Inert Higgs extension of the NMSSM
  We introduce one pair of inert Higgs doublets {H_d, H_u} and singlets {N^c, N}, and consider their couplings with the Higgs doublets of the minimal supersymmetric standard model (MSSM), W \supset y_N N^c h_u H_d + y_N' N h_d H_u. We assign extra U(1)_{Z'} gauge charges only to the extra vector-like superfields, and so all the MSSM superfields remain neutral under the new U(1)_{Z'}. They can be an extension of the "\lambda term," W \supset \lambda S h_u h_d in the next-to-MSSM (NMSSM). Due to the U(1)_{Z'}, the maximally allowed low energy value of y_N can be lifted up to 0.85, avoiding a Landau-pole (LP) below the grand unification scale. Such colorless vector-like superfields remarkably enhance the radiative MSSM Higgs mass particularly for large tan\beta through the y_N term and the corresponding holomorphic soft term. As a result, the lower bound of \lambda and the upper bound of tan\beta can be relaxed to disappear from the restricted parameter space of the original NMSSM, 0.6 < \lambda < 0.7 and 1< tan\beta < 3. Thus, the valid parameter space significantly expands up to 0 < \lambda < 0.7, 0 < y_N < 0.85, and 2 < tan\beta < 50, evading the LP problem and also explaining the 126 GeV Higgs mass naturally. 
Bumseok Kyae
hep-ph