$W^+-H^+$ Interference and Partial Width Asymmetry in Top and Antitop Decays

We re-examine the question of a possible difference in the partial decay widths of $t$ and $\overline t$, induced by an intermediate scalar boson $H^+$ with $CP$-violating couplings. The interference of $W^+$ and $H^+$ exchanges is analysed by constructing the $2\times 2$ propagator matrix of the $W^+-H^+$ system, and determining its absorptive part in terms of fermion loops. Results are obtained for the partial rate difference in the channels $t\to bl^+\nu_l $ and $t\to bc\overline s$, which fulfil explicitly the constraints of $CPT$ invariance. These results are contrasted with those in previous work.