Symmetry in neutrino oscillation in matter with non-unitarity

TL;DR

This paper develops a method called Symmetry Finder to identify reparametrization symmetries in neutrino oscillations in matter, extended to include unitarity violation, revealing new symmetries and their implications for physics beyond the Standard Model.

Contribution

The paper extends the Symmetry Finder method to include unitarity violation in neutrino oscillations, identifying eight new symmetries and analyzing their implications for new physics diagnostics.

Findings

Identified eight DMP-UV symmetries in neutrino oscillations with unitarity violation.

Discovered that UV parameters transform only by rephasing, maintaining Hamiltonian invariance.

Revealed the joint transformation of SM and UV variables, linking their responses.

Abstract

Recently we have developed a method called ``Symmetry Finder'' (SF) for hunting the reparametrization symmetry in the three-neutrino system in matter. Here, we apply SF to the Denton {\it et al.} (DMP) perturbation theory extended by including unitarity violation (UV), a possible low-energy manifestation of physics beyond the $\nu$SM. Implementation of UV into the SF framework yields the additional two very different constraints, which nonetheless allow remarkably consistent solutions, the eight DMP-UV symmetries. Treatment of one of the constraints, the genuine non-unitary part, leads to the key identity which entails the UV $\alpha$ parameter transformation only by rephasing, which innovates the invariance proof of the Hamiltonian. The quantum mechanical nature of the symmetry dictates the both $\nu$SM and UV variables to transform jointly, through which the response of the two sectors are related to reveal their interplay. Thus, the symmetry can serve for a tool for diagnostics, probing the interrelation between the $\nu$SM and a low-energy description of new physics. Problem of SF symmetry in vacuum is revisited to complete eight symmetries akin to DMP's.