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 $Z_2$ mu--tau reflection symmetry, broken at $\mathcal{O}(ϵ)$ to generate a nonzero reactor angle and CP-violating phase. The PMNS matrix factorizes as $U_{\mathrm{PMNS}}=U_e^{†}{U}_{\nu }$, 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 $J_{\mathrm{CP}}\simeq -0.03$ 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.