Relation Between the Neutrino and Quark Mixing Angles and Grand Unification

Abstract

We argue 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. In this framework the quark mixing matrix is a parameter matrix describing the deviation of neutrino mixing from exactly bimaximal, predicting ${\ensuremath{\theta}}_{\mathrm{s}\mathrm{o}\mathrm{l}}+{\ensuremath{\theta}}_{C}=\ensuremath{\pi}/4$, where ${\ensuremath{\theta}}_{C}$ is the Cabibbo angle, ${\ensuremath{\theta}}_{\mathrm{a}\mathrm{t}\mathrm{m}}+{\ensuremath{\theta}}_{23}^{\mathrm{C}\mathrm{K}\mathrm{M}}=\ensuremath{\pi}/4$ and ${\ensuremath{\theta}}_{13}^{\mathrm{M}\mathrm{N}\mathrm{S}}\ensuremath{\sim}{\ensuremath{\theta}}_{13}^{\mathrm{C}\mathrm{K}\mathrm{M}}\ensuremath{\sim}\mathcal{O}({\ensuremath{\lambda}}^{3})$, in perfect agreement with experimental data. Both non-Abelian and Abelian flavor symmetries are needed for such a prediction to be realistic. An example flavor model capable of explaining this flavor mixing pattern and inducing the measured quark and lepton masses is outlined.