Quantum and Material Effects in Undulator-Based LSW Searches for Dark Photons

Abstract

The dark photon is one of the simplest extensions of the Standard Model and provides a minimal laboratory for quantum-mechanical phenomena. Light-shining-through-a-wall (LSW) searches often adopt the dark photon-photon oscillation formula as if the sensitivity were independent of the light source, the wall, and the surrounding medium. In this paper, I revisit an LSW experiment whose light source is an undulator and systematically include various quantum effects: finite wave packets, kinematical suppression due to the microscopic structure of the source, and mixing suppression/enhancement in the wall and the air. We find that the resulting sensitivities deviate significantly from those obtained with the na\"{i}ve oscillation formula, especially depending on the mass of the dark photon, relevant to reflective index of the medium or walls, there can be resonance effects enhancing the sensitivity significantly. Accounting for these effects, we show that placing a photon detector outside the shielding along the beamline of a synchrotron facility enables an economical, parasitic LSW search for dark photons.