τ→μη in supersymmetric models -: art. no. 057301

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