Effective Vacuum Dynamics and Lepton Anomalous Magnetic Moments: A Phenomenological Approach

Quantum electrodynamics (QED) provides extraordinarily accurate predictions for charged lepton properties, although its formalism offers limited intuitive insight into the geometrical and energetic scales associated with vacuum effects. In this work, a phenomenological representation is introduced to describe the leading-order contribution to the anomalous magnetic moment of charged leptons. By combining characteristic length and energy scales associated with the Compton radius and rest energy with geometric arguments, the Schwinger correction to the electron magnetic moment is recovered. Within this framework, the fine-structure constant acquires the meaning of a characteristic angular scale associated with the effective vacuum dressing of the particle. The construction naturally extends to the muon, indicating the universality of the angular structure underlying anomalous magnetic moments. The model does not replace quantum electrodynamics but tries to provide an effective geometric representation of its lowest-order result, offering an intuitive picture of vacuum dressing and interaction scales.