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

We study the possibility of obtaining large direct CP violation in the charmed hadron decays $D^+ \to \rho^+ \rho^0 (\omega) \to \rho^+ \pi^+\pi^-$, $D^+ \to \pi^+ \rho^0 (\omega) \to \pi^+ \pi^+\pi^-$, $D^0 \to \phi \rho^0 (\omega) \to\phi \pi^+\pi^-$, $D^0 \to\eta \rho^0 (\omega) \to\eta \pi^+\pi^-$, $D^0 \to \eta' \rho^0 (\omega) \to\eta' \pi^+\pi^-$, $D^0 \to \pi^0 \rho^0 (\omega) \to \pi^0 \pi^+\pi^-$, and $\Lambda_c \ra p \rho^0 (\omega) \to p \pi^+\pi^-$ 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 $1.98\leq N_c \leq 1.99$ and $1.95\leq N_c \leq 2.02$, 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.