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The lepton flavor violation $\mu\to e\gamma$, $\tau\to e\gamma$,$\tau\to\mu\gamma$, $\mu\to3e$, $\tau\to3e$, $\tau\to3\mu$ and $\mu-e$conversion in Al and Ti are studied in both the Altarelli-Feruglio $A_4$ modeland the $S_4$ model of Ding. The rates of these lepton flavor violation processfor the inverted hierarchy neutrino mass spectrum are enhanced considerably bythe next to leading order contributions. For both models, we find that the$\mu-e$ conversion in Ti is within the precision of next generation experimentsin all the parameter space considered, the $\mu-e$ conversion in Al should beobservable at least in a very significant part of the parameter space, whereas$\tau\to e\gamma$, $\tau\to\mu\gamma$, $\tau\to3e$ and $\tau\to3\mu$ are belowthe expected future sensitivity. The detectability of $\mu\to e\gamma$ and$\mu\to3e$ in near future depends on the models and the neutrino mass spectrum.We suggest that a comprehensive consideration of the lepton flavor violationprocesses is important to test and distinguish both discrete flavor symmetrymodels.

Lepton Flavor Violation in Models with $A_4$ and $S_4$ Flavor Symmetries