Seeking massless dark photons in the decays of charmed hadrons

We entertain the possibility that massless dark photons exist and have nonnegligible flavor-changing dipole-type couplings to the $u$ and $c$ quarks. Such interactions give rise to the flavor-changing neutral current decays of charmed hadrons into a lighter hadron plus missing energy carried away by the dark photon. We investigate specifically the decays of the charmed mesons $D^{+,0}$ and $D_s^+$, bottom charmed meson $B_c^+$, singly charmed baryons $\Lambda_c^+$, $\Xi_c^+$, and $\Xi_c^0$, and doubly-charmed baryon $\Xi_{cc}^{++}$. Employing a simplified new-physics model satisfying the relevant constraints, we find that these processes can have branching fractions reaching the $10^{-4}$ level, implying that one or more of these modes may be accessible in the near future by the ongoing Belle II and BESIII experiments. Since the same underlying interaction is responsible for all of these transitions, detecting one of them automatically implies predictions for the others, allowing for additional experimental checks on the massless dark photon scenario.