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We present the first QCD-based calculation of hadronic matrix elements withpenguin topology determining direct CP-violating asymmetries in $D^0\to\pi^-\pi^+$ and $D^0\to K^- K^+$ nonleptonic decays. The method is based on theQCD light-cone sum rules and does not rely on any model-inspired amplitudedecomposition, instead leaning heavily on quark-hadron duality. We provide aStandard Model estimate of the direct CP-violating asymmetries in both pion andkaon modes and their difference and comment on further improvements of thepresented computation.

Direct CP asymmetry in $D\to \pi^-\pi^+$ and $D\to K^-K^+$ in QCD-based approach