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We update phenomenological constraints on a Two Higgs Doublet Model withlepton flavour non-conserving Yukawa couplings. We review that $\tan \beta$ isambiguous in such "Type III" models, and define it from the $\tau$ Yukawacoupling. The neutral scalars $\phi$ could be searched for at hadron collidersin $ \phi \to \tau \bar{\mu}$, and are constrained by the rare decay $\tau \to\mu \gamma$. The Feynman diagrams for the collider process, with Higgsproduction via gluon fusion, are similar to the two-loop "Barr-Zee" diagramswhich contribute to $\tau \to \mu \gamma$. Some "tuning" is required to obtaina collider cross-section of order the Standard Model expectation for $\sigma(gg \to h_{SM} \to \tau^+ \tau^-)$, while agreeing with the current bound from$\tau \to \mu \gamma$.

Lepton flavour violating Higgs and tau to mu gamma