# Magnetic field effects on neutrino oscillations

## TL;DR

This paper calculates how strong magnetic fields influence neutrino oscillations by deriving exact propagators and effective potentials, revealing potential resonance effects near highly magnetized stars.

## Contribution

It provides the first exact calculation of neutrino self-energy in a magnetic field to all orders, extending the understanding of neutrino oscillations in astrophysical environments.

## Key findings

- Resonance conditions for neutrino oscillations in magnetic fields are established.
- The oscillation length varies with magnetic field strength.
- Resonant oscillations of electron and muon neutrinos are likely near highly magnetized stars.

## Abstract

Using the exact propagators in a constant magnetic field, the neutrino self-energy has been calculated to all orders in the field strength $B$ within the minimal extension of the Weinberg-Salam model with massive Dirac neutrinos. A neutrino dispersion relation, effective potential and effective mass have been obtained that depend on $B$. The consequences of this effective potential on neutrino oscillations have been explored, and resonance conditions have been obtained for magnetic fields $0<eB \le 4m^2_e$, where $e$ is the elementary charge and $m_e$ is the electron mass. The oscillation length has also been obtained, showing that $\nu_e$-$\nu_\mu$ resonant oscillations in magnetic field are likely to occur in the proximity of most stars generating high magnetic fields.