Direct CP Violation in Charmed Hadron Decays via $\rho -\omega$ Mixing

Abstract

We study the possibility of obtaining large direct CP violation in the charmed hadron decays $D^{+}\to {\rho }^{+}{\rho }^0(\omega )\to {\rho }^{+}{\pi }^{+}{\pi }^{-}$, $D^{+}\to {\pi }^{+}{\rho }^0(\omega )\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$, $D^0\to \varphi {\rho }^0(\omega )\to \varphi {\pi }^{+}{\pi }^{-}$, $D^0\to \eta {\rho }^0(\omega )\to \eta {\pi }^{+}{\pi }^{-}$, $D^0\to {\eta }^{\prime }{\rho }^0(\omega )\to {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$, $D^0\to {\pi }^0{\rho }^0(\omega )\to {\pi }^0{\pi }^{+}{\pi }^{-}$, and ${\Lambda }_c\text{ra}p{\rho }^0(\omega )\to p{\pi }^{+}{\pi }^{-}$ via $\rho -\omega$ mixing. The analysis is carried out in the factorization approach. The CP violation parameter depends on the effective parameter, $N_c$, which is relevant to hadronization dynamics of each decay channel and should be determined by experiments. It is found that for fixed $N_c$ the CP violation parameter reaches its maximum value when the invariant mass of the ${\pi }^{+}{\pi }^{-}$ pair is in the vicinity of the $\omega$ resonance. For $D^0\to {\pi }^0{\rho }^0(\omega )\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and ${\Lambda }_c\to p{\rho }^0(\omega )\to p{\pi }^{+}{\pi }^{-}$ the maximum CP violating asymmetry is bigger than 1% when $1.98\le N_c\le 1.99$ and $1.95\le N_c\le 2.02$, respectively. We also estimate the decay branching ratios for $D^0\to {\pi }^0{\rho }^0$ and ${\Lambda }_c\to p{\rho }^0$ for these values of $N_c$, which should be tested by future experimental data.

Comments: 25 pages, 2 figures