Just-So Oscillation: as Just as MSW?

The neutrino long wavelength (just-so) oscillation is reconsidered as a solution to the solar neutrino problem. In the light of the presently updated results of the four solar neutrino experiments, the data fit in the just-so scenario substantially improves and becomes almost as good as in the MSW scenario. Surprising result of our analysis is that best fit is achieved when the oscillation occurs only between two neutrino states: switching on the oscillation into third neutrino increases the χ value. Namely, we consider the vacuum oscillation scenario in the three-neutrino system (4 parameters) and find out that the χ minimum is always achieved in the two parameter subspace in which actually only two neutrino states oscillate. This holds in the framework of any solar model with relaxed prediction of the various neutrino fluxes. The possible theoretical implications of this observation are also discussed. E-mail: [email protected] E-mail: [email protected] There are strong arguments to believe that the Solar Neutrino Problem (SNP), i.e. the deficit of the solar neutrino fluxes indicated by four operating experiments [1, 2, 3, 4] as compared to the predictions of the Standard Solar Models (SSM) [5, 6], cannot be explained by the nuclear/astrophysical reasons. Namely, the results of different detectors cannot be reconciled among each other by varying the SSM parameters as are the central solar temperature, nuclear cross sections etc. [7]. The problem is essentially related to the peculiar energy dependence needed for the suppression of different solar neutrino components, so that the intermediate energy Be neutrinos are to be killed more than the lower energy (pp) or higher energy (B) neutrinos. This points that the SNP is rather due to the ”non-standard” neutrino properties. The most natural and plausible possibility is the oscillation of the solar νe into another type of neutrino νx. The neutrino oscillation picture can provide the necessary energy dependence in two regimes, which are known as the Mikheyev-Smirnov-Wolfenstein (MSW) [8] and the long wavelength vacuum oscillation (so called just-so) [9] scenarios. The MSW resonant conversion in matter offers a natural possibility of selective strong reduction of the Be neutrinos and thus appears to be the most attractive and elegant solution to the SNP. It provides a very good fit of the experimental data, implying the mass range δm ∼ 10 eV 2 and small mixing angle, sin 2θ ∼ 10 [12]. The just-so scenario, with the oscillation wavelength comparable to the sun-earth distance, needs δm of about 10 eV 2 and large mixing angle, sin 2θ ∼ 1 [13, 14], which parameter range can be naturally generated by non-perturbative quantum gravitational effects [10, 11]. Both the MSW and just-so mechanisms are theoretically motivated and so far the experimental data do not allow to discriminate them. Hence, both these scenarios should be considered as realistic candidates to the SNP solution. However, the peculiar ”just-so” predictions as are the seasonal time variation of the neutrino signals and the specific deformation of the original solar neutrino spectra [13, 14], will allow to test the long wavelength oscillation scenario at the future real time detectors like Superkamiokande, SNO, Borexino, etc., and to discriminate it from the MSW picture. In the present paper we present an updated analysis of the just-so scenario. The earlier analysis [13, 14] has shown that the experimental data fit in this scheme is acceptable, but somewhat worse than that of MSW picture. However, after publication of these papers the experimental data have been changed. In particular, the result of the Homestake experiment has been recalibrated [1] and the new data of GALLEX experiment became available [3]. On the other hand, the SSM predictions have been reconsidered by taking into account the helium and heavy element diffusion [6]. The changes are small and rather confirm the stability of both the experimental and theoretical results. Nevertheless, as we show below, these small changes make the ”just-so” data fit substantially better so that it becomes almost as good as in the MSW picture. Another issue which we address in this paper is the following. Up to now, in the literature all the analysis of the vacuum oscillation scenario was performed within the simplified case of two neutrino (2ν) system, which case employs only two parameters: the νe − νx mixing In the language of the Standard Model (SM) the neutrino masses emerge through the higher order operators of the type 1 M (liClj)HH , where li (i = 1, 2, 3) and H are respectively the lepton and Higgs doublets and M is some regulator scale. (For example, the famous “seesaw” scenario effectively reduces to these operators with M of the order or the right-handed neutrino mass). Then the neutrino mass range needed for the just-so scenario corresponds to the Planck scale, M ∼ 10 GeV , whereas the MSW scenario requires M to be of the order of the supersymmetric grand unification scale, M ∼ 10 GeV .