The neutrino self-energy in a magnetized medium

TL;DR

This paper derives a comprehensive expression for neutrino self-energy in a magnetized medium, accounting for Landau quantization effects and background CP symmetry, with implications for astrophysical plasma environments.

Contribution

It provides the most general neutrino self-energy expression in a magnetized medium without Landau quantization of charged gauge fields, including linear magnetic field corrections.

Findings

Derived the general neutrino self-energy in a magnetized medium.

Analyzed the impact of Landau quantization on neutrino properties.

Applicable to CP symmetric plasma conditions.

Abstract

In this work we calculate the neutrino self-energy in presence of a magnetized medium. The magnetized medium consists of electrons, positrons, neutrinos and a uniform classical magnetic field. The calculation is done assuming the background magnetic field is weak compared to the $W$-Boson mass squared, as a consequence of which only linear order corrections in the field are included in the $W$ boson propagator. The electron propagator consists all order corrections in the background field. Although the neutrino self-energy in a magnetized medium in various limiting cases has been calculated previously in this article we produce the most general expression of the self-energy in absence of the Landau quantization of the charged gauge fields. We calculate the effect of the Landau quantization of the charged leptons on the neutrino self-energy in the general case. Our calculation is specifically suited for situations where the background plasma may be CP symmetric.