Spontaneous supersymmetry breaking with anomalous U(1) symmetry in metastable vacua and moduli stabilization

We show that in (anomalous) U(1) gauge theories with the Fayet-Iliopoulos term and with generic interactions, there are metastable vacua in which supersymmetry (SUSY) is spontaneously broken even without U(1)R symmetry. In this vacua, various hierarchical structures such as Yukawa hierarchy can be explained by the smallness of the Fayet-Iliopoulos parameter. It is shown that, by adding just one positively charged field to phenomenologically viable models, spontaneous SUSY breaking is realized. Moreover, we propose a new scenario for the stabilization of the moduli in the SUSY breaking models. It is a new feature that the moduli can be stabilized without the superpotential being dependent on them.