Solar Mikheyev-Smirnov-Wolfenstein Effect with Three Generations of Neutrinos

TL;DR

This paper analyzes the solar neutrino oscillation effect with three neutrino generations, deriving exact solutions involving hypergeometric functions to improve understanding of neutrino masses and mixing.

Contribution

It provides a detailed study of the three-generation solar neutrino effect using hypergeometric functions and introduces a numerical evaluation method for these functions.

Findings

Exact solutions for the three-generation neutrino oscillation problem.

A numerical method for evaluating hypergeometric functions involved.

Insights into neutrino mass differences and mixing patterns.

Abstract

Under the assumption that the density variation of the electrons can be approximated by an exponential function, the solar Mikheyev-Smirnov-Wolfenstein effect is treated for three generations of neutrinos. The generalized hypergeometric functions that result from the exact solution of this problem are studied in detail, and a method for their numerical evaluation is presented. This analysis plays a central role in the determination of neutrino masses, not only the differences of their squares, under the assumption of universal quark-lepton mixing.