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The size of the branching ratios for the $\tau \to \mu \gamma$ and $\tau \to\mu \gamma \gamma$ decays induced by a lepton flavor violating Higgsinteraction $H\tau \mu$ is studied in the frame of effective field theories.The best constraint on the $H\tau \mu$ vertex, derived from the knowmeasurement on the muon anomalous magnetic moment, is used to impose the upperbounds $Br(\tau \to \mu \gamma)<2.5\times 10^{-10}$ and $Br(\tau \to \mu \gamma\gamma)<2.3\times 10^{-12}$, which are more stringent than current experimentallimits on this class of transitions.

Higgs mediated lepton flavor violating tau decays $\tau \to \mu \gamma$ and $\tau \to \mu \gamma \gamma$ in effective theories