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

Abstract

Abstract 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 $$D^+ \rightarrow {\bar{K}}^0 \pi ^+$$D+→K¯0π+ and the doubly Cabibbo-suppressed decay mode $$D^+ \rightarrow K^0 \pi ^+$$D+→K0π+ 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 the generated phases are so tiny leading to null direct CP asymmetries of both decay modes. Regarding the two Higgs doublet model with generic Yukawa structure, after taking into account all constraints on the parameter space of the model, we show that the weak phases of the amplitudes can be enhanced compared to the standard model ones. However, the enhancement is still not enough to have sizable direct CP asymmetries. Finally, within left right symmetric models, we find that $$|A^{SM+LR}_{CP} (D^+ \rightarrow {\bar{K}}^0 \pi ^+)|\lesssim \mathcal {O}(10^{-3})$$|ACPSM+LR(D+→K¯0π+)|≲O(10-3) after respecting all relevant constraints on the parameter space of the model.