Earth effect in the MSW analysis of the solar neutrino experiments.

We consider the Earth effect in the MSW analysis of the Homestake, Kamiokande, GALLEX, and SAGE solar neutrino experiments. Using the time-averaged data and assuming two-flavor oscillations, the large-angle region of the combined fit extends to much smaller angles (to sin 2θ ≃ 0.1) than when the Earth effect is ignored. However, the additional constraint from the Kamiokande II day-night data excludes most of the parameter space sensitive to the Earth effect independent of astrophysical uncertainties, and leaves only a small large-angle region close to maximal mixing at 90% C.L. The nonadiabatic solution remains unaffected by the Earth effect and is still preferred. Both theoretical and experimental uncertainties are included in the analysis. Typeset using REVTEX 1 The recent results from SAGE, GALLEX, and Kamiokande III confirmed the deficit of the neutrino flux from the Sun, and thus all existing solar neutrino experiments report a discrepancy at some level between the neutrino flux observed and predicted [1–5]. If the experiments are correct, the implications are significant: first the standard solar model is excluded by the data [6,7]. Secondly, the smaller chlorine rate relative to the Kamiokande rate makes astrophysical explanations difficult and excludes a wide class of nonstandard solar models described by a lower core temperature [8,9,5]. On the other hand, among many proposed particle physics solutions, the Mikheyev-Smirnov-Wolfenstein (MSW) mechanism [10] remains as a viable description of the data, giving a strong hint for neutrino mass. To explore this possibility, it is important to determine the MSW parameter space from the available data. The MSW effect is an experimentally verifiable hypothesis; once the parameter space is constrained, one can provide robust predictions for the next-generation detectors such as SNO, Super-Kamiokande, BOREXINO, and ICARUS. Theoretically, the neutrino mass and mixing angle, along with the seesaw mechanism, can be a probe of the physics at higher energy scales (e.g., the grand unification scale) inaccessible to laboratory experiments. If we assume two-flavor MSW oscillations into νμ or ντ , the combined data of all experiments allow two solutions 1 with the squared mass difference ∆m ∼ 10eV: one in the nonadiabatic region with mixing angle sin 2θ ∼ 0.01 and the other in the large-angle region with sin 2θ ∼ 0.8, the former solution giving the better fit [8] (see also [5,11–14]). There is one complication in the large-angle MSW solution. For the B neutrino energy range, the MSW parameters satisfy the resonance condition for the electron density corresponding to the core and mantle of the Earth. The νx’s, into which electron neutrinos convert in 1 There is also a nonadiabatic solution for oscillations into sterile neutrinos, which is not affected significantly by the Earth effect. There is no large-angle solution for sterile neutrinos at 90% C.L. [8].