  Kinematical distributions of decay products of the top quark carry
information on the polarisation of the top as well as on any possible new
physics in the decay of the top quark. We construct observables in the form of
asymmetries in the kinematical distributions to probe their effects.
Charged-lepton angular distributions in the decay are insensitive to anomalous
couplings to leading order. Hence these can be a robust probe of top
polarisation. However, these are difficult to measure in the case of highly
boosted top quarks as compared to energy distributions of decay products. These
are then sensitive, in general, to both top polarisation and top anomalous
couplings. We compare various asymmetries for their sensitivities to the
longitudinal polarisation of the top quark as well as to possible new physics
in the $Wtb$ vertex, paying special attention to the case of highly boosted top
quarks. We perform a $\chi ^2$- analysis to determine the regions in the
longitudinal polarisation of the top quark and the couplings of the $Wtb$
vertex constrained by different combinations of the asymmetries. Moreover, we
find that use of observables sensitive to the longitudinal top polarisation can
add to the sensitivity to which the $Wtb$ vertex can be probed.
