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Violation of charge conjugation-parity ($\rm CP$) symmetry plays a major rulein the dominance of matter in our universe. A kind of $\rm CP$ violationresults 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 theliterature as $A_{\Gamma}^f$. In this paper, we give an estimation of the upperbound 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: $(A^f_{\Gamma})^{Exp.}= (1.6 \pm 1)\times10^{-4}$. This result motivates further studies on $A_{\Gamma}^f$ in beyondstandard model physics. In the framework of two Higgs doublet model withgeneric Yukawa structure, we show that $|A_\Gamma^{f}|\lesssim \mathcal{O}(10^{-7})$ which is several orders of magnitude smaller than the currentexperimental value. Finally, in the framework of left-right symmetric models inwhich the mixing between the left and the right gauge bosons is allowed and theleft-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 valueby LHCb collaborators.

New Physics signature in $D^0 (\bar{D}^0)\to f$ effective width asymmetries