Heavy Quark Expansion for the Inclusive Decay $\bar{B}\to \tau \bar{\nu }X$

Abstract

We calculate the differential decay rate for inclusive $\bar{B}\to \tau \bar{\nu }X$ transitions to order $1/m_b^2$ in the heavy quark expansion, for both polarized and unpolarized tau leptons. We show that using a systematic $1/m_b$ expansion significantly reduces the theoretical uncertainties in the calculation. We obtain for the total branching ratio $\mathrm{BR}(\bar{B}\to \tau \bar{\nu }X)=2.30\pm 0.25\%$, and for the tau polarization $A_{\mathrm{pol}}=-0.706\pm 0.006$. {}From the experimental measurement of the branching ratio at LEP, we derive the upper bound $\text{lo}\le 0.8{\text{gev}}^2$ for one of the parameters of the heavy quark effective theory.

Comments: 16pages harvmac