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

Understand

In order to relax the Landau pole constraint on "\lambda", which is a coupling constant between a singlet S and the MSSM Higgs, \lambda Sh_uh_d in the next-to-MSSM (NMSSM), and also maintain the gauge coupling unification, we consider U(1) gauge extensions of the NMSSM.

• 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 U(1)_Z [U(1)_Z\times U(1)_X] extension, the low energy value of \lambda can be lifted up to 0.85-0.95 [0.9-1.0], depending on the employed charge normalizations, when \lambda and the new gauge couplings are required not to blow up below the 10^{16} GeV energy scale.
• Introduction of extra vector-like superfields can induce the desired Yukawa couplings for the first two families of the chiral matter.