  Violation of charge conjugation-parity ($\rm CP$) symmetry plays a major rule
in the dominance of matter in our universe. A kind of $\rm CP$ 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.
