Relaxing the Landau-pole constraint in the NMSSM with the Abelian gauge symmetries

Abstract

In order to relax the Landau pole constraint on ``$\ensuremath{\lambda}$,'' which is a coupling constant between a singlet $S$ and the minimal supersymmetric standard model (MSSM) Higgs, $\ensuremath{\lambda}S{h}_{u}{h}_{d}$ in the next-to MSSM, and also maintains the gauge coupling unification, we consider perturbative U(1) gauge extensions of the next-to MSSM. For relatively strong U(1) gauge interactions down to low energies, we assign U(1) charges only to the Higgs and the third family of the chiral matter among the MSSM superfields. In the $\mathrm{U}(1{)}_{Z}$ $[\mathrm{U}(1{)}_{Z}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{X}]$ extension, the low-energy value of $\ensuremath{\lambda}$ can be lifted up to 0.85--0.95 [0.9--1.0], depending on the employed charge normalizations, when $\ensuremath{\lambda}$ and the new gauge couplings are required not to blow up below the ${10}^{16}\text{ }\text{ }\mathrm{GeV}$ energy scale. The introduction of extra vectorlike superfields can induce the desired Yukawa couplings for the first two families of the chiral matter. We also discuss various phenomenological constraints associated with extra U(1) breaking.