Measurements of BR(b $\to \tau^- \bar{\nu}_{\tau}$X) and BR(b$\to \tau^- \bar{\nu}_{\tau}{\mathrm D}^{\ast\pm}$ X) and upper limits on BR(B$^- \to \tau^- \bar{\nu}_{\tau})$ and BR(b $\to{\mathrm s} \nu \bar{\nu})$

Abstract.

Inclusive branching ratios involving b $\to \tau$ transitions are measured in approximately four million hadronic Z decays collected by the ALEPH detector at LEP. The fully-inclusive branching ratio BR(b $\to \tau^- \bar{\nu}_{\tau}$ X) and the semi-inclusive branching ratio BR(b $\to \tau^- \bar{\nu}_{\tau} {\rm D}^{\ast\pm}$X) are measured to be $(2.43 \pm 0.20 \pm 0.25)%$ and $(0.88\pm 0.31\pm 0.28)%$, in agreement with the standard model predictions. Upper limits on the branching fractions BR(B$^- \to \tau^- \bar{\nu}_{\tau})$ and BR(b $\to{\mathrm s} \nu \bar{\nu})$ are set to $8.3 \times 10^{-4}$ and $6.4 \times 10^{-4}$ at the 90% C.L. These results allow a 90% C.L. lower limit of 0.40 GeV/$c^2)^{-1}$ to be set on the $\tan\beta/m_{{\mathrm H}^\pm}$ ratio, in the framework of type-II two-Higgs-doublet models.