Emergence of Lepton Mass

The baryon-lepton mass hierarchy problem is addressed from the perspective of an Effective Field Theory (EFT) with a hydrodynamic $SU(2)$ vacuum structure. It is proposed that, unlike baryons (topological solitons), lepton mass originates from electromagnetic self-energy regularized by the natural cutoff scale of the condensate ($\Lambda_{UV} \sim f_\pi$). Without introducing arbitrary Yukawa couplings, the electron mass is derived analytically as: $$m_e \approx \frac{3}{4} \alpha f_\pi$$ The resulting theoretical value (0.509 MeV) presents a 99.6% agreement with the experimental value, suggesting that the hadronic scale and leptonic mass share a common geometric origin in the microphysics of the DBI vacuum.