A Structural Origin of the Charged-Lepton Hierarchy
Abstract
The charged-lepton masses are free Yukawa-sector parameters in the Standard Model, whereas their measured pole-mass ratios display a highly structured hierarchy and satisfy the Koide relation to notable accuracy. This paper develops a conditional mathematical-physics proposal in which these dimensionless regularities arise from a charge-neutral parent carrier-defect architecture before effective Higgs–Yukawa read-out. The assumptions of the construction are stated explicitly as structural postulates and are separated from their derived consequences. The central rule assigns equal primitive weight to admissible internal sectors that are indistinguishable at the level where they first become exposed; protected sectors are removed before counting, and later refinements are conditional on previously selected sectors. Under this rule, the Koide relation follows as an equal-power theorem between the democratic parent component and the orthogonal branch-splitting component of the charged-lepton root-amplitude state. A minimal endpoint construction then yields a rapidly stabilizing charged tower for the electron–muon ratio. Because deeper charged terms are too small to remove the remaining residual, the framework assigns that residual to the continuation-dual neutral branch. The resulting neutral overlap gives a leading solar-angle target of 33.21 degrees and closes the electron–muon ratio at the present experimental precision; the Koide relation then fixes the corresponding tau ratios. The construction does not replace the Standard Model but is proposed as a selection rule for the boundary values of effective charged-lepton Yukawa parameters, with pole masses used because the claimed invariant is attached to completed asymptotic particle read-out. Running parameters, the absolute mass scale, and the full Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix remain outside the present derivation. The proposal has explicit failure conditions: improved measurements can exclude the predicted tau ratios or solar-angle target, and the claimed conditional uniqueness fails if a different counting scheme satisfies the same postulates while producing different endpoint weights.
Related
- Effective flavor interaction for the charged-lepton mass hierarchy and the Koide relation
- Charged Lepton Flavor Violation: A Theory Overview
- Searching for Charged Lepton Flavor Violation
- The conformal origin of the lepton flavor mixing matrix
- Charged-Lepton Koide Geometry from a Green-Dressed Compact Family Cycle
BibTeX
@article{li2026structural,
title = {{A Structural Origin of the Charged-Lepton Hierarchy}},
author = {Bin Li},
journal = {Symmetry},
year = {2026},
month = jul,
doi = {10.3390/sym18071232},
url = {https://doi.org/10.3390/sym18071232},
note = {CC BY},
}
RIS
TY - JOUR
TI - A Structural Origin of the Charged-Lepton Hierarchy
AU - Bin Li
PY - 2026
DA - 2026/07/21
JO - Symmetry
DO - 10.3390/sym18071232
UR - https://doi.org/10.3390/sym18071232
AB - The charged-lepton masses are free Yukawa-sector parameters in the Standard Model, whereas their measured pole-mass ratios display a highly structured hierarchy and satisfy the Koide relation to notable accuracy. This paper develops a conditional mathematical-physics proposal in which these dimensionless regularities arise from a charge-neutral parent carrier-defect architecture before effective Higgs–Yukawa read-out. The assumptions of the construction are stated explicitly as structural postulates and are separated from their derived consequences. The central rule assigns equal primitive weight to admissible internal sectors that are indistinguishable at the level where they first become exposed; protected sectors are removed before counting, and later refinements are conditional on previously selected sectors. Under this rule, the Koide relation follows as an equal-power theorem between the democratic parent component and the orthogonal branch-splitting component of the charged-lepton root-amplitude state. A minimal endpoint construction then yields a rapidly stabilizing charged tower for the electron–muon ratio. Because deeper charged terms are too small to remove the remaining residual, the framework assigns that residual to the continuation-dual neutral branch. The resulting neutral overlap gives a leading solar-angle target of 33.21 degrees and closes the electron–muon ratio at the present experimental precision; the Koide relation then fixes the corresponding tau ratios. The construction does not replace the Standard Model but is proposed as a selection rule for the boundary values of effective charged-lepton Yukawa parameters, with pole masses used because the claimed invariant is attached to completed asymptotic particle read-out. Running parameters, the absolute mass scale, and the full Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix remain outside the present derivation. The proposal has explicit failure conditions: improved measurements can exclude the predicted tau ratios or solar-angle target, and the claimed conditional uniqueness fails if a different counting scheme satisfies the same postulates while producing different endpoint weights.
SN - 2073-8994
ER -