Analysis of $CP$ violation in $D^0\to K^{+}{K}^{-}{\pi }^0$

Abstract

We study the $CP$ violation induced by the interference between two intermediate resonances $K^{\ast }(892{)}^{+}$ and $K^{\ast }(892{)}^{-}$ in the phase space of singly-Cabibbo-suppressed decay $D^0\to K^{+}{K}^{-}{\pi }^0$. We adopt the factorization-assisted topological approach in dealing with the decay amplitudes of $D^0\to K^{\pm }{K}^{\ast }(892{)}^{\mp }$. The $CP$ asymmetries of two-body decays are predicted to be very tiny, which are $(-1.27\pm 0.25)\times 10^{-5}$ and $(3.86\pm 0.26)\times 10^{-5}$ respectively for $D^0\to K^{+}{K}^{\ast }(892{)}^{-}$ and $D^0\to K^{-}{K}^{\ast }(892{)}^{+}$. While the differential $CP$ asymmetry of $D^0\to K^{+}{K}^{-}{\pi }^0$ is enhanced because of the interference between the two intermediate resonances, which can reach as large as $3\times 10^{-4}$. For some NPs which have considerable impacts on the chromomagnetic dipole operator $O_{8g}$, the global $CP$ asymmetries of $D^0\to K^{+}{K}^{\ast }(892{)}^{-}$ and $D^0\to K^{-}{K}^{\ast }(892{)}^{+}$ can be then increased to $(0.56\pm 0.08)\times 10^{-3}$ and $(-0.50\pm 0.04)\times 10^{-3}$, respectively. The regional $CP$ asymmetry in the overlapped region of the phase space can be as large as $(1.3\pm 0.3)\times 10^{-3}$.

Comments: 24 pages