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

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 ($ε\equiv 1/B\simeq 0.19$) generates charged-lepton mass hierarchies and a normal-ordered neutrino spectrum; large neutrino mixing angles require an additional approximate mu-tau symmetry, broken at $\mathcal{O}(ε)$ to generate a nonzero reactor angle and CP-violating phase. The Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix factorizes as $U_{\rm PMNS}=U_e^\dagger U_ν$, with near-tribimaximal $U_ν$ 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 $(θ_{23},δ)$ plane: a lower-octant solution with $θ_{23}\approx 43^\circ$, $δ\approx 286^\circ$, and an upper-octant solution with $θ_{23}\approx 46^\circ$, $δ\approx 304^\circ$. 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.

Figures (3)

• Figure 1: Schematic logic of the single-$B$ lattice-flavon lepton analysis. Neutrino-dominant mixing corrected by $B$-lattice charged-lepton rotations produces an interference-controlled reactor element $U_{e3}$, implying a predictive two-branch octant--$\delta$ structure.
• Figure 2: Two-branch structure in the $(\theta_{23},\delta)$ plane from the $\mathcal{O}(1)$ coefficient scan. Left: NO-I (lower octant, $\theta_{23}<45^\circ$); Right: NO-II (upper octant, $\theta_{23}>45^\circ$). NuFIT 6.0 $2\sigma$ cuts on $\sin^2\theta_{12}$ and $\sin^2\theta_{13}$ are applied; the NuFIT 6.0 (NO) $1\sigma$--$3\sigma$ ranges for $\theta_{23}$ are indicated by the shaded bands. The star marks the benchmark of Table \ref{['tab:PMNSnum']}. The lower octant is favored $\sim\!4{:}1$ by point count.
• Figure 3: Summary of mixing angles and phases in the lattice-flavon lepton model. Top row: PDG mixing angles $\theta_{12}$, $\theta_{23}$, $\theta_{13}$ compared with the neutrino-sector values ($\theta_{12}^\nu$, $\theta_{23}^\nu$, $\theta_{13}^\nu$) for the two normal-ordering branches (NO-I and NO-II); dashed lines mark the tribimaximal and maximal reference values. Middle row: charged-lepton correction angles $\theta_{ij}^e$ at the $B$-lattice base scale ($c=1$, solid bars) and at the benchmark values (hatched bars), on an expanded vertical scale; labels indicate the $\epsilon$-power scaling. Bottom left: Fritzsch--Xing rotation angles $(\theta_\ell,\,\theta,\,\theta_\nu)$ for NO-I (green) and NO-II (purple), with tribimaximal and maximal reference lines. Bottom right: Dirac phase $\delta$, FX phase $\phi_{\rm FX}$, and neutrino-sector phase $\delta_\nu$ for both branches; the dashed line marks the quark-sector reference $\pm 90^\circ$.