Symmetry Finder applied to the 1-3 mass eigenstate exchange symmetry

TL;DR

This paper extends the Symmetry Finder method to identify 1-3 neutrino mass eigenstate exchange symmetries in matter, revealing sixteen such symmetries and discussing their relation to vacuum and matter Hamiltonians.

Contribution

It applies the SF method to atmospheric-resonance perturbation theory to uncover new 1-3 state exchange symmetries in matter, expanding previous symmetry classifications.

Findings

Identifies sixteen 1-3 state exchange symmetries in matter.

Shows the pure 1-3 symmetry is hard to formulate in vacuum.

Discusses the relation between symmetries in Hamiltonian and diagonalized system.

Abstract

In a previous paper, Symmetry Finder (SF) method is proposed to find the reparametrization symmetry of the state-exchange type in neutrino oscillation in matter. It has been applied successfully to the 1-2 state exchange symmetry in the DMP perturbation theory, yielding the eight symmetries. In this paper, we apply the SF method to the atmospheric-resonance perturbation theory to uncover the 1-3 state relabeling symmetries. The pure 1-3 state symmetry takes the unique position that it is practically impossible to formulate in vacuum under the conventional choice of the flavor mixing matrix. In contrast, our SF method produces the sixteen 1-3 state exchange symmetries in matter. The relationship between the symmetries in the original (vacuum plus matter) Hamiltonian and the ones in the diagonalized system is discussed.