Mass hierarchy from the flavor symmetry in supersymmetric multi-Higgs doublet model

We study the supersymmetric standard model with multiple Higgs doublets with gauged U(1)_X flavor symmetry. When the flavor symmetry is broken by the vacuum expectation value of flavon, the ℤ₃ symmetry M₃ called matter triality remains and it prohibits the baryon number violation up to dimension-5 operators. We study the contribution of the extra-Higgs fields to the anomaly cancellation of flavor symmetry and analyze the mass spectra including the multiple generations of Higgs fields as well as quarks and leptons. We show a series of U(1)_X charge assignments, which reproduce the observed masses and mixing angles of quark and lepton. We also find that, with such realistic charge assignments, the extra-Higgs fields obtain masses around the intermediate scale and decouple from the electroweak physics because of the holomorphy of superpotential.