The Inevitable Two-Scale Architecture of Charged Leptons: A Structural Constraint from Photon Collisions and Precision Measurements

Abstract

We derive an operational structural constraint on charged leptons using only established experimental facts and standard principles of relativistic kinematics and classical electromagnetism. Starting from the experimentally verified process γγ → e +e − and precision measurements of electron properties, we show that any stable charged particle described within Maxwell theory and special relativity is constrained to exhibit two distinct characteristic length scales. A compact core scale, of order the Compton wavelength, localizes the dominant rest-energy contribution, while a larger scale governs charge distribution to avoid prohibitive Coulomb self-energy. The resulting scale separation naturally appears at the level of the fine-structure constant, Rq/Rm ∼ α. This result is not a model of particle composition, but an effective constraint on electromagnetic descriptions consistent with known physics. A representative Gaussian realization illustrates compatibility with precision measurements, including form-factor limits and the electron anomalous magnetic moment, without introducing new particles, fields, or modified dynamics.

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