Parameter degeneracy in neutrino oscillation — Solution network and structural overview

Abstract

It is known that there is a phenomenon called “parameter degeneracy” in neutrino oscillation measurement of lepton mixing parameters; A set of the oscillation probabilities, e.g., P(ν μ → ν e ) and its CP-conjugate \( P\left( {{{\bar \nu }_\mu } \to {{\bar \nu }_e}} \right) \) at a particular neutrino energy does not determine uniquely the values of θ 13 and δ. With use of the approximate form of the oscillation probability á la Cervera et al., a complete analysis of the eightfold parameter degeneracy is presented. We propose a unified view of the various types of the degeneracy as invariance of the oscillation probabilities under discrete mappings of the mixing parameters. Explicit form of the mapping is obtained either by symmetry argument, or by deriving exact analytic expressions of all the degeneracy solutions for a given true solution. Due to the one-to-one mapping structure the degeneracy solutions are shown to form a network. We extend our analysis into the parameter degeneracy in T- and CPT-conjugate measurement as well as to the setup with the golden and the silver channels, P(ν e → ν μ ) and P(ν e → ν τ ). Some characteristic features of the degeneracy solutions in CP-conjugate measurement, in particular their energy dependences, are illuminated by utilizing the explicit analytic solutions.