Inclusive Semileptonic Decays of Polarized $\Lambda_b$ Baryons into Polarized $\tau$-Leptons

We employ OPE techniques within HQET to calculate the inclusive semileptonic decays of polarized $\Lambda_b$ baryons. Lepton mass effects are included which enables us to also discuss rates into polarized $\tau$-leptons. We present explicit results for the longitudinal polarization of the $\tau$ in the $\Lambda_b$ rest frame as well as in the $(\tau ^-, \bar \nu_\tau)$ c.m. frame. In both cases we make use of novel calculational techniques which considerably simplify the calculations. The transverse polarization components of the $\tau$ are calculated in the $(\tau^-,\bar\nu_\tau)$ c.m. frame. We delineate how to measure the full set of 14 polarized and unpolarized structure functions of the decay process by angular correlation measurements. A set of observables are identified that allow one to isolate the contributions of the two $O(1/m_b^2)$ nonperturbative matrix elements $K_b$ and $\epsilon_b$.