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Recently Murayama and Nomura proposed a simple scheme to construct the gaugemediation models, using metastable supersymmetry breaking vacua. It has apossibility to predict the ultra light gravitino mass m_{3/2} \lesssim 16 eV,while such a light gravitino may destabilize the metastable vacua. Weinvestigate stability of the metastable vacuum of their model. The transitionrate from the false vacuum to true ones is evaluated by numerical calculation,including the Coleman-Weinberg potential destabilizing the metastable vacuum.It is found that when the messenger sector is minimal, stability of themetastable vacuum imposes an upperbound on squark mass M_{\tilde q} for theultra light gravitino as M_{\tilde q} \lesssim 1800 GeV at most. Squarks withthis mass may be found in the LHC experiments.

Stability of Metastable Vacua in Gauge Mediated SUSY Breaking Models with Ultra Light Gravitino