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

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 Higgs interaction $Htau mu$ is studied in the frame of effective field theories. The best constraint on the $Htau mu$ vertex, derived from the know measurement on the muon anomalous magnetic moment, is used to impose the upper bounds $Br(tau to mu gamma)<2.5times 10^{-10}$ and $Br(tau to mu gamma gamma)<2.3times 10^{-12}$, which are more stringent than current experimental limits on this class of transitions.