Searching for New Physics in Rare $B \to τ$ Decays

The rare $B$ decays $B^- \to \tau \bar\nu$, $B \to \tau^+ \tau^-$, $b \to X \nu \bar\nu$ and $b \to X \tau^+ \tau^-$ all contain third generation leptons in the final state, and hence are sensitive to new physics that couples more strongly to the third generation. We carry out a model independent analysis of these decays which allows studying several types of new physics effects. We apply our results to analyze the effects of the lepton number violating couplings present in supersymmetric models without R-parity. Under reasonable theoretical assumptions, we derive numerical predictions for the branching ratios of the different decays, as well as for a set of observables measurable in $b \to X \tau^+ \tau^-$ (the inclusive rate, the forward-backward asymmetry and the $\tau$ polarization components). For natural values of the parameters, the branching ratio for this decay is enhanced by more than one order of magnitude, rendering foreseeable its detection at upcoming B-factories. Most of the other processes appear to be less sensitive to the effects of new physics. We also discuss how a measurement of the $\tau$ polarization asymmetries in $b \to X \tau^+ \tau^-$ can be crucial in distinguishing between different sources of new physics.