New Parametrization of Neutrino Mixing Matrix

Abstract

Global fits to neutrino oscillation data are compatible with tri-bimaximal mixing pattern, which predicts ${\theta }_{23}=\frac{\pi }{4},{\theta }_{12}={\sin }^{-1}(\frac{1}{\sqrt{3}})$ and ${\theta }_{13}=0$. We propose here to parametrize the tri-bimaximal mixing matrix $V_{TBM}$ by its hermitian generator $H_{TBM}$ using the exponential map. Then we use the exponential map to express the deviations from tri-bimaximal pattern by deriving the hermitian matrices $H_{z=0}$ and $H_1$. These deviations might come from the symmetry breaking of the neutrino and charged lepton sectors.

Comments: 10 pages, no figures, correted minor typos