Important remarks to Wolfenstein's equation for passing neutrino through the matter

TL;DR

This paper critiques Wolfenstein's equation for neutrino oscillations in matter, identifies a conservation law oversight, and proposes a corrected solution showing minimal oscillation enhancement.

Contribution

It highlights a key disadvantage in Wolfenstein's equation and provides a revised solution that accounts for momentum conservation, refining neutrino oscillation predictions.

Findings

Wolfenstein's equation neglects momentum conservation.

Corrected solution shows negligible oscillation enhancement.

Effective neutrino mass change is minimal due to small energy polarization.

Abstract

It is supposed that while neutrino passing through the matter a resonance enhancement of neutrino oscillations in the matter appears. It is shown that Wolfenstein's equation, for neutrino passing through the matter, contains a disadvantage (does not take into account the law of momentum conservation). It leads, for example, to changing of the effective mass of neutrino by the value of $0.87 \cdot 10^{-2} eV$ from the very small value of the energy polarization of the matter caused by neutrino which is equal to $5 \cdot 10^{-12} eV$. After removing this disadvantage (i.e., taking into account this law) we have obtained a solution of this equation. In this solution a very small enhancement of neutrino oscillations in the matter appears due to the smallness of the energy polarization of the matter caused by neutrino.