Dark Charge Conjugation and Complementary Constraints from $D^0$ Mixing and Rare Decays with Massless Dark Photons
We investigate how dark charge conjugation organizes rare $D^0$ decays involving a massless dark photon and how these decays complement neutral charm mixing in constraining a common flavor changing interaction. Within a simplified framework with a real pseudoscalar mediator, $D^0\to\gamma_{\mathrm D}\gamma_{\mathrm D}$ probes the portal that preserves $\mathcal{C}_{\mathrm D}$, whereas $D^0\to\gamma\gamma_{\mathrm D}$ probes the portal associated with $\mathcal{C}_{\mathrm D}$ breaking. Because the two decay channels and $D^0$ mixing share the same flavor normalization and mediator propagator, the flavor dependence can be eliminated analytically, converting the mixing constraint into a direct upper bound on the invisible decay rate. Combining current constraints from mixing, invisible decay, and the single dark photon channel, we identify a transition between regions dominated by mixing and regions dominated by invisible decay in mediator parameter space. The single dark photon search then yields conditional upper limits on the portal associated with $\mathcal{C}_{\mathrm D}$ breaking once the flavor normalization is fixed at its maximal value allowed by mixing and invisible decay. These results demonstrate a symmetry resolved complementarity between neutral meson mixing and rare charm decays in probing flavor changing interactions with a massless dark sector.