Lepton flavor violating Higgs bosons and τ → μγ

We update phenomenological constraints on a two Higgs doublet model with lepton flavor non-conserving Yukawa couplings. We review that tan beta is ambiguous in such type III'' models and define it from the tau Yukawa coupling. The neutral scalars phi could be searched for at hadron colliders in phi -> tau(mu) over bar and are constrained by the rare decay tau -> mu gamma. The Feynman diagrams for the collider process with Higgs production via gluon fusion are similar to the two-loop Barr-Zee'' diagrams which contribute to tau -> mu gamma. Some tuning'' is required to obtain a collider cross section of order the standard model expectation for sigma(gg -> h(SM) -> tau(+)tau(-)) while agreeing with the current bound from tau -> mu gamma.