discussed. If we extend the vector-like MSSM theory into NMSSM and let the vector-like particles couple with the singlet (S), we find out a natural way to generate the vector-like particle masses near 1TeV through the breaking of the Z_3 group. Compared with MSSM+vectorlike models, vector-like models extended into NMSSM contain more yukawa couplings and can help us adjust the renormalization group (RG) trajectories of the gauge couplings in order to unify the intersections. They can also help press down the gauge RG-beta functions for a 5+5bar+10+10bar model, in order for the RG-trajectories of the gauge couplings to unify before the Landau-pole. We also discuss the higgs mass contributed from the vector-like sectors in this case.