SYMMETRY IN NEUTRINO OSCILLATION IN MATTER WITH NON-UNITARITY

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 et al. (DMP) perturbation theory extended by including unitarity violation (UV), a possible low-energy manifestation of physics beyond the ?SM. Implementation of UV into the SF framework yields the additional two very different constraints, which nonetheless allow for 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 a parameter transformation only by rephasing, which innovates the invariance proof of the Hamiltonian. The quantum mechanical nature of the symmetry dictates the both ?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 as a tool for diagnostics, probing the interrelation between the ?SM and a low-energy description of new physics. The problem of SF symmetry in vacuum is revisited to complete eight symmetries akin to DMPs.