Mixed mediation of supersymmetry breaking with anomalous U(1) gauge symmetry

Models with anomalous U(1) gauge symmetry contain various superfields which can have nonzero supersymmetry breaking auxiliary components providing the origin of soft terms in the visible sector, e.g. the U(1) vector superfield, the modulus or dilaton superfield implementing the Green-Schwarz anomaly cancellation mechanism, U(1)-charged but standard model singlet matter superfield required to cancel the Fayet-Iliopoulos term, and finally the supergravity multiplet. We examine the relative strength between these supersymmetry breaking components in a simple class of models, and find that various different mixed mediations of supersymmetry breaking, involving the modulus, gauge, anomaly and D-term mediations, can be realized depending upon the characteristics of D-flat directions and how those D-flat directions are stabilized with a vanishing cosmological constant. We identify two parameters which represent such properties and thus characterize how the various mediations are mixed. We also discuss the moduli stabilization and soft terms in a variant of KKLT scenario, in which the visible sector Kähler modulus is stabilized by the D-term potential of anomalous U(1) gauge symmetry.