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Two-over-two lattice flavor from a single flavon with three messenger chains

Department of Physics, University of Wisconsin–Madison, Madison, Wisconsin 53706, USA

Phys. Rev. D 113, 053003 – Published 11 March, 2026

DOI: https://doi.org/10.1103/bhvv-tpfh

Abstract

Flavor hierarchies are organized by a single parameter $B ≃ 5.357$ in a single-flavon Froggatt-Nielsen (FN) framework, in which each effective Yukawa entry arises from the sum of three unit-magnitude messenger chains. We present benchmark complex $O (1)$ Yukawa matrices that reproduce quark and charged-lepton masses at $M_{Z}$ as powers of $ε \equiv 1 / B$ . The organizing principle is a two-over-two ( $2 / 2$ ) lattice of quadrilateral mass ratios, which maps directly to a rational lattice of FN exponents. Sequential dominance preserves the leading-power exponent matrices, while subleading messenger chains generate entry-dependent complex $O (1)$ coefficients and provide a UV-friendly origin for $C P$ violation. Neutrino masses are discussed at the level of eigenvalues within the same $B^{n}$ counting.

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References (12)

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Phys. Rev. D 113, 053003– Published 11 March, 2026

Vol. 113, Iss. 5 — 1 March 2026

Received 26 December 2025
Accepted 19 February 2026

DOI: https://doi.org/10.1103/bhvv-tpfh

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

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Two-over-two lattice flavor from a single flavon with three messenger chains

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