DirectCPviolation in charmed hadron decays viaρ−ωmixing

We study the possibility of obtaining large direct $\mathrm{CP}$ violation in the charmed hadron decays $D^{+}\to {\rho }^{+}{\rho }^0\left(\omega \right)\to {\rho }^{+}{\pi }^{+}{\pi }^{-},$ $D^{+}\to {\pi }^{+}{\rho }^0\left(\omega \right)\to {\pi }^{+}{\pi }^{+}{\pi }^{-},$ $D^0\to \phi {\rho }^0\left(\omega \right)\to \phi {\pi }^{+}{\pi }^{-},$ $D^0\to \eta {\rho }^0\left(\omega \right)\to \eta {\pi }^{+}{\pi }^{-},$ $D^0\to {\eta }^{\prime }{\rho }^0\left(\omega \right)\to {\eta }^{\prime }{\pi }^{+}{\pi }^{-},$ $D^0\to {\pi }^0{\rho }^0\left(\omega \right)\to {\pi }^0{\pi }^{+}{\pi }^{-},$ and ${\Lambda }_c\to p{\rho }^0\left(\omega \right)\to p{\pi }^{+}{\pi }^{-}$ via $\rho -\omega$ mixing. The analysis is carried out in the factorization approach. The $\mathrm{CP}$ violation parameter depends on the effective parameter $N_c$ which is relevant to the hadronization dynamics of each decay channel and should be determined by experiment. It is found that for fixed $N_c$ the $\mathrm{CP}$ violation parameter reaches its maximum value when the invariant mass of the ${\pi }^{+}{\pi }^{-}$ pair is in the vicinity of the $\omega$ resonance. For most of the parameter space explored the $\mathrm{CP}$ violating asymmetry is of order ${10}^{-4}.$ However, over a small range, $1.98<~N_c<~1.99$ and $1.95<~N_c<~2.02,$ the asymmetries for $D^0\to {\pi }^0{\rho }^0\left(\omega \right)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and ${\Lambda }_c\to p{\rho }^0\left(\omega \right)\to p{\pi }^{+}{\pi }^{-}$ (respectively) can exceed 1%, at the cost of a small branching ratio. 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.