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 ($\epsilon\equiv 1/B\simeq 0.19$) generates charged-lepton mass hierarchies and a normal-ordered neutrino spectrum; large neutrino mixing angles require an additional approximate $Z_2$ mu--tau reflection symmetry, broken at $\mathcal{O}(\epsilon)$ to generate a nonzero reactor angle and CP-violating phase. The 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 aligned by the single-flavon origin of the Yukawa textures. A single interference relation expresses the observed Dirac phase $\delta$ as the neutrino-sector phase $\delta_\nu$ shifted by a calculable charged-lepton correction, and correlates the sign of that shift with the atmospheric octant; this 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 $\theta_{23}\approx 46^\circ$, $\delta\approx 299^\circ$. This structure has a geometric form as a $\nu_3$-column normalization triangle whose base angle is $2\theta_{23}$, with maximal mixing the $90^\circ$ limit and the octant fixed by the side of $90^\circ$ on which the base angle falls. The lower octant is mildly favored, by a margin that depends on the coefficient prior. Both branches place the Dirac phase above $270^\circ$, i.e. near-maximal leptonic CP violation, favored by T2K. The Jarlskog invariant $J_{\rm CP}\simeq -0.03$ 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.