Stable SUSY breaking model with O(10) eV gravitino from combined D-term gauge mediation and U(1)' mediation

We show a calculable example of stable supersymmetry (SUSY) breaking models with O(10) eV gravitino mass based on the combination of D-term gauge mediation and U(1)' mediation. A potential problem of the negative mass squared for the SUSY standard model (SSM) sfermions in the D-term gauge mediation is solved by the contribution from the U(1)' mediation. On the other hand, the splitting between the SSM gauginos and sfermions in the U(1)' mediation is circumvented by the contributions from the D-term gauge mediation. Since the U(1)' mediation does not introduce any new SUSY vacua, we achieve a completely stable model under thermal effects. Our model, therefore, has no cosmological difficulty