QCD-based estimate of direct $CP$ asymmetry in charm decays

I discuss the calculation of the direct CP-asymmetry in $D\to \pi^+\pi^-$ and $D\to K^+K^-$ decays with the method of QCD light-cone sum rules. The main result is the upper limit for the difference of the two asymmetries $\left|\Delta a_{CP}^{dir}\right| < 0.020\pm 0.003\%$ which is significantly smaller than the recent measurement of this quantity by the LHCb collaboration