  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.
