Unified Flavor: Lattice Quantization, Chain Locality, and a Dynamical Origin of Hierarchical Yukawas

TL;DR

Unified Flavor (UF) is a novel framework combining lattice flavor hierarchies with dynamical TeV-scale vectorlike fermion chains, naturally explaining quark and lepton mass hierarchies, CP violation, and addressing flavor and strong CP problems.

Contribution

It introduces a unified lattice-based approach with vectorlike fermion chains that reproduces fermion masses, mixing, and CP phases while satisfying flavor constraints and connecting to collider and neutrino experiments.

Findings

Reproduces all six quark masses with O(1) coefficients.

Derives CKM hierarchy and CP phases from lattice algebra and multi-messenger interference.

Predicts TeV-scale vectorlike quarks accessible at HL-LHC and testable neutrino mixing correlations.

Abstract

We present Unified Flavor (UF), a framework that synthesizes the $B$-lattice flavor hierarchy with a dynamical realization based on TeV-scale vectorlike fermion (VLF) chains. Hierarchical Yukawa couplings arise from discrete ninths-quantized lattice exponents enforced by a single flavon $\Phi$ with $\epsilon\equiv\langle\Phi\rangle/\Lambda=1/B$, $B=75/14$. Effective Yukawa entries are generated as algebraic path sums along nearest-neighbor chains of vectorlike quarks (VLQs), factorizing into entry, chain-propagation, and exit amplitudes controlled by the discrete gauge charges. A multi-messenger structure -- in which each Yukawa entry receives coherent contributions from several chain configurations -- generates O(1) complex coefficients whose phases are the physical origin of CP violation. We derive a general chain-inversion theorem, perform systematic perturbative diagonalization of both up- and down-type Yukawa textures, and show that the Cabibbo--Kobayashi--Maskawa (CKM) mixing hierarchy and CP-phase structure emerge naturally from the lattice exponent algebra and multi-messenger interference. All six quark masses are reproduced with O(1) coefficients that are essentially unity. The chain locality simultaneously suppresses dangerous flavor-changing neutral currents (FCNCs) and satisfies electroweak precision constraints, while requiring VLQs with masses in the multi-TeV range accessible at the High-Luminosity Large Hadron Collider (HL-LHC). The same discrete gauge symmetry that enforces the lattice structure also protects the Peccei--Quinn axion quality, unifying flavor, CP violation, and the strong CP problem. The framework extends to the lepton sector, reproducing charged-lepton mass hierarchies, the normal-ordered neutrino spectrum, and PMNS mixing with a predictive two-branch octant--$\delta$ correlation testable at DUNE and Hyper-Kamiokande.