  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.
