Super-Kamiokande Solar Neutrino Data Research Articles

A generalized entropy optimization and Maxwell\u2013Boltzmann distribution

Based on the results of the diffusion entropy analysis of Super-Kamiokande solar neutrino data, a generalized entropy, introduced earlier by the first author is optimized under various conditions and it is shown that Maxwell–Boltzmann distribution, Raleigh distribution and other distributions can be obtained through such optimization procedures. Some properties of the entropy measure are examined and then Maxwell–Boltzmann and Raleigh densities are extended to multivariate cases. Connections to geometrical probability problems, isotropic random points, and spherically symmetric and elliptically contoured statistical distributions are pointed out.

An analysis of apparent r-mode oscillations in solar activity, the solar diameter, the solar neutrino flux, and nuclear decay rates, with implications concerning the Sun’s internal structure and rotation, and neutrino processes

This article presents a comparative analysis of solar activity data, Mt Wilson diameter data, Super-Kamiokande solar neutrino data, and nuclear decay data acquired at the Lomonosov Moscow State University (LMSU). We propose that salient periodicities in all of these datasets may be attributed to r-mode oscillations. Periodicities in the solar activity data and in Super-Kamiokande solar neutrino data may be attributed to r-mode oscillations in the known tachocline, with normalized radius in the range 0.66–0.74, where the sidereal rotation rate is in the range 13.7–14.6year−1. We propose that periodicities in the Mt Wilson and LMSU data may be attributed to similar r-mode oscillations where the sidereal rotation rate is approximately 12.0year−1, which we attribute to a hypothetical “inner” tachocline separating a slowly rotating core from the radiative zone. We also discuss the possible role of the Resonant Spin Flavor Precession (RSFP) process, which leads to estimates of the neutrino magnetic moment and of the magnetic field strength in or near the solar core.

FALSE-ALARM PROBABILITY IN RELATION TO OVERSAMPLED POWER SPECTRA, WITH APPLICATION TO SUPER-KAMIOKANDE SOLAR NEUTRINO DATA

The term "false-alarm probability" denotes the probability that at least one out of M independent power values in a prescribed search band of a power spectrum computed from a white-noise time series is expected to be as large as or larger than a given value. The usual formula is based on the assumption that powers are distributed exponentially, as one expects for power measurements of normally distributed random noise. However, in practice, one typically examines peaks in an oversampled power spectrum. It is therefore more appropriate to compare the strength of a particular peak with the distribution of peaks in oversampled power spectra derived from normally distributed random noise. We show that this leads to a formula for the false-alarm probability that is rather more conservative than the familiar formula. We also show how to combine these results with a Bayesian method for estimating the probability of the null hypothesis (that there is no oscillation in the time series), and we discuss as an example the application of these procedures to Super-Kamiokande solar neutrino data.

Solar Neutrino Variability and Its Implications for Solar Physics and Neutrino Physics

Recent coordinated power-spectrum analyses of radiochemical solar neutrino data and the solar irradiance have revealed a highly significant, high-Q common modulation at 11.85 yr−1. Since the stability of this frequency points to an explanation in terms of rotation, this result may be attributable to non-spherically-symmetric nuclear burning in a solar core with sidereal rotation frequency 12.85 yr−1. The variability of the amplitude (on a timescale of years) suggests that the relevant nuclear burning is variable as well as asymmetric. Recent analysis of Super-Kamiokande solar neutrino data has revealed r-mode-type modulations with frequencies corresponding to a region with sidereal rotation frequency 13.97 yr−1. If this modulation is attributed to the RSFP (resonant spin flavor precession) process, it provides a measurement of the rotation rate deep in the radiative zone. These two results suggest that the core rotates significantly more slowly than the radiative zone. If one accepts an upper limit of 7 MG for the Sun's internal magnetic field, an RSFP interpretation of the Super-Kamiokande results leads to a lower limit of 10−12 Bohr magnetons for the neutrino transition magnetic moment.

Power-spectrum analyses of Super-Kamiokande solar neutrino data: Variability and its implications for solar physics and neutrino physics

Since rotational or similar modulation of the solar neutrino flux would seem to be incompatible with the currently accepted theoretical interpretation of the solar neutrino deficit, it is important to determine whether or not such modulation occurs. There have been conflicting claims as to whether or not power-spectrum analysis of the Super-Kamiokande solar neutrino data yields indication of variability. Comparison of these claims is complicated by the fact that the relevant articles may use different data sets, different methods of analysis, and different procedures for significance estimation. The purpose of this article is to clarify the role of power-spectrum analysis. To this end, we analyze primarily the Super-Kamiokande 5-day data set, and we use a standard procedure for significance estimation as used by the Super-Kamiokande collaboration. We then analyze this data set, with this method of significance estimation, using six methods of power-spectrum analysis. Five of these have been used in published articles, and the other is a method that might have been used. We find that, with one exception, the results of these calculations are consistent with those of previously published analyses. We find that the power of the principal modulation (that at 9.43 yr{sup -1}) is greater inmore » analyses that take account of error estimates than in the basic Lomb-Scargle analysis that does not take account of error estimates. The corresponding significance level ranges between 98% and 99.3%, depending on the details of the analysis. Concerning the recent article by Koshio, we find that we can reproduce the results of his power-spectrum analysis but not the results of his Monte Carlo simulations, and we have a suggestion that may account for the difference. We also comment on a recent article by Yoo et al. We discuss, in terms of subdominant processes, possible neutrino-physics interpretations of the apparent variability of the Super-Kamiokande measurements, and we suggest steps that could be taken to resolve the question of variability of the solar neutrino flux.« less

The hep reaction and the solar neutrino problem

The results of a new calculation of the astrophysical S-factor for the proton weak capture on 3He are here reviewed. The methods used to obtain very accurate initial and final state wave functions and to construct the nuclear weak current operator are described. Finally the implications of these results for the Super-Kamiokande solar neutrino data are discussed.

Neutrino Magnetic Moments, Flavor Mixing, and the Super-Kamiokande Solar Data

We find that magnetic neutrino-electron scattering is unaffected by oscillations for vacuum mixing of Dirac neutrinos with only diagonal moments and for Majorana neutrinos with two flavors. For Mikheyev-Smirnov-Wolfenstein mixing, these cases are again obtained, though the effective moments can depend on the neutrino energy. Thus, e.g., the magnetic moments measured with ${\overline{\ensuremath{\nu}}}_{e}$ from a reactor and ${\ensuremath{\nu}}_{e}$ from the Sun could be different. With minimal assumptions, we find a new limit on ${\ensuremath{\mu}}_{\ensuremath{\nu}}$ using the 825-d Super-Kamiokande solar neutrino data: $|{\ensuremath{\mu}}_{\ensuremath{\nu}}|\ensuremath{\le}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}{\ensuremath{\mu}}_{B}$ at $90%$ CL, comparable to the existing reactor limit.

Electron capture on [formula omitted] nuclei and Superkamiokande results

The energy spectrum of recoil electrons from solar neutrino scattering, as observed by Superkamiokande, is deformed with respect to that expected from SSM calculations. We considered ν− e scattering from neutrinos produced by the electron-capture on 8 B nuclei, e −+ 8 B→ 8 Be ∗+ν e , as a possible explanation of the spectral deformation. A flux Φ eB≃10 4 cm −2 s −1 could account for Superkamiokande solar neutrino data. However this explanation is untenable, since the theoretical prediction, Φ eB=(1.3±0.2) cm −2 s −1 , is smaller by four orders of magnitude.