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Direct CP Violation in Charmed Hadron Decays via $ρ-ω$ Mixing

We study the possibility of obtaining large direct CP violation in the charmed hadron decays $D^+ \to ρ^+ ρ^0 (ω) \to ρ^+ π^+π^-$, $D^+ \to π^+ ρ^0 (ω) \to π^+ π^+π^-$, $D^0 \to ϕρ^0 (ω) \toϕπ^+π^-$, $D^0 \toηρ^0 (ω) \toηπ^+π^-$, $D^0 \to η' ρ^0 (ω) \toη' π^+π^-$, $D^0 \to π^0 ρ^0 (ω) \to π^0 π^+π^-$, and $Λ_c \ra p ρ^0 (ω) \to p π^+π^-$ via $ρ-ω$ 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 $π^+π^-$ pair is in the vicinity of the $ω$ resonance. For $D^0 \to π^0 ρ^0 (ω) \to π^0 π^+π^-$ and $Λ_c \to p ρ^0 (ω) \to p π^+π^-$ 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 $D^0 \to π^0 ρ^0$ and $Λ_c \to p ρ^0$ for these values of $N_c$, which should be tested by future experimental data.