Direct CP violation in two-body hadronic charmed meson decays

Motivated by the recent observation of CP violation in the charm sector by LHCb, we study direct CP asymmetries in the standard model (SM) for the singly Cabibbo-suppressed two-body hadronic decays of charmed mesons using the topological-diagram approach. In this approach, the magnitude and the phase of topological weak annihilation amplitudes which arise mainly from final-state rescattering can be extracted from the data. Consequently, direct CP asymmetry $a_{dir}^{\rm (tree)}$ at tree level can be reliably estimated. In general, it lies in the range $10^{-4}<a_{dir}^{\rm (tree)}<10^{-3}$. Short-distance QCD penguins and penguin annihilation are calculated using QCD factorization. Their effects are generally small, especially for $D\to VP$ modes. Since weak penguin annihilation receives long-distance contributions from the color-allowed tree amplitude followed by final-state rescattering, it is expected to give the dominant contribution to the direct CP violation in the decays $D^0\to K^+K^-$ and $D^0\to \pi^+\pi^-$ in which $a_{dir}^{\rm (tree)}$ is absent. The maximal $\Delta a_{CP}^{\rm dir}$, the direct CP asymmetry difference between the above-mentioned two modes, allowed in the SM is around -0.25%, more than $2\sigma$ away from the current world average of $-(0.645\pm 0.180)%$.