Toward charge-dependent tests of the equivalence principle: A phenomenological parameter and an unexplored frontier

We introduce and define the phenomenological parameter $κ$, defined by $Δa/g = κ\, Δ(q/m)$, to quantify potential linear coupling between electric charge and gravitational acceleration. A synthesis of existing precision equivalence principle experiments yields the first quantitative estimate of the effective sensitivity to this coupling: |κ| < 2.1 × 10⁻⁴~ at 95% confidence level. This constraint is approximately eleven orders of magnitude less stringent than corresponding bounds on composition-dependent violations, revealing that the electromagnetic axis remains a largely underexplored frontier in empirical gravity. We connect $κ$ to established frameworks -- the Standard-Model Extension and the $THεμ$ formalism -- showing that it occupies a region of parameter space untouched by existing high-precision tests. An effective field theory analysis shows that dimension-six operators that couple curvature directly to the electromagnetic field strength are suppressed by the minuscule terrestrial spacetime curvature (GN ρ_⊕ ~ 10⁻⁵⁵~GeV²) and are therefore phenomenologically irrelevant. Consequently, a future measurement of $κ$ at an accessible level would not probe minimal geometric couplings but would signal physics beyond minimal gravitational EFT, such as mediation by light scalar fields as in Einstein-Maxwell-Dilaton theory. We examine the Schiff-Barnhill effect, the primary systematic background for any such measurement, and show how it can be separated from a genuine signal. We outline the necessary experimental strategy, focused on maximizing charge-to-mass ratio differences, to transform this overlooked axis into a targeted probe for new physics.