Abstract:The semileptonic decays of polarised top quarks are analysed for a general chiralityconserving tbW vertex. We calculate double differential distributions for the charged lepton and the neutrino to order α s in the QCD coupling. We present these QCD corrections in terms of compact parameterisations that should be useful for the future investigation of the structure of the top decay vertex on the basis of large data samples. PACS number(s): 12.60.Cn, 13.88.+e, 14.65.Ha Keywords: top quark decay, spin polarisation, anomalous couplings, QCD corrections 1 E-mail address: breuther@physik.rwth-aachen.de 2 supported by D.F.G. SFB/TR9 3 supported by BMBF contract 05 HT1PAA/4So far the experimental information about the decays of top quarks is not very detailed. Data from the Tevatron are consistent with the expectation that these decays are governed by the V − A charged current interactions of the standard model (SM); but because of the size of the present experimental errors sizable new physics effects can not be excluded (c.f. for instance [1]).In view of the extremely large mass of the top quarks and the circumstance that they do not hadronise these particles are excellent probes of new interactions that may uncover at energies of a few hundred GeV. There is a vast literature on the phenomenology of such interactions in top quark decays (for overviews, see for instance [2,3]). One possibility is a small V + A admixture to the standard lefthanded t → b current as is predicted for instance by SU(2) L × SU(2) R × U(1) extensions of the standard model. The measured branching ratio of the radiative weak decay b → sγ provides a stringent constraint [4,5,6,7] on the coupling strength κ R of such a right-handed admixture: |κ R | 0.04. Of course, one may envisage contrived scenarios where other contributions to b → sγ lead to cancellations that invalidate this bound -in any case, a direct search for such a coupling in t andt decays is indispensable. Sensitive tests require polarised top quarks. At the LHC the single top production processes will yield large samples of polarised t andt quarks, and it has been estimated [8,9] that a statistical sensitivity δκ R ≃ 0.06 can be reached. From tt pair production at a high-luminosity linear e + e − collider a sensitivity δκ R ≃ 0.03 will be feasible [10,11,3].Energy and angular distributions for polarised top quark decays with a V + A admixture in the tbW vertex were investigated in a number of articles, including [12,13,14,15]. In ref.[13] semileptonic t decays were analysed and it was pointed out that the polarisation-dependent part of the neutrino distribution (which can be determined experimentally by measuring the missing momentum) is very sensitive to κ R . The order α s QCD corrections for the V − A part of the charged current [16,17] were incorporated in [13]. In view of the above-mentioned expected sensitivity to κ R at future colliders one should note that taking into account QCD corrections in future data analysis is mandatory, because they can mimic a small V +A a...