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.

10 pages, no figures, correted minor typos

References in corpus (9)

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• Minimal Modification To The Tri-bimaximal Neutrino Mixing
• Parametrizing the lepton mixing matrix in terms of deviations from tri-bimaximal mixing
• TriMinimal Parametrization of the Neutrino Mixing Matrix
• U_{PMNS} = U_ell^dagger U_nu
• Deviations from Tri-bimaximal Mixing: Charged Lepton Corrections and Renormalization Group Running
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• Corrections to Tri-bimaximal Neutrino Mixing: Renormalization and Planck Scale Effects
• Tribimaximal Neutrino Mixing and a Relation Between Neutrino- and Charged Lepton-Mass Spectra