τ→μηin supersymmetric models

Abstract

The existence of large ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ mixing suggests the likelihood of large smuon-stau mixing in supersymmetric models, leading to \ensuremath{\mu} and \ensuremath{\tau} number violation. In addition to interesting signatures in slepton and neutralino production and decay, this will lead to rare \ensuremath{\tau} decays, such as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\gamma}.$ Recently, it has been pointed out that the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}3\ensuremath{\mu}$ branching ratio could be substantial in the large $\mathrm{tan}\ensuremath{\beta}$ region of parameter space, due to an induced $\ensuremath{\mu}\ensuremath{-}\ensuremath{\tau}$-Higgs vertex. In this paper, another signature, $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\eta}$ is considered. In the large $\mathrm{tan}\ensuremath{\beta}$ region, it is shown that the branching ratio of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\eta}$ is 8.4 times the branching ratio of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}3\ensuremath{\mu},$ independent of any unknown parameters, and it will thus give the most stringent bound on Higgs-mediated lepton flavor violation, and may provide its first signature. In the other regions of parameter space, where $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\gamma}$ is the most prominent decay, the branching ratio for $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\eta}$ is always substantially lower.