Direct CP violation in two-body hadronic charmed meson decays

Abstract: 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 $-(0.645\pm 0.180)%$.