Analysis of Solar Neutrino Data from Super-Kamiokande I and II

Abstract

Abstract:We are going back to the roots of the original solar neutrino problem: the analysis of data from solar neutrino experiments. The application of standard deviation analysis (SDA) and diffusion entropy analysis (DEA) to the Super-Kamiokande I and II data reveals that they represent a non-Gaussian signal. The Hurst exponent is different from the scaling exponent of the probability density function, and both the Hurst exponent and scaling exponent of the probability density function of the Super-Kamiokande data deviate considerably from the value of 0.5, which indicates that the statistics of the underlying phenomenon is anomalous. To develop a road to the possible interpretation of this finding, we utilize Mathai's pathway model and consider fractional reaction and fractional diffusion as possible explanations of the non-Gaussian content of the Super-Kamiokande data.

Operational Approach and Solutions of Hyperbolic Heat Conduction Equations

“…The mathematical instruments, used to solve DE, generally range from a variety of integral transforms [41,42] to expansion in a series of generalized orthogonal polynomials [43] with many variables and indices [44][45][46], which arise naturally in studies of physical problems, such as the radiation and dynamics of beams of charges [47][48][49][50][51][52][53][54], heat and mass transfer [55][56][57][58][59], etc. Moreover, exponential operators and matrices are currently used also for description of such nature fundamentals as neutrino and quarks in theoretical [60][61][62][63][64][65] and in experimental [66][67][68] frameworks. The method of inverse differential and exponential operators has multiple applications for treating the above mentioned problems and related processes; some examples of DE solution by the inverse derivative method with regard to the heat equation, the diffusion equation, and their extensions, involving the Laguerre derivative, were given in [46,[69][70][71][72][73].…”

A generalized entropy optimization and Maxwell–Boltzmann distribution

“…The Hurst exponent is different from the scaling exponent of the probability density function and both Hurst exponent and scaling exponent of the SuperKamiokande data deviate considerably from the value of 1/2 which indicates that the statistics of the underlying phenomenon is anomalous. We recapitulate arguments from the so-called Boltzmann-Planck-Einstein discussions related to Planck's discovery of the black-body radiation law and emphasize from this discussion that a meaningful implementation of the complex entropyprobability-dynamics may offer two ways for explaining the results of DEA and SDA [20]. One way is to consider an anomalous diffusion process that needs to use the fractional space-time diffusion equation and the other way to generalize Boltzmann's entropy by assuming a power law probability density function.…”

“…Following the above reasoning of Boltzmann, Planck, and Einstein, in this paper we utilize the statistical methodology developed by Scafetta [16] by evaluating the scaling exponent of the probability density function through Boltzmann's entropy of a kind of diffusion process generated by complex fluctuations in the measurements of the solar neutrino flux in the Super-Kamiokande experiment [17][18][19][20]. This method does focus on the scaling properties of the Super-Kamiokande time series (see Fig.…”

Generalized Langevin Equation and the Prabhakar Derivative

“…Here we note that different fractional equations have been used for modeling anomalous diffusion in various systems, including fractional reaction-diffusion equations [27,28] and their application [29], fractional relaxation and diffusion equations [5,6,9,10,[24][25][26], fractional cable equation [30], etc.…”