Direct CP violation in $D^+ \to K^0(\bar K^0) \pi^+$ decays as a probe for new physics

In this paper we investigate CP violation in charged decays of $D$ meson. Particularly, we study the direct CP asymmetry of the Cabibbo favored non-leptonic $D^+ \rightarrow \bar K^0 \pi^+$ and the doubly Cabibbo-suppressed decay mode $D^+ \rightarrow K^0 \pi^+$ within standard model, two Higgs doublet model with generic Yukawa structure and left right symmetric models. In the standard model, we first derive the contributions from box and di-penguin diagrams contributing to their amplitudes which are relevant to the generation of the weak phases essential for non-vanishing direct CP violation. Then, we show that these phases are so tiny leading to a direct CP asymmetry of order $10^{-11}$ in both decay modes. Regarding the two Higgs doublet model with generic Yukawa structure and after taking into account all constraints on the parameter space of the model, we show that the enhanced direct CP asymmetries can be 6 and 7 orders of magnitudes larger than the standard model prediction for $D^+ \rightarrow \bar K^0 \pi^+$ and $D^+ \rightarrow K^0 \pi^+$ respectively. Finally, within left right symmetric models, we find that sizable direct CP asymmetry of ${\mathcal O } (10^{-3})$ can be obtained for the decay mode $D^+ \rightarrow \bar K^0 \pi^+$ after respecting all relevant constraints.