Resonance catalyzed CP asymmetries in D -> P l+ l-

Recently observed increase of direct CP asymmetry in charm meson nonleptonic decays is difficult to explain within the SM. If this effect is induced by new physics, this might be investigated in other charm processes. We propose to investigate new CP violating effects in rare decays $D \to P \ell^+ \ell^-$, which arise due to the interference of resonant part of the long distance contribution and the new physics affected short distance contribution. Performing a model independent analysis, we identify as appropriate observables the differential direct CP asymmetry and partial decay width CP asymmetry. We find that in the most promising decays $D^+ \to \pi^+ \ell^+ \ell^-$ and $D_s^+ \to K^+ \ell^+ \ell^-$ the "peak-symmetric" and "peak-antisymmetric" CP asymmetries are strong phase dependent and can be of the order 1% and 10%, respectively.