Quark Mixing from a Lattice Flavon Model: A Four-Magnitude Parameterization

TL;DR

This paper introduces a novel four-magnitude parameterization within a Froggatt--Nielsen framework to predict quark mixing from a lattice-structured flavon model, linking Yukawa textures to observable mixing parameters.

Contribution

It develops a new four-magnitude parameterization that connects flavon Yukawa textures with quark mixing observables using a lattice structure and hierarchy parameter.

Findings

Provides sharp predictions for quark mixing angles and phases.

Establishes a ratio test framework for lattice Yukawa textures.

Links fermion mass hierarchies to mixing observables.

Abstract

We present the quark weak-mixing component of a Froggatt--Nielsen program, with one flavon and three messengers, in which a single hierarchy parameter $B$ (with $\epsilon\equiv 1/B$) and a rational-exponent ``$B$-lattice'' organize fermion Yukawa textures. Building on companion mass-fit work, we translate the lattice into sharp predictions for quark mixing. The four-magnitude parameterization serves as a practical interface between the flavon Yukawa textures and quark weak mixing observables, yielding coefficient-free ratio tests of the lattice structure.