A Fixed-Constant Algebraic Formula for the Charged Fermion Mass Spectrum from Quantum Numbers and Mathematical Constants: A Phenomenological Report

Background: The Standard Model of particle physics contains 19 free parameters, 9 of which are the Yukawa coupling constants for fermion masses. The Standard Model itself provides no explanation for why these parameters take their specific values.

Purpose: This paper reports the identification of a phenomenological regularity: the masses of all twelve fundamental fermions (three neutrinos and nine charged fermions) can be described by a unified algebraic formula, using only their quantum numbers and fixed mathematical and physical constants, without any continuously adjustable free fitting parameters.

Method: The formula adopts a unified log-cubic structure for all fermions, where the generational expansion parameters are automatically determined by the quantum number combinations through parameter source formulas. The baseline length takes different forms for neutrinos and charged fermions, reflecting the fundamental influence of the presence or absence of electric charge on the origin of mass. The formula was discovered through a step-by-step extension methodology.

Results: The calculated masses of all nine charged fermions deviate from experimental values by less than 2%, with eight particles deviating by less than 1%, and six particles deviating by less than 0.5%. The predicted neutrino masses for the three generations are 2.9×10⁻⁵ eV, 9.0×10⁻³ eV, and 4.7×10⁻² eV, respectively, consistent with the mass-squared difference constraints from neutrino oscillation experiments to within ±15%, with a total sum of 0.056 eV, well below the cosmological upper bound of 0.12 eV.

Conclusion: A fixed-constant algebraic formula for the fermion mass spectrum has been identified. All coefficients are fixed mathematical or physical constants. The physical mechanism behind this formula, if any, remains to be elucidated.