Hidden Sector Photon Coupling of Resonant Cavities

Many beyond the standard model theories introduce light paraphotons, a hypothetical spin-1 field that kinetically mixes with photons. Microwave cavity experiments have traditionally searched for paraphotons via transmission of power from an actively driven cavity to a passive receiver cavity, with the two cavities separated by a barrier that is impenetrable to photons. We extend this measurement technique to account for two-way coupling between the cavities and show that the presence of a paraphoton field can alter the resonant frequencies of the coupled cavity pair. We propose an experiment that exploits this effect and uses measurements of a cavities resonant frequency to constrain the paraphoton-photon mixing parameter, chi. We show that such an experiment can improve sensitivity to chi over existing experiments for paraphoton masses less than the resonant frequency of the cavity, and eliminate some of the most common systematics for resonant cavity experiments.