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Top polarisation studies in $H^-t$ and $Wt$ production

The polarisation of top quarks produced in high energy processes can be a very sensitive probe of physics beyond the Standard Model. The kinematical distributions of the decay products of the top quark can provide clean information on the polarisation of the produced top and thus can probe new physics effects in the top quark sector. We study some of the recently proposed polarisation observables involving the decay products of the top quark in the context of $H^-t$ and $Wt$ production. We show that the effect of the top polarisation on the decay lepton azimuthal angle distribution, studied recently for these processes at leading order in QCD, is robust with respect to the inclusion of next-to-leading order and parton shower corrections. We also consider the leptonic polar angle, as well as recently proposed energy-related distributions of the top decay products. We construct asymmetry parameters from these observables, which can be used to distinguish the new physics signal from the $Wt$ background and discriminate between different values of $\tanβ$ and $m_{H^-}$ in a general type II two-Higgs doublet model. Finally, we show that similar observables may be useful in separating a Standard Model $Wt$ signal from the much larger QCD induced top pair production background.