ar X iv : h ep - p h / 02 09 37 3 v 3 2 3 A pr 2 00 3 The Hidden Sterile Neutrino and the ( 2 + 2 ) Sum Rule

We discuss oscillations of atmospheric and solar neutrinos into sterile neutrinos in the 2+2 scheme. A zero order sum rule requires equal probabilities for oscillation into νs and ντ in the solar+atmospheric data sample. Data does not favor this claim. Here we use scatter plots to assess corrections of the zero order sum rule when (i) the 4× 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. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] 1