An extension for direct gauge mediation of metastable supersymmetry breaking

We study the direct mediation of metastable supersymmetry breaking by a $\Phi ^{2}$-deformation to the ISS model and extend it by splitting both ${\rm Tr}\Phi $ and ${\rm Tr}\Phi ^{2}$ terms in the superpotential and gauging the flavor symmetry. We find that with such an extension enough-long-lived metastable vacua can be obtained and the proper gaugino masses can be generated. Also, this allows for constructing a kind of models which can avoid the Landau pole problem. Especially, in our metastable vacua there exist a large region for the parameter m3 which can satisfy the phenomenology requirements and allow for a low SUSY-breaking scale ($h\mu _{2}$ ~ 100 TeV)