Relativistic Shedding (RS) as Threshold Emission into Hidden Sectors

“Relativistic Shedding” (RS) is the threshold turn-on of emission into a weakly coupled eigenmode when a relativistic charge crosses a phase-velocity condition. The original RS motivation was that a missing-momentum experiment (LDMX-like) could bracket such a threshold by toggling a dielectric configuration and searching for an on/off excess. In Version 5 we keep that LDMX language as the historical motivation and as an analysis pattern (ABAB threshold bracketing), _but_ we correct the physics mapping: for the canonical MeV–GeV dark-photon mediator regime, an ordinary dielectric does not furnish a subluminal propagating eigenmode at \(\omega \gtrsim m\), so the “dielectric light-switch” implementation is kinematically closed. This closure is a mismatch of scales (medium response vs \(m^{2}\)), not an exposure problem. RS remains a well-defined and testable laboratory mechanism for _light_ hidden states (sub-eV) and, more generally, for any weakly coupled eigenmode whose phase velocity can be tuned below \(c\) in an engineered structure. Accordingly, this complete Version 5 specifies a stand-alone RS laboratory program: a _thresholded source_ built from a tunable slow-wave/dielectric eigenmode excited by a relativistic beam, combined with a resonant “light shining through a wall” (LSW) receiver in the spirit of CROWS/Dark SRF. The RS-specific element is the physics-driven threshold modulation variable (phase-velocity bracketing) and the associated falsifier map. We provide: (i) a consolidated operational definition of RS and its minimal experimental signatures; (ii) expanded derivations of threshold conditions in both homogeneous-media and guided-mode language; (iii) the in-medium effective mixing formalism and its relevant limits; (iv) a concrete “where to look” procedure in a CROWS/Dark SRF-compatible receiver; (v) a worked sensitivity estimate (radiometer-limited) with an illustrative reach curve; and (vi) built-in falsifiers designed to separate RS-correlated signals from electromagnetic leakage and instrumental lines. UPDATE NOTE: Superconducting RF cavity LSW searches have demonstrated kinetic-mixing reach at the \(\epsilon \sim 10^{- 9}\) level in the \(\mu\)eV mass range [1], with refined modeling of frequency instability/microphonics indicating that existing pathfinder data can imply an order-of-magnitude stronger constraint [2][3]. Longitudinal-mode transmission can parametrically enhance LSW sensitivity compared to the commonly quoted transverse \({({m/\omega})}^{8}\) suppression, provided the emitter/receiver geometry is optimized [4][5][6]. Recent “thin-wall” proposals extend regeneration-style searches into the off-shell/evanescent regime \(m > \omega\) [7][8].