
Motivated by the possibility that light scalar fields exist beyond the Standard Model, we propose a targeted way to test their presence in radio-frequency cavities by exploiting an in-cavity dynamical handle: a finite response time (phase lag) of the scalar sector to the local electromagnetic invariant (energy-density-like) drive within the resonator volume. Starting from a Jordan-frame scalar–tensor action, we derive the covariant electromagnetic exchange current and recast the predicted observable in a control-volume formulation appropriate for cycle-averaged axial traction (support-load) readouts under radio-frequency driving. To represent the in-situ phase lag generated after coarse graining additional scalar-sector degrees of freedom, we introduce a minimal causal, passive, single-timescale constitutive closure for a reduced response variable ψ(t, x) driven by the cavity field configuration, which is explicitly distinguished from the EFT perturbation δΦ. The framework yields theorem-level null gates: the leading demodulated axial quadrature component vanishes in the conservative (no-lag) limit and under a symmetry phase-gradient condition, providing built-in systematic suppression. The same closure implies a one-parameter matched-filter template S(2ωτ), peaking at 2ωτ = 1, furnishing a low-dimensional falsification target for resonant-cavity null tests that can either reveal an in-cavity phase-lagged scalar response or set direct constraints on the coupling. We also discuss how short-range (massive or screened) scalar regimes can remain compatible with long-range fifth-force bounds.
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