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The hidden sterile neutrino and the (2+2) sum rule

H. Päs·L. Song·T. J. Weiler
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Abstract

We discuss oscillations of atmospheric and solar neutrinos into sterile neutrinos in the 2+2 scheme. A zeroth order sum rule requires equal probabilities for oscillation into nu_s and nu_tau in the solar+atmospheric data sample. Data does not favor this claim. Here we use scatter plots to assess corrections of the zeroth order sum rule when (i) the 4 x 4 neutrino mixing matrix assumes its full range of allowed values, and (ii) matter effects are included. We also introduce a related "product rule". We find that the sum rule is significantly relaxed, due to both the inclusion of the small mixing angles (which provide a short-baseline contribution) and to matter effects. The product rule is also dramatically altered. The observed relaxation of the sum rule weakens the case against the 2+2 model and the sterile neutrino. To invalidate the 2+2 model, a global fit to data with the small mixing angles included seems to be required.

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H. Päs, L. Song, T. J. Weiler. 2003-04-23. The hidden sterile neutrino and the (2+2) sum rule. https://doi.org/10.1103/physrevd.67.073019

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