Inclusive Semileptonic Decays of Polarized ${\Lambda }_b$ Baryons into Polarized $\tau$-Leptons

Abstract

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 ${ϵ}_b$.

Comments: 32 pages RevTex with 2 included figures