Quasifixed point scenarios and the Higgs mass in the E6 inspired supersymmetric models

We analyze the two-loop renormalization group (RG) flow of the gauge and Yukawa couplings within the E-6 inspired supersymmetric models with extra U(1)(N) gauge symmetry under which right-handed neutrinos have zero charge. In these models, single discrete Z(2)(H) symmetry forbids the tree-level flavorchanging transitions and the most dangerous baryon and lepton number violating operators. We consider two different scenarios A and B that involve extra matter beyond the minimal supersymmetric Standard Model contained in three and four 5 + 5 representations of SU(5), respectively, plus three SU(5) singlets which carry U(1)(N) charges. In scenario A, the measured values of the SU(2)(W) and U(1)(Y) gauge couplings lie near the fixed points of the RG equations. In scenario B, the contribution of two-loop corrections spoils the unification of gauge couplings, resulting in the appearance of the Landau pole below the grand unification scale M-X. The solutions for the Yukawa couplings also approach the quasifixed points with increasing their values at the scale M-X. We calculate the two-loop upper bounds on the lightest Higgs boson mass in the vicinity of these quasifixed points and compare the results of our analysis with the corresponding ones in the next-to-minimal supersymmetric Standard Model. In all these cases, the theoretical restrictions on the Standard-Model-like Higgs boson mass are rather close to 125 GeV.