τ→μη in supersymmetric models

The existence of large νμ-ντ mixing suggests the likelihood of large smuon-stau mixing in supersymmetric models, leading to μ and τ number violation. In addition to interesting signatures in slepton and neutralino production and decay, this will lead to rare τ decays, such as τ→μγ. Recently, it has been pointed out that the τ→3μ branching ratio could be substantial in the large tan β region of parameter space, due to an induced μ-τ-Higgs vertex. In this paper, another signature, τ→μη is considered. In the large tan β region, it is shown that the branching ratio of τ→μη is 8.4 times the branching ratio of τ→3μ, 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 τ→μγ is the most prominent decay, the branching ratio for τ→μη is always substantially lower