NMSSM in gauge-mediated SUSY breaking without domain wall problem

A problem of the gauge-mediated SUSY breaking model is its difficulty to generate a natural value of μ/Bμ, while the NMSSM is a natural framework to solve the μ/Bμ-problem. The NMSSM in gauge-mediated SUSY breaking in its original form does not work well since the singlet field cannot develop a desired vacuum expectation value. It also suffers from the cosmological domain wall problem. We study an extension of the model to include additional vector-like matter, which is charged under the hidden QCD. It is shown that this simple extension solves both the problems. We study phenomenological and cosmological implications of this extended models. The lightest Higgs mass can be as large as 130-140 GeV for some model points.