Lepton Mixing from a Lattice Flavon Model: A Two-Branch Octant-delta Prediction

TL;DR

This paper extends a lattice flavon model to the lepton sector, predicting two possible octant and CP phase solutions for neutrino mixing angles, which can be tested by upcoming experiments.

Contribution

It introduces a novel lattice flavon framework for leptons that predicts a two-branch solution for neutrino mixing parameters, linking flavor structure to observable CP phases.

Findings

Predicts two solutions for 3 and 4

Identifies a nearly branch-independent Jarlskog invariant of .027

Suggests future experiments can distinguish the two solutions

Abstract

We extend the single-flavon $B$-lattice Froggatt-Nielsen (FN) framework -- previously successful for quark masses and Cabibbo-Kobayashi-Maskawa (CKM) mixing -- to the lepton sector. The same $B$-lattice power structure ($\epsilon\equiv 1/B\simeq 0.19$) generates charged-lepton mass hierarchies and a normal-ordered neutrino spectrum; large neutrino mixing angles require an additional approximate mu-tau symmetry, broken at $\mathcal{O}(\epsilon)$ to generate a nonzero reactor angle and CP-violating phase. The Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix factorizes as $U_{\rm PMNS}=U_e^\dagger U_\nu$, with near-tribimaximal $U_\nu$ corrected by small charged-lepton rotations whose phases are naturally aligned by the single-flavon origin of the Yukawa textures. This alignment produces a two-branch prediction in the $(\theta_{23},\delta)$ plane: a lower-octant solution with $\theta_{23}\approx 43^\circ$, $\delta\approx 286^\circ$, and an upper-octant solution with $\theta_{23}\approx 46^\circ$, $\delta\approx 304^\circ$. The lower octant is favored by a $\sim\!4{:}1$ theoretical prior. The Jarlskog invariant $J_{\rm CP}\simeq -0.027$ is nearly branch-independent; only precision measurements of the atmospheric octant and Dirac phase at DUNE, Hyper-Kamiokande, IceCube, and JUNO can distinguish the two solutions.