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In this paper we study the direct CP asymmetry of the doublyCabibbo-suppressed decay mode $D^0 \to K^+ \pi^- $ within standard model andtwo Higgs doublet model with generic Yukawa structure. In the standard model wederive the corrections to the tree level amplitude, generated from the box anddi-penguin diagrams, required for generating the weak CP violating phases. Weshow that these phases are so tiny leading to a direct CP asymmetry of order$10^{-9}$. Regarding the two Higgs doublet model with generic Yukawa structurewe derive the Wilson coefficients relevant to $D^0 \to K^+ \pi^- $. Aftertaking into account all constraints on the parameter space of the model we showthat charged Higgs couplings to quarks can lead to a direct CP asymmetry oforder $10^{-3}$ which is $6$ orders of magnitude larger than the standard modelprediction.

CP violation in $D^0 \to K^+ \pi^- $