
We calculate the density matrix for the decay of a polarised top quark into a polarised W boson and a massive b quark, for the most general Wtb vertex arising from dimensionsix gaugeinvariant effective operators. We show that, in addition to the wellknown W helicity fractions, for polarised top decays it is worth to define and study the transverse and normal W polarisation fractions, that is, the W polarisation along two directions orthogonal to its momentum. In particular, a rather simple forwardbackward asymmetry in the normal direction is found to be very sensitive to complex phases in one of the Wtb anomalous couplings. This asymmetry, which indicates a normal W polarisation, can be generated for example by a Podd, Todd transition electric dipole moment. We also investigate the angular distribution of decay products in the top quark rest frame, calculating the spin analysing powers for a general Wtb vertex. Finally we show that, using a combined fit to top decay observables and the tW cross section, at LHC it will be possible to obtain modelindependent measurements of all the (complex) Wtb couplings as well as the single top polarisation. Implications for spin correlations in top pair production are also discussed.
