A study of the solar neutrino survival probability

We present a study of the recent solar neutrino data using a Bayesian approach. The survival probability for neutrinos as a function of the energy has been extracted by two independent methods. The results of our analysis, assuming that only νe are observed in the Super-Kamiokande experiment, show a distinct supression of the survival probability at about 1 MeV, in good agreement with previous χ2-based analyses. When the detection of νμ by Super-Kamiokande is taken into account, assuming νe to νμ oscillations, we find a significant suppression in survival probability at about 8.5 MeV. PACS numbers : 26.65.+t,13.15.+g Typeset using REVTEX 1 One of the most intriguing problems of the past two decades has been the observation of a deficit of neutrinos of solar origin as compared to the predictions of standard solar models [1–3]. Many attempts have been made to explain this discrepancy either as a consequence of astrophysical processes or new physics such as neutrino oscillations in vacuum [4] or in matter [5]. The astrophysical solutions have not been successful [6]. However, the solutions that invoke new physics provide excellent descriptions of the solar neutrino data (see, e.g., Ref. [7]). Should these hints of non-zero neutrino masses and mixing prove to be true they would be the first observation of physics beyond the standard model of particle physics. As such, these observations would represent a major breakthrough. It is therefore of the utmost importance to have a clear understanding of how the discrepancy and its uncertainties affect conclusions about the neutrino survival probability and the models used to explain the discrepancy. The solar neutrino problem has been the subject of an enormous amount of work. Traditionally, the discrepancy has been analyzed using χ methods [7–9]. This has led to a consensus about the general shape of the survival probability and about which models best fit the data. What is less well established is a clear quantitative understanding of the uncertainty in our knowledge of the neutrino survival probability as a function of the neutrino energy. This paper provides such an understanding and describes the method we have used to obtain it. We have adopted a Bayesian method which allows us to extract, in a rather direct way, the neutrino survival probability and its uncertainty without making any particular assumptions about the mechanism producing the deficit in the neutrino flux. (For an interesting example of the use of Bayesian methods in astrophysics see Ref. [10]). In our analysis of the solar neutrino data we assume that the solar neutrino spectrum is that predicted by the standard solar models [1,2,11]. However, it is known that the spectrum is insensitive to the details of these models [12]. The experimental data are from Homestake (Cl) [13], SAGE (Ga) [14], GALLEX (Ga) [15] and Super-Kamiokande (H2O) [16,17]. These results together with the predictions of the standard solar model of Bahcall and Pinsonneault [1] are shown in Table I. Our method of analysis does not require the imposition 2 of the solar luminosity constraint. In accordance with our minimalist approach we choose not to impose it. Bayes’ theorem, P (H|D, I) = L(D|H, I)P (H|I)