Upper Limit for the Decay $B^{-} \to \tau^{-}\overline{\nu}_{\tau}$ and Measurement of the $b \to \tau\overline{\nu}_{\tau}X$ Branching Ratio

Using the data sample of hadronic$Z^0$ decays collected by the DELPHI experiment in the 1992-1995 LEP1 period, the leptonic decay of the charged $ B$ mesons(\btauex) has been studied. The analysis was done in both leptonic \taulm and hadronic\tauxmm decay channels. No excess was observed in data and the upper limit BR(\btauex) $ 1.1 \times 10^{-3}$ at the 90\aonfidence level was obtained. This result is consistent with Standard Modelexpectations and puts a constraint on the ratio $\tan \beta / M_{H^{\pm}} 0.45$~(GeV$/c^2)^{-1} $ in the framework of models with two Higgs doublets (any type II Higgs doublet model). From the missing energydistribution, the branching ratio of \btau was measured in the hadronicchannel \tauxm. The result, BR(\btau)$ = (2.19 \pm 0.24 \ (stat) \pm 0.40\; (syst)) \$, is consistent with the Standard Modelprediction and with previous experimental measurements.