Z -boson decays into an invisible dark photon at the LHC, HL-LHC, and future lepton colliders

We study the decay of the Z vector boson into a photon and a massless (invisible) dark photon in high-energy collisions. The photon can be used as a trigger for the event, while the dark photon is detected indirectly as missing momentum in the event final state. We investigate the possibility of searching for such a dark photon at the LHC, HL-LHC, and future lepton colliders, and compare the respective sensitivities. As expected, the best result is found for the lepton colliders running at the Z mass, FCC-ee and CEPC, with a final sensitivity to branching ratios of order O(10-11). We also discuss how to use the photon angular distribution of the events in lepton collisions to discriminate between the dark photon and a pseudoscalar state like the axion.