Polarized top decay into polarized W t(↑)→W(↑)+b at O(αs)

We consider the decay of a polarized top quark into a polarized W-boson plus a bottom quark, followed by the decay of the W-boson into a pair of leptons or quarks. The polar angle distribution of the top spin relative to the W-momentum and the polar angle distribution of the lepton (or quark) in the W-rest frame is governed by three polarized and three unpolarized rate functions which are related to the double density matrix elements of the decay t→W++b. We obtain analytical expressions for the O(αs) radiative corrections to the three polarized and three unpolarized rate functions. We also provide a comprehensive discussion of the dependence of the longitudinal, transverse and normal polarization of the top quarks produced at e+e−-colliders on beam polarization parameters.