The UD Derivation of the Muon-Electron Mass Ratio
Dan Zhu · Zenodo (CERN European Organization for Nuclear Research) · 2026
TABSTRACT The muon-electron mass ratio m_μ/m_e ≈ 207 is an important constant in particle physics. The Standard Model cannot explain this ratio; it must be taken as a free input parameter. This paper derives the muon-electron mass ratio from first principles within the UD theory framework. The electron is identified as the bound state of D_U (quantum fluctuations) with the scalar background field D_D (matter condensation). The muon is identified as the bound state of D_U with the vector background field U_D (dark matter). The background field ratio U_D/D_D = e^π follows rigorously from the mutual containment principle and the total normalization axiom. The factor 2π√2 emerges from the spherical wavefunction normalization and spin-1/2 normalization. The vector coupling renormalization gives 1/(1-α). Combining all factors yields m_μ/m_e = 2π√2 e^π/(1-α) = 207.13, which differs from the experimental value 206.768 by only 0.18%. Including the estimated scalar vertex correction (~0.23%) would bring the prediction to ≈206.6, even closer to experiment. This is the second piece of the three-generation fermion mass puzzle in UD theory. KEY FINDINGS 1. The electron is the bound state of D_U with the scalar background D_D; the muon is the bound state of D_U with the vector background U_D. 2. The background field ratio U_D/D_D = e^π is rigorously derived from the UD axioms (total normalization + mutual containment). 3. The mass of each bound state is proportional to its background field value, justified by first-order perturbation theory. 4. The quantum characteristic factor 2π√2 emerges from spherical wavefunction normalization and spin-1/2 normalization. 5. The vector coupling renormalization factor 1/(1-α) is adopted from standard QED, which UD theory reduces to in the appropriate limit. 6. The theoretical prediction 207.13 differs from the experimental value 206.768 by only 0.18%. 7. Including the estimated scalar vertex correction (~0.23%) would bring the prediction to ≈206.6. 8. The muon is heavier but rarer than the electron because the U_D background is stronger but more diffuse and less stable. 9. Internal consistency with the proton-electron mass ratio is verified: m_p/m_μ ≈ 8.88. ELIMINATED ASSUMPTIONS - Muon mass as free parameter → Derived from UD axioms- Lepton generations as independent → Bound states with different backgrounds- Mass hierarchy as unexplained → Consequence of background field asymmetry Keywords: UD theory, muon mass, electron mass, lepton generations, bound states, mass ratio