Does SuperKamiokande Observe Levy Flights of Solar Neutrinos?

Abstract

The paper utilizes data from the SuperKamiokande solar neutrino detection experiment and analyzes them by diffusion entropy analysis and standard deviation analysis to evaluate the scaling exponent of the probability density function. The result indicates that solar neutrinos are subject to Levy flights. Subsequently, the paper derives the probability density function, represented as the Fox H-function, and the governing fractional diffusion equation for solar neutrino Levy flights.

Figures (6)

• Figure 1: Yearly solar neutrino flux measured by SuperKamiokande. The redfilled circle points show the SuperKamiokande data with statistical uncertainty and the gray striped area show the systematic uncertainty for each phase. The horizontal black solid line (red shaded area) shows the combined value of measured flux (its combined uncertainty). The black-blank circle points show the sunspot numbers from 1996 to 2018 (Abe et al., 2024)
• Figure 2: Measured $^8B$ solar neutrino fuxes for 5-day (top five panels, black data points) and 45-day (bottom panel, blue data points) intervals without 1/$R^2$ correction. The errors in the 5-day (the 45-day) plot are asymmetric (symmetric) errors of the average fluxes. The solid-red curve in the 45-day plot is the expected sinusoidal solar neutrino flux based on the elliptical orbit of the Earth Abe et al., 2023.
• Figure 3: The Diffusion Entropy Analysis (DEA) of the $^8B$ solar neutrino data from the SuperKamiokande I and II experiment.
• Figure 4: The Diffusion Entropy Analysis (DEA) of the $hep$ solar neutrino data from the SuperKamiokande I and II experiment.
• Figure 5: The Standard Deviation Analysis (SDA) of the $^8B$ solar neutrino data from the SuperKamiokande I and II experiment.