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

We present the first QCD-based calculation of hadronic matrix elements with penguin 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 the QCD light-cone sum rules and does not rely on any model-inspired amplitude decomposition, instead leaning heavily on quark-hadron duality. We provide a Standard Model estimate of the direct CP-violating asymmetries in both pion and kaon modes and their difference and comment on further improvements of the presented computation.