String inspired singlet extensions of the minimal supersymmetric Standard Model

The only allowed Higgs superpotential term at stringy tree level in the string derived Singlet Extensions of the Minimal Supersymmetric Standard Model (SEMSSM) is hSHdHuhSHdHu, which leads to an additional global U(1)U(1) symmetry in the Higgs potential. We propose the string inspired SEMSSM where the global U(1)U(1) symmetry is broken by the additional superpotential terms or supersymmetry breaking soft terms that can be obtained naturally due to the instanton effects or anomalous U(1)AU(1)A gauge symmetry. In these models, we can solve the μ problem and the fine-tuning problem for the lightest CP-even Higgs boson mass in the MSSM, generate the baryon asymmetry via electroweak baryogenesis, and predict the new Higgs physics which can be tested at the LHC and ILC.