2026/07/25 by Jianlong Lu
#hep-ph
We investigate the exact phenomenology of a geometric neutrino cuboid defined by m1=m0sinξ, m2=m0cosξsinζ, and m3=m0cosξcosζ, whose cubic point corresponds to mass degeneracy and the tribimaximal values of the solar and atmospheric mixing angles. Imposing the mass-mixing alignment ξ=θ12 and ζ=θ23, we derive closed-form consistency relations without relying on an expansion about the cubic limit. These relations show that the observed condition sin2θ12<1/3 selects normal mass ordering and, in the resulting normal-ordering regime, the physical condition 0<Δm212/Δm312<1 requires θ23 to lie in the lower octant. Representative JUNO-based inputs give sin2θ23≃0.440, (m1,m2,m3)≃(0.0938,0.0942,0.1063)eV, and ∑i mi≃0.294eV. We demonstrate that the first-order expansion around the tribimaximal point is numerically unstable for the solar-to-atmospheric mass-splitting ratio because of a leading-order cancellation. Present atmospheric-angle data yield only mild tension with exact alignment, whereas stringent neutrino-mass bounds in baseline ΛCDM cosmology strongly disfavor it; its viability under extended cosmological models remains model dependent. We finally formulate geometric alignment residuals as general null-test observables, providing a systematic framework for testing the neutrino cuboid with future oscillation and absolute-mass measurements.