Probing the Geometry of Viable Froggatt-Nielsen-like Flavor Textures
Abstract
We investigate the geometry of viable Froggatt--Nielsen-like flavor textures in a controlled toy landscape. In this first texture-level analysis, each point is represented by the eighteen integer exponents entering the up- and down-type Yukawa matrices, without imposing the additional charge-factorization constraints of specific Froggatt--Nielsen models. Viability is imposed through cuts on quark mass ratios and selected CKM observables. We construct four benchmark ensembles, ranging from masses-only constraints to the inclusion of the full set of CKM observables considered in this work, and study the resulting point clouds in the raw exponent space. Principal-component analysis shows no evidence for strong linear compression: in all benchmarks, fifteen principal components are required to account for 90% of the variance. Nearest-neighbour intrinsic-dimensionality diagnostics, including TwoNN and Levina--Bickel estimators, support the same qualitative conclusion, yielding high effective dimensions of order 10-12. These results do not rule out hidden flavor-theory geometry in other coordinates; rather, they suggest that raw Froggatt--Nielsen exponents may not provide natural coordinates for revealing such a geometry.
Related
- Lightest-mass suppression and weaker Majorana cancellation in Froggatt--Nielsen textures
- How natural are Froggatt-Nielsen Models?
- Froggatt-Nielsen mechanism with non-invertible symmetry
- Non-Invertible Froggatt-Nielsen Symmetry
- Variable-Cliff Nielsen Geometry and an Exponent -4/3 Lower Bound for the Infinite-Cliff Diameter
BibTeX
@misc{meloni2026probing,
title = {{Probing the Geometry of Viable Froggatt-Nielsen-like Flavor Textures}},
author = {Davide Meloni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03812},
eprint = {2609.03812},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03812},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Probing the Geometry of Viable Froggatt-Nielsen-like Flavor Textures
AU - Davide Meloni
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03812
UR - https://arxiv.org/abs/2609.03812
AB - We investigate the geometry of viable Froggatt--Nielsen-like flavor textures in a controlled toy landscape. In this first texture-level analysis, each point is represented by the eighteen integer exponents entering the up- and down-type Yukawa matrices, without imposing the additional charge-factorization constraints of specific Froggatt--Nielsen models. Viability is imposed through cuts on quark mass ratios and selected CKM observables. We construct four benchmark ensembles, ranging from masses-only constraints to the inclusion of the full set of CKM observables considered in this work, and study the resulting point clouds in the raw exponent space. Principal-component analysis shows no evidence for strong linear compression: in all benchmarks, fifteen principal components are required to account for 90% of the variance. Nearest-neighbour intrinsic-dimensionality diagnostics, including TwoNN and Levina--Bickel estimators, support the same qualitative conclusion, yielding high effective dimensions of order 10-12. These results do not rule out hidden flavor-theory geometry in other coordinates; rather, they suggest that raw Froggatt--Nielsen exponents may not provide natural coordinates for revealing such a geometry.
ER -