Relativity and Cosmology

Constraining Conformal Scalar-Tensor Activation: Density-Based Geometric Recovery (DBGR) Bounds from the Historic Proton Radius Anomaly

Authors: Bhasanpal Thiru

We formalize a phenomenological Density-Based Geometric Recovery (DBGR) model within anextended Einstein-Cartan-Sciama-Kibble (ECSK) scalar-tensor framework to establish bounds onlepton-induced metric deformations. Standard algebraic spin-torsion interactions are kinematicallysuppressed by O(10−40). However, transforming to the Einstein frame reveals a dynamic scalar fieldΦ capable of chameleon-like de-screening. Governed by quartic mass scaling (ρ ∝ µ4r), a muonicstate generates a localized density perturbation ∼ 1.82 × 109times greater than an electronic state.We test the boundary condition where this localized muonic threshold un-screens a macroscopicYukawa potential, evaluating the geometric contraction required to explain the historic proton radiusanomaly. Utilizing first-order perturbation theory with the exact 2S radial wavefunction, recoveringa −0.31 meV geometric binding requires a dimensionless effective coupling of αscalar ≈ 2.91 × 10−7.Because this violates established atom interferometry fifth-force bounds (α ≲ 10−11) by over fourorders of magnitude, DBGR excludes macroscopic geometric torsion as the source of the historicanomaly. This provides independent scalar-tensor validation for the CODATA QED consensus(Rp = 0.8413 ± 0.0016 fm) and establishes strict upper limits for the ongoing MUSE form-factordivergence.Keywords: Proton Radius Anomaly, Density-Based Geometric Recovery (DBGR), Chameleon Mechanism, Scalar-Tensor Theory, Metric Torsion, Yukawa Potential, MUSE Experiment, Fifth-Force Exclusion.

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[v1] 2026-03-09 14:28:00

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