Procedure for recasting dark-photon limits in the linearly polarized scenario

Determine the appropriate analysis procedure to recast axion–photon coupling limits into the dark-photon kinetic mixing parameter χ for a linearly polarized dark-photon scenario in haloscope experiments, specifically prescribing how to average cosθ = X · B over acquisition time in the relation χ = g_{aγγ} B / (m_DP |cosθ|), so that consistent experimental limits on χ can be derived.

Background

In the dark-photon reinterpretation of axion haloscope results, the kinetic mixing parameter χ can be related to the measured axion–photon coupling g_{aγγ} via χ = g_{aγγ} B / (m_DP |cosθ|), where B is the magnetic field magnitude in natural units, m_DP is the dark-photon mass, and cosθ = X * B depends on the dark-photon field polarization X relative to the magnetic field.

The authors consider two polarization scenarios: (i) random polarization, for which cos^2θ = 1/3 is conventionally used, and (ii) linear polarization, for which cosθ must be averaged over the acquisition time. They restrict their analysis to the random polarization scenario because, for the linearly polarized case, a standardized analysis prescription has not been established in the literature, preventing a consistent recast of their results.