Seeking massless dark photons in the decays of charmed hadrons

A massless dark photon could affect standard-model particles only via higher-dimensional operators and would therefore have eluded recent searches for its massive counterpart, which were based on the assumption that the latter had renormalizable interactions with known fermions due to gauge kinetic mixing. In this study we entertain the possibility that the massless dark photon has nonnegligible flavor-changing dipole-type couplings with the $u$ and $c$ quarks, giving rise to the decays of charmed hadrons into a lighter hadron plus missing energy carried away by the dark photon. We propose to investigate decays of this kind, especially those in which the parents are the charmed pseudoscalar-mesons $D^+$, $D^0$, and $D_s^+$ and singly charmed baryons $\Lambda_c^+$, $\Xi_c^+$, and $\Xi_c^0$. Employing a simplified new-physics model satisfying the relevant constraints, we find that the branching fractions of these processes could be as large as several times $10^{-5}$. This suggests that one or more of them might in the near future fall within reach of the ongoing Belle II and BESIII experiments. Since the same underlying operators are responsible for all of these transitions, detecting one of them automatically implies particular predictions for the others, allowing for additional experimental checks on the massless-dark-photon scenario.