Common origin for the solar and atmospheric neutrino deficits.

Large mixing induced νμ ↔ νe transitions can explain the deficit in the flux of the low energy atmospheric νμ whereas the solar neutrino deficit can be simultaneously explained through MSW transitions νe → ντ . A combined analysis of both these effects is presented. The large νe − νμ mixing affects the MSW transition between νe and ντ significantly. As a consequence, a large region of parameters ruled out by experiment in the two generation case is now allowed. The mass hierarchy as well as the mixing pattern required arise naturally in a model for neutrino masses proposed by Zee. Permanent address: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, BG–1784 Sofia, Bulgaria. 0 Two independent sets of experiments point towards the existence of neutrino oscillations. The flux of the solar neutrinos is found to be depleted by varied amounts compared to the expectations based on the standard solar model in four different experiments namely, Homestake [1], Kamioka [2], GALLEX [4] and SAGE [3]. Similarly, the flux ratio of the low energy (≤ GeV) νμ to νe of atmospheric origin is seen to be smaller than the theoretically expected one in experiments by the Kamioka II [5] and IMB [6] group. Independent measurements by the Soudan [7] and the Frejus collaborations [8] are not inconsistent with the above but the statistical significance of these results is much less than the corresponding one in cases of Kamioka and IMB results. Theoretically, both these deficits could originate from the same common source, namely neutrino oscillations. However the range of the relevant parameters ((mass) difference ∆ and mixing angle θ ) required by the solar and atmospheric neutrino data are quite different. The solar neutrino deficit can be explained through neutrino oscillations occurring either in vacuum [9] or in the presence of solar matter [10]. The former requires ∆ ≈ 10 (eV), sin2θ ≈ 0.75−1.0 [9] while the latter becomes important if either ∆ ≈ (5−10)×10−6 (eV), sin 2θ ≈ (0.2−0.9) or ∆ sin 2θ ≈ (3−4)×10−8 (eV) corresponding respectively to the large angle adiabatic and non adiabatic Mikheyev Smirnov Wolfenstein (MSW) solutions [11]. In contrast, the deficit in the atmospheric muon neutrinos can be explained by means of neutrino oscillations [12] when parameters assume typical values ∆ ≈ 10−3−10−2 (eV) and sin 2θ ≈ 0.5. It is quite clear that a simple two generation picture used in deriving above restrictions is inadequate to simultaneously explain the solar and the atmospheric neutrino deficits. A natural possibility is to consider more realistic three generation picture. When all three neutrino flavors are involved, the vacuum oscillations can account [13] for both the deficits The latest, still preliminary result from the SOUDAN–II detector seems to confirm the results of Kamiokande and IMB, albeit with larger statistical errors.