Bayesian view of solar neutrino oscillations

Abstract

We present the results of a Bayesian analysis of solar neutrino data in terms of ν e → ν µ,τ and ν e → ν s oscillations, where ν s is a sterile neutrino. We perform a Rates Analysis of the rates of solar neutrino experiments, including the first SNO CC result, and spectral data of the CHOOZ experiment, and a Global Analysis that takes into account also the Super-Kamiokande day and night electron energy spectra. We show that the Bayesian analysis of solar neutrino data does not suffer any problem from the inclusion of the numerous bins of the CHOOZ and Super-Kamiokande electron energy spectra and allows to reach the same conclusions on the favored type of neutrino transitions and on the determination of the most favored values of the oscillation parameters in both the Rates and Global Analysis. Our Bayesian analysis shows that ν e → ν s transitions are strongly disfavored with respect to ν e → ν µ,τ transitions. In the case of ν e → ν µ,τ oscillations, the Large Mixing Angle region is favored by the data (86% probability), the LOW region has some small chance (13% probability), the Vacuum Oscillation region is almost excluded (1% probability) and the Small Mixing Angle region is practically excluded (0.01% probability). We calculate also the marginal posterior probability distributions for tan 2 ϑ and ∆m 2 in the case of ν e → ν µ,τ oscillations and we show that the data imply large mixing almost with certainty and large values of ∆m 2 are favored (2 × 10 −6 eV 2 < ∆m 2 < 10 −3 eV 2 with 86% probability). We present also the results of a standard least-squares analysis of solar neutrino data and we show that the standard goodness of fit test is not able to reject pure ν e → ν s transitions. The likelihood ratio test, which is insensitive to the number of bins of the CHOOZ and Super-Kamiokande energy spectra, allows to reject pure ν e → ν s transitions in favor of ν e → ν µ,τ transitions only in the Global Analysis.

Before and After: How has the SNO NC measurement changed things?

“…As shown in ref. [25] the allowed regions obtained in this way are very similar to those obtained by a Bayesian analysis. Table 1 gives for our standard analysis strategy (cf.…”

“…The interested reader may wish to consult in addition a number of recent papers, refs. [21,22,23,24,25,26], that have determined from a variety of perspectives the allowed solar neutrino oscillation solutions following the June, 2001 announcement of the SNO CC measurement [9].…”

Robust signatures of solar neutrino oscillation solutions

“…As shown in ref. [26] the allowed regions obtained in this way are very similar to those obtained by a bayesian analysis. Table 3 gives for our standard analysis strategy (cf.…”

“…The interested reader may wish to consult also a number of recent papers, refs. [16,21,22,25,26,27], that have determined the allowed solar neutrino oscillation solutions including the CC data from SNO. We will spare the reader erudite comparisons, in the cases where there is overlap in the calculated quantities, between our detailed results and those of the other authors referred to above.…”

Testing the Stability of the Solar Neutrino Lma Solution With a Bayesian Analysis

“…This prior knowledge must be quantified by a function which is called "prior probability distribution function" (see Refs. [17,[20][21][22]). The Bayes' Theorem allows the calculation of the "posterior probability distribution function", which quantifies the knowledge of the values of the parameters provided by the data viewed in the light of the prior knowledge.…”