New physics signature in ${D}^{0}\left({\overline{D}}^{0}\right)\to f$ effective width asymmetries

Violation of charge conjugation-parity ( $CP$ ) symmetry plays a major rule in the dominance of matter in our universe. A kind of $CP$ violation results from the asymmetry of the life time measured in ${M}^{0}$ and ${\overline{M}}^{0}$ , 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 ${D}^{0}\to {K}^{-}{\pi }^{+}$ decay process in different models. We show that in the standard model, $|{A}_{\Gamma }^{f}|\lesssim O\left({10}^{-10}\right)$ . Recently a bound on ${A}_{\Gamma }^{f}$ has been obtained: ${\left({A}_{\Gamma }^{f}\right)}^{Exp.}=\left(1.6±1\right)×{10}^{-4}$ . 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 $|{A}_{\Gamma }^{f}|\lesssim O\left({10}^{-7}\right)$ 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 $|{A}_{\Gamma }^{f}|\lesssim O\left({10}^{-5}\right)$ which is one order of magnitude smaller than the experimentally measured value by LHCb collaborators.