Lepton flavour violating Higgs and tau to mu gamma

Abstract

We update phenomenological constraints on a Two Higgs Doublet Model with lepton flavour 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 $\varphi$ could be searched for at hadron colliders in $\varphi \to \tau \bar{\mu }$, and are constrained by the rare decay $\tau \to \mu \gamma$. 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 $\tau \to \mu \gamma$. Some "tuning" is required to obtain a 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 $\tau \to \mu \gamma$.

Comments: 20 pages, 5 figures, version accepted for publication