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Urgent theoretical progress is needed in order to provide an estimate in theStandard Model of the recent measurement by LHCb of direct CP violation incharm-meson two-body decays. Rescattering effects must be taken into accountfor a meaningful theoretical description of the amplitudes involved in suchcategory of observables, as signaled by the presence of large strong phases. Wediscuss the computation of the latter effects based on a two-channel coupleddispersion relation, which exploits isospin-zero phase-shifts and inelasticityparameterizations of data coming from the rescattering processes $ \pi \pi \to\pi \pi $, $ \pi K \to \pi K $, and $ \pi \pi \to K \overline{K} $. Thedetermination of the subtraction constants of the dispersive integrals relieson the leading contributions to the transition amplitudes from the $ 1/N_C $counting, where $N_C$ is the number of QCD colours. Furthermore, we use themeasured values of the branching ratios to help in selecting thenon-perturbative inputs in the isospin limit, from which we predict values forthe CP asymmetries. We find that the predicted level of CP violation is muchbelow the experimental value.

Final-state interactions in the CP asymmetries of charm-meson two-body decays