Perturbation Theory of Neutrino Oscillation with Nonstandard Neutrino Interactions
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We discuss various physics aspects of neutrino oscillation with non-standard interactions (NSI). We formulate a perturbative framework by taking Δm^2_{21} / Δm^2_{31}, s_{13}, and the NSI elements ε_{αβ} (α, β= e, μ, τ) as small expansion parameters of the same order ε. Within the εperturbation theory we obtain the S matrix elements and the neutrino oscillation probability formula to second order (third order in ν_e related channels) in ε. The formula allows us to estimate size of the contribution of any particular NSI element ε_{αbeta} 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 θ_{13}, δ, and the NSI elements in ν_e sector can in principle be determined, complete measurement of the NSI parameters in the ν_μ- ν_τsector 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.
manuscript restructured, discussion of new type of parameter degeneracy added. 47 pages
manuscript restructured, discussion of new type of parameter degeneracy added. 47 pages