What question did this study set out to answer?

The aim is to derive the proton charge radius using a theoretical framework without relying on quark models or QCD parameters.

March 8, 2026Open Access

Case 05 — Derivation of the Proton Charge Radius as the B=1 Toroidal Resonance of the Vibrational Field Sₕ

Key Points

The aim is to derive the proton charge radius using a theoretical framework without relying on quark models or QCD parameters.
Applied Unified Vibrational Force Theory (UVFT) to derive proton charge radius.
Utilized a topological invariant based on the virial theorem.
Examined the energy functional of a B=1 soliton.
Proton charge radius derived as 0.841 fm.
Identified the source of discrepancy in measurements between muonic and electronic values.
Provided a new perspective on the 'Proton Radius Puzzle', correlating findings with theoretical principles.

Abstract

The proton charge radius rₚ = 0. 841 fm is derived from the Unified Vibrational Force Theory (UVFT) as the spatial extension of the B=1 toroidal stable resonance of the vibrational field Sₕ without any quark model or QCD parameters. The derivation rests on a single topological invariant, mₚ rₚ = 4 c, following from the virial theorem applied to the B=1 soliton energy functional. This case also provides a first-principles resolution to the "Proton Radius Puzzle" by identifying the discrepancy between muonic and electronic measurements as a phase distortion induced by the muon's torsional mass residual (₂), establishing total consistency with Case 01.

Case 05 — Derivation of the Proton Charge Radius as the B=1 Toroidal Resonance of the Vibrational Field Sₕ

Key Points

Abstract

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