  Many attempts have been made to observe the decay of the Higgs boson to a
photon and an invisible massless dark photon. For this decay to be potentially
observable at the LHC, new mediators that communicate between the Standard
Model and the dark photon must exist. In this Letter, we study bounds on such
mediators coming from the Higgs signal strengths, oblique parameters, electric
dipole moment of the electron and unitarity. We find that the branching ratio
of the Higgs boson to a photon and a dark photon is constrained to be far
smaller than the sensitivity of current collider searches, thus calling for a
reconsideration of current experimental efforts.
