New Parametrization of Neutrino Mixing Matrix

Global fits to neutrino oscillation data are compatible with tri-bimaximal mixing pattern, which predicts $θ_{23} = \fracπ{4}, θ_{12} = \sin^{-1} (\frac{1}{\sqrt{3}})$ and $θ_{13} = 0$. 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.

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