Extended Higgs sector of supersymmetric models

The Higgs sector of the MSSM may be extended to solve the mu problem by the addition of a gauge singlet scalar field. We consider two singlet extended Higgs models. For the first model, we prove that in the absence of soft supersymmetry (SUSY) breaking terms a true SUSY breaking minimum does not exist. For the second model, we show that an electroweak symmetry breaking transition from a broken SUSY phase to our current universe is allowed.