Impact of Resonance on Thermal Targets for Invisible Dark Photon Searches

Dark photons in the MeV to GeV mass range are important targets for experimental searches. We consider the case where dark photons $A'$ decay invisibly to hidden dark matter $X$ through $A' \to XX$. For generic masses, proposed accelerator searches are projected to probe the thermal target region of parameter space, where the $X$ particles annihilate through $XX \to A' \to \text{SM}$ in the early universe and freeze out with the correct relic density. However, if $m_{A'} \approx 2m_X$, dark matter annihilation is resonantly enhanced, shifting the thermal target region to weaker couplings. For $\sim 10\%$ degeneracies, we find that the annihilation cross section is generically enhanced by four (two) orders of magnitude for scalar (pseudo-Dirac) dark matter. For such moderate degeneracies, the thermal target region drops to weak couplings beyond the reach of all proposed accelerator experiments in the scalar case and becomes extremely challenging in the pseudo-Dirac case. Proposed direct detection experiments can probe moderate degeneracies in the scalar case. For greater degeneracies, the effect of the resonance can be even more significant, and both scalar and pseudo-Dirac cases are beyond the reach of all proposed accelerator and direct detection experiments. For scalar dark matter, we find an absolute minimum that sets the ultimate experimental sensitivity required to probe the entire thermal target parameter space, but for pseudo-Dirac fermions, we find no such thermal target floor.