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Inclusive Semileptonic Decays of Polarized $Λ_b$ Baryons into Polarized $τ$-Leptons

We employ OPE techniques within HQET to calculate the inclusive semileptonic decays of polarized $Λ_b$ baryons. Lepton mass effects are included which enables us to also discuss rates into polarized $τ$-leptons. We present explicit results for the longitudinal polarization of the $τ$ in the $Λ_b$ rest frame as well as in the $(τ^-, \bar ν_τ)$ c.m. frame. In both cases we make use of novel calculational techniques which considerably simplify the calculations. The transverse polarization components of the $τ$ are calculated in the $(τ^-,\barν_τ)$ 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 $ε_b$.