A Catalog of Lepton Mass Textures from Koide and Alikhanov Relations
Abstract
The empirical Koide relation for charged-lepton masses and the recently proposed Alikhanov relation for neutrino mass-squared differences offer intriguing hints toward understanding the structure of lepton mass matrices. Motivated by these observations, we systematically explore charged-lepton and neutrino mass-matrix textures that satisfy these relations and confront their predictions for lepton mixing with experimental data. For the charged-lepton sector, we investigate representative positive Hermitian square-root matrices classified by the number of common eigenvector directions of their generators: three, one, or none. For the neutrino sector, an exhaustive enumeration of real symmetric integer matrices with entries between −5 and $5$ identifies six signed-permutation classes with m1=0 and six with m1>0 that satisfy the Alikhanov relation. Combining these neutrino textures with the charged-lepton constructions, allowing for different relative flavor orientations and phase alignments, yields $400$ viable structural pairs consistent with the measured lepton mixing parameters. All retained solutions satisfy the adopted cosmological bound on the sum of neutrino masses and existing laboratory constraints. In particular, the full-rank neutrino textures predict m1≃16.77-17.22 meV. Representative viable solutions yield effective Majorana masses mββ≃1.29-4.03 meV and $4.07−18.67\,\mathrm{meV}$ for the m1=0 and m1>0 branches, respectively, providing potential targets for future high-sensitivity searches.
Related
- A Texture of Leptons for the Koide and Alikhanov relations
- Effective flavor interaction for the charged-lepton mass hierarchy and the Koide relation
- Charged-Lepton Koide Geometry from a Green-Dressed Compact Family Cycle
- Yukawa textures due to selection rules in magnetized orbifold models
- Spin textures at the Fermi surface of ferromagnets and associated torque
BibTeX
@misc{saad2026catalog,
title = {{A Catalog of Lepton Mass Textures from Koide and Alikhanov Relations}},
author = {Shaikh Saad},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28143},
eprint = {2610.28143},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28143},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Catalog of Lepton Mass Textures from Koide and Alikhanov Relations
AU - Shaikh Saad
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28143
UR - https://arxiv.org/abs/2610.28143
AB - The empirical Koide relation for charged-lepton masses and the recently proposed Alikhanov relation for neutrino mass-squared differences offer intriguing hints toward understanding the structure of lepton mass matrices. Motivated by these observations, we systematically explore charged-lepton and neutrino mass-matrix textures that satisfy these relations and confront their predictions for lepton mixing with experimental data. For the charged-lepton sector, we investigate representative positive Hermitian square-root matrices classified by the number of common eigenvector directions of their generators: three, one, or none. For the neutrino sector, an exhaustive enumeration of real symmetric integer matrices with entries between −5 and $5$ identifies six signed-permutation classes with m_1=0 and six with m_1>0 that satisfy the Alikhanov relation. Combining these neutrino textures with the charged-lepton constructions, allowing for different relative flavor orientations and phase alignments, yields $400$ viable structural pairs consistent with the measured lepton mixing parameters. All retained solutions satisfy the adopted cosmological bound on the sum of neutrino masses and existing laboratory constraints. In particular, the full-rank neutrino textures predict m_1≃16.77-17.22 meV. Representative viable solutions yield effective Majorana masses m_ββ≃1.29-4.03 meV and $4.07−18.67\,\mathrm{meV}$ for the m_1=0 and m_1>0 branches, respectively, providing potential targets for future high-sensitivity searches.
ER -