Violation of charge conjugation-parity ( $$\mathrm CP$$ ) symmetry plays a major rule in the dominance of matter in our universe. A kind of $$\mathrm CP$$ violation results from the asymmetry of the life time measured in $$M^0$$ and $${\bar{M}}^0$$ , here M is a heavy meson, decays to final states which is referred in the literature as $$A_{\Gamma }^f$$ . In this paper, we give an estimation of the upper bound on $$|A_{\Gamma }^f|$$ for the Cabibbo Favored $$D^0 \rightarrow K^- \pi ^+$$ decay process in different models. We show that in the standard model, $$|A_{\Gamma }^f| \lesssim {\mathcal {O}} (10^{-10})$$ . Recently a bound on $$A_{\Gamma }^f$$ has been obtained: $$(A^f_{\Gamma })^{Exp.}= (1.6 \pm 1)\times 10^{-4}$$ . This result motivates further studies on $$A_{\Gamma }^f$$ in beyond standard model physics. In the framework of two Higgs doublet model with generic Yukawa structure, we show that $$|A_\Gamma ^{f}|\lesssim {\mathcal {O}} (10^{-7})$$ which is several orders of magnitude smaller than the current experimental value. Finally, in the framework of left-right symmetric models in which the mixing between the left and the right gauge bosons is allowed and the left-right symmetry is not manifest at unification scale, we find that $$A_{\Gamma }^f$$ can be as large as $$|A_{\Gamma }^f|\lesssim {\mathcal {O}} (10^{-5})$$ which is one order of magnitude smaller than the experimentally measured value by LHCb collaborators.