Search for lepton flavor violation in supersymmetric models via meson decays

Considering the constraints from the experimental data on $\mu\rightarrow e\gamma$,$\mu\rightarrow3e$,$\mu-e$ conversion etc., we analyze the Lepton Flavor Violating decays $\phi(J/\Psi,\Upsilon(1S)) \rightarrow e^+\mu^-(\mu^+\tau^-)$ in the scenarios of the minimal supersymmetric extensions of Standard Model with seesaw Mechanism. Numerically, there is parameter space that the LFV processes of $J\mathrm{/}\mathrm{\Psi }(\mathrm{{\rm Y}})\to {\mu }^{+}{\tau }^{-}$ can reach the upper experimental bounds, meanwhile the theoretical predictions on $\mu \to e\gamma$, $\mu \to 3e$, $\mu -e$ conversion satisfy the present experimental bounds. For searching of new physics, Lepton Flavor Violating processes $J\mathrm{/}\mathrm{\Psi }(\mathrm{{\rm Y}})\to {\mu }^{+}{\tau }^{-}$ may be more promising and effective channels.