Describing Analytically the Matter-Enhanced Two-Neutrino Transitions in a Medium

TL;DR

This paper derives an exact analytic expression for matter-enhanced two-neutrino transition probabilities in a medium, applicable to solar and supernova neutrino studies, and discusses a similarity with hydrogen atom wave functions.

Contribution

It provides a novel exact analytic formula for neutrino transition probabilities in matter, incorporating transition phases and jump probabilities.

Findings

Derived an exact formula for transition probabilities in various matter profiles.

Expressed probabilities using three real functions of transition parameters.

Discussed a mathematical similarity with hydrogen atom wave functions.

Abstract

A general exact analytic expression for the probability of matter-enhanced two-neutrino transitions in a medium (MSW, RSFP, generated by neutrino FCNC interactions, etc.) is derived. The probability is expressed in terms of three real functions of the parameters of the transitions: the ``jump'' probability and two phases (angles). The results obtained can be utilized, in particular, in the studies of the matter-enhanced transitions/conversions of solar and supernova neutrinos. An interesting similarity between the Schroedinger equation for the radial part of the non-relativistic wave function of the hydrogen atom and the equation governing the MSW transitions of solar neutrinos in the exponentially varying matter density in the Sun is also briefly discussed.