Perturbation theory of neutrino oscillation with nonstandard neutrino interactions

We discuss various physics aspects of neutrino oscillation with non-standard interactions (NSI). We formulate a perturbative framework by taking Δm221/Δm231, s13, and the NSI elements εαβ (α,β = e,μ,τ) as small expansion parameters of the same order ε. Within the ε perturbation theory we obtain the S matrix elements and the neutrino oscillation probability formula to second order (third order in νe related channels) in ε. The formula allows us to estimate size of the contribution of any particular NSI element εαβ to the oscillation probability in arbitrary channels, and gives a global bird-eye view of the neutrino oscillation phenomena with NSI. Based on the second-order formula we discuss how all the conventional lepton mixing as well as NSI parameters can be determined. Our results shows that while θ13, δ, and the NSI elements in νe sector can in principle be determined, complete measurement of the NSI parameters in the νμ-ντ sector is not possible by the rate only analysis. The discussion for parameter determination and the analysis based on the matter perturbation theory indicate that the parameter degeneracy prevails with the NSI parameters. In addition, a new solar-atmospheric variable exchange degeneracy is found. Some general properties of neutrino oscillation with and without NSI are also illuminated.