$B\to\tau\mu (X)$ decays in SUSY models without R-parity

Being strictly forbidden in the standard model, experimental detection of the lepton flavor violating decays $B(\bar B)\to\tau^+\mu^-$ and $b(\bar b)\to X\tau^+\mu^-$ would constitute an unmistakable indication of new physics. We study these decays in supersymmetric models without R-parity and without lepton number. In order to derive order of magnitude predictions for the branching ratios, we assume a horizontal U(1) symmetry with horizontal charges chosen to explain the magnitude of fermion masses and quark mixing angles. We find that the branching ratios for decays with a $\tau\mu$ pair in the final state are not particularly suppressed with respect to the lepton flavor conserving channels. In general in these models ${\rm B}[b\to\mu^+\mu^-(X)]\lsim {\rm B}[b(\bar b)\to\tau^+\mu^-(X)] \lsim {\rm B}[b\to\tau^+\tau^-(X)]$. While in some cases the rates for final states $\tau^+\tau^-$ can be up to one order of magnitude larger than the lepton flavor violating channel, due to better efficiencies for muon detection and to the absence of standard model contributions, decays into $\tau\mu$ final states appear to be better suited to reveal this kind of new physics.