Direct CP violation in two-body hadronic charmed meson decays

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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 adir (tree) at tree level can be reliably estimated. In general, it lies in the range 10⁻⁴<adir (tree)<10⁻³. Short-distance QCD penguins and penguin annihilation are calculated using QCD factorization. Their effects are generally small, especially for D→ 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 D⁰→ K+K- and D⁰→ π+π- in which adir (tree) is absent. The maximal ΔaCP dir, the direct CP asymmetry difference between the above-mentioned two modes, allowed in the SM is around -0.25%, more than 2σ away from the current world average of -(0.645± 0.180)%.