We calculate the full O(α s ) radiative corrections to the three spin independent and five spin dependent structure functions that describe the angular decay distribution in the decay of a polarized top quark into a W -boson (followed by the decay W + → l + + ν l or by W + →q + q) and a bottom quark. The angular decay distribution is described in cascade fashion, i.e. the decay t(↑) → W + + X b is analyzed in the top rest system while the subsequent decay W + → l + + ν l (or W + →q + q) is analyzed in the W rest frame. Since the structure function ratios depend on the ratio m W /m t we advocate the use of such angular decay measurements for the determination of the top quark's mass. Our results for the eight O(α s ) integrated structure functions are presented in analytical form keeping the mass of the bottom quark finite. In the limit m b → 0 the structure function expressions reduce to rather compact forms. We also present results on the m b = 0 unpolarized and polarized O(α s ) scalar structure functions relevant to the semiinclusive decay of a polarized top quark into a charged Higgs boson t(↑) → H + + X b in the Two Higgs Doublet Model when m b = 0 .1 From this point on we shall drop explicit reference to the W + →q + q decay channel since it has the same angular decay distribution as W + → l + + ν l . In fact the branching fraction into the two hadronic channels (d + u) and (s + c) exceeds that of the sum of the three leptonic channels by a factor of approximately two because of the colour enhancement factor. Although not explicitly mentioned further on, the existence of the hadronic decay mode of the W + is always implicitly assumed in the following.

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(α s ) 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.

We consider the O(αs) radiative corrections to the decay of an unpolarized top quark into a bottom quark and a W -gauge boson where the helicities of the W are specified as longitudinal, transverse-plus and transverse-minus. The O(αs) radiative corrections lower the normalized longitudinal rate ΓL/Γ by 1.06% and increase the normalized transverse-minus rate Γ−/Γ by 2.17%. We find that the normalized transverse-plus rate Γ+/Γ, which vanishes at the Born term level for m b → 0, receives radiative correction contributions at the sub-percent level. We discuss m b = 0 effects for the Born term and the αs-contributions but find these to be small. Our results are discussed in the light of recent measurements of the helicity content of the W in top quark decays by the CDF Collaboration.

We calculate the radiative corrections to the unpolarized and the four polarized spectrum and rate functions in the leptonic decay of a polarized µ into a polarized electron. The new feature of our calculation is that we keep the mass of the final state electron finite which is mandatory if one wants to investigate the threshold region of the decay. Analytical results are given for the energy spectrum and the polar angle distribution of the final state electron whose longitudinal and transverse polarization is calculated. We also provide analytical results on the integrated spectrum functions. We analyze the m e → 0 limit of our general results and investigate the quality of the m e → 0 approximation. In the m e → 0 case we discuss in some detail the role of the O(α) anomalous helicity flip contribution of the final electron which survives the m e → 0 limit. The results presented in this paper also apply to the leptonic decays of polarized τ -leptons for which we provide numerical results.

The dominant contribution to the inclusive decays of B mesons into the charmstrangeness mesons D s and D * s is expected to be given by the partonic process