A Precise Unified Mass Scaling Law for Leptons and Quarks: Implications for Their Internal Geometric Structures governed by Hypercomplex Algebra
Abstract
Jau Tang and Qiang Tang
We propose a geometric mass scaling law for charged leptons and quarks based on a unified logarithmic formula, log m = Alog x + B + Cx that accurately describes the masses of charged leptons (x=1, 2, and 3) and light and heavy quarks (x=13 , 23 , and 33 ) across all generations. This simple three-parameter structure precisely reproduces experimental mass values, suggesting a deep correlation between their mass hierarchies and internal geometrical spinor structures governed by hypercomplex algebra. The distinct scaling behaviors among leptons and quarks emerge naturally from internal symmetry differences embedded in the spinor structure of 16-dimensional sedenion algebra. In contrast to a purely empirical model, our approach derives these patterns from algebraic and topological principles. The result offers insight into the three-generation structure, SU(2) versus SU(3) couplings, and mass regularities without relying on the Higgs mechanism or arbitrary parameterization.
