Threefold Precise Patterns in Quark Mass Algebra:A Unified Link to Leptons and Nucleons

This work unveils three classes of hitherto unrecognized, precise algebraic patterns within the quark mass spectrum, forging a novel theoretical bridge to lepton and nucleon properties. First, we discover that the sum of the ultraviolet (UV) and infrared (IR) generalized Koide ratios for fundamental quark sets—the up-type, down-type, and the full six-quark set—converge to the simple rational numbers 9/5, 3/2, and 4/3,respectively, with deviations below 0.5%. Second, we demonstrate that specific contracted mass combinations exhibit Koide ratios approaching 7/9 at a UV fixed point (the grand unification scale) and 2/3 at an IR fixed point (the hadronic scale). The value 7/9 is rigorously derived from the representation theory of a ∆(27) × U(1) flavor symmetry model. Third, and most profound, we find that the ratio R = SΣ/S|∆| of the UV-IR sums for intra-generation symmetric and antisymmetric combinations, when computed with the latest lattice QCD inputs, coincides with the neutron-proton mass ratio mn/mp to within an accuracy of 10−6 (R ≈ 1.001378419). This equality establishes a direct quantitative bridge from fundamental quark level parameters to composite nucleon properties. We construct a unified particle physics model based on ∆(27)×Z4 flavor symmetry, which naturally accommodates the core features of all three patterns. Our work establishes a comprehensive framework connecting quark mass algebra, lepton electromagnetic properties,and nucleon structure, providing a novel, principled pathway towards understanding the origin of elementary particle masses.