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We consider the Higgs Lepton Flavor Violating process $h \rightarrow \tau \mu$, in which CMS found a $2.5 \sigma$ excess of events, from a model independent perspective, and find that it is difficult to generate this operator without also obtaining a sizeable Wilson coefficient for the dipole operators responsible for tau radiative decay, constrained by BABAR to ${BR}(\tau \rightarrow \mu \gamma)< 4.4 \times 10^{-8} $.
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