A correlated radion–tensor Yukawa pair from a stabilised braneworld: predictions and comparison with single-Yukawa limits

Short-range gravity tests can probe the correlated scalar and tensor forces of a stabilised extra dimension. We compute their ranges and couplings in a Goldberger–Wise-stabilised two-brane Randall–Sundrum model with matter on the positive-tension brane. The brane separation and anti-de Sitter length provide two parameters fixing four observables at fixed stabilisation inputs. At the reference separation and an anti-de Sitter length of 10–20 μm, the radion gives (α, λ) = (0.045, 68–136 μm), while the first transverse-traceless Kaluza–Klein mode gives (≈0.6, 5.3–10.5 μm). The stabilising scalar tower adds a third term at 0.38% of the radion coupling. Comparison with published torsion-balance limits and their reconstructions gives a radion crossing at ℓ_AdS = 12.9 μm, with ±3.0% from reconstruction-form spread, and a first-tensor crossing at ℓ_AdS = 89.47 μm. Because these limits bound a single Yukawa, the crossings are single-term consistency tests, not exclusions of the correlated prediction. The metric coupling preserves universality of free fall at tree level. In the reduced stiff-pin family, stable members end at kJ* ≃ 6.661, which corresponds to a leading-coupling value α* ≈ 5.5 × 10⁻⁷ for that family; the fully backreacted endpoint is not located. The radion coupling agrees to about 2% with the coupled-mode calculation at the reference parameters, linking the correlated force signature to the stabilised geometry.