New Parametrization of Neutrino Mixing Matrix

TL;DR

This paper introduces a new parametrization of the neutrino mixing matrix using the exponential map of its hermitian generator, allowing for a systematic description of deviations from the tri-bimaximal pattern.

Contribution

It proposes a novel parametrization method of the neutrino mixing matrix via its hermitian generator and the exponential map, facilitating analysis of deviations from tri-bimaximal mixing.

Findings

Derived hermitian matrices for deviations from tri-bimaximal mixing.

Provided a framework to relate deviations to symmetry breaking.

Enhanced understanding of neutrino mixing deviations.

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.