Relation Between the Neutrino and Quark Mixing Angles and Grand Unification

It is argued that there exists a simple relation between the quark and lepton mixings, which supports the idea of grand unification and probes the underlying robust bimaximal fermion mixing structure of still unknown flavor physics.

Abstract

We conjecture that quark and lepton mixing angles in the 2-3 sector satisfy a conservation law: θ₂₃^CKM + θ₂₃^PMNS = 45°. With θ₂₃^CKM = 2.38° from |V_cb|, this predicts θ₂₃^PMNS = 42.62°, yielding sin²θ₂₃ = 0.458 (lower octant). This value lies within 1σ of current global fits (NuFIT 6.0: 0.470 ± 0.017) and agrees with atmospheric neutrino data (Super-Kamiokande: 0.450 ± 0.02). The prediction is falsifiable: confirmation of the upper octant (sin²θ₂₃ > 0.5) at 5σ refutes the conjecture. Hyper-Kamiokande and DUNE will provide definitive tests by 2031.