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Neutrino Oscillations With Recently Measured Sterile-Active Neutrino Mixing Angle

This brief report is an extension of a prediction of neutrino oscillation with a sterile neutrino using parameters of the sterile neutrino mass and mixing angle recently extracted from experiment.


Introduction
Recently there was an investigation of how the neutrino transition probability P(ν µ → ν e ) is modified by the introduction of a sterile neutrino [1], motivated in part by recent experiments on neutrino oscillations [2], which suggested the existence of at least one sterile neutrino. The 3x3 U-matrix method of Sato and collaborators for three active neutrino oscillations [3,4] was extended to 4x4 with a sterile neutrino.
In the present brief report we use the formalism of Ref [1] with parameters for the sterile neutrino that have recently been extracted by a global fit to neutrino oscillation data [5].
2 P(ν µ → ν e ) Using a 4x4 U Matrix Active neutrinos with flavors ν e , ν µ , ν τ and a sterile neutrino ν s are related to neutrinos with definite mass by where U is a 4x4 matrix and ν f , ν m are 4x1 column vectors, which is an extension of the 3x3 matrix used in Refs. [3,4].

Conclusions
As shown in the figure, the neutrino oscillation probability, P(ν µ → ν e ), is quite different for a model with four neutrinos, ν e , ν µ , ν τ , ν s than with three active neutrinos. The effect of the sterile neutrino is largest for large values of E/L, as seen in the figure for MiniBooNE, which has a baseline of L=0.5 km. Although Double CHOOZ has a baseline of only 1.03 km, the energy is only about 3 MeV, so the effects of a sterile neutrino are smaller, but are still important for the extraction of neutrino parameters from neutrino oscillation data.
In the present work we have used the sterile-active neutrino mixing angle α ( sin(α) ≃ 0.1), which is now known to be approximately correct for δm 2 j4 = 0.9(eV ) 2 , rather than the mixing angles used in Ref [1]. Therefore the present results are more reliable for comparison with future neutrino oscillation experiments, inlcuding measurements of CP and T-reversal violations, than the previous publication.