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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 $\epsilon_b$., Comment: 32 pages RevTex with 2 included figures

Starting from an Operator Product Expansion in the Heavy Quark Effective Theory up to order 1/m_b^2 we calculate the inclusive semileptonic decays of unpolarized bottom hadrons including lepton mass effects. We calculate the differential decay spectra d\Gamma/(dE_\tau ), and the total decay rate for B meson decays to final states containing a \tau lepton., Comment: 16 pages + 4 figs. appended in uuencoded form, LaTeX, MZ-TH/93-32

We point out that there exist two different formulations of the Heavy Quark Effective Theory (HQET). One formulation of HQET was mostly developed at Harvard and involves the use of the equation of motion to eliminate the small components of the heavy quark field. The second formulation, developed in Mainz, involves a series of Foldy-Wouthuysen-type field transformations which diagonalizes the heavy quark Lagrangian. Starting at O($1/m_Q^2$) the two formulations are different in that their effective Lagrangians, their effective currents, and their fields differ. However, when these three differences are properly taken into account, the two alternative formulations lead to identical S-matrix elements. This is demonstrated in an explicit example at O($1/m_Q^2$). We point to an essential difficulty of the Harvard HQET in that the Harvard effective fields are not properly normalized starting at order $O(1/m_Q^2)$., Comment: 12 pages, 2 figures (available upon request), LaTeX (no macros required), minor typos corrected MZ-TH/93-33

The existing derivations of a heavy quark effective theory (HQET) are analyzed beyond the next-to-leading order in $1/m$. With one exception they are found to be incorrect. The problem is a wrong normalization of the heavy quark field in the effective theory. We argue that the correct effective theory should be given by a Foldy--Wouthuysen type field transformation to all orders in $1/m$. The renormalization of the resulting Lagrangian to order $1/m^2$ is performed allowing for inclusion of effects arising through vacuum polarization. Our results for the anomalous dimensions disagree with the existing ones. Some applications are considered., Comment: 24 pages, LaTeX, MZ-TH/93-13 (revised). Major changes