Hidden sterile neutrino and the 2+2 sum rule -: art. no. 073019

We discuss the 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 do not favor this claim. Here we use scatter plots to assess the corrections of the zeroth order sum rule when (i) the 4x4 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, the daunting task of fitting global data with the small mixing angles included seems to be required.