Wave packet description of Majorana neutrino oscillations in a magnetic field

TL;DR

This paper develops a wave packet formalism to analyze Majorana neutrino oscillations in magnetic fields, deriving analytical expressions for oscillation probabilities and coherence lengths, with implications for supernova neutrino propagation.

Contribution

It introduces an analytical wave packet approach to Majorana neutrino oscillations in magnetic fields, including decoherence effects and coherence length calculations.

Findings

Coherence length matches vacuum oscillations when $\, ext{ω}_{vac} \,\gg \, ext{ω}_B$.

Coherence length scales with the cube of neutrino momentum when $\, ext{ω}_{vac} \,\ll \, ext{ω}_B$.

Decoherence effects can occur during supernova neutrino propagation.

Abstract

Majorana neutrino oscillations in a magnetic field are considered using the wave packets formalism. The modified Dirac equation for Majorana neutrinos with non-zero transition magnetic moments propagating in a magnetic field is solved analytically in the two flavour case. The expressions for the oscillations probabilities are derived accounting for the decoherence effect emerging at distances exceeding the coherence length. It is shown that for Majorana neutrinos propagating in a magnetic field the coherence length coincides with the coherence length for neutrino oscillations in vacuum when the vacuum frequency is much greater than the magnetic frequency ($\omega_{vac} \gg \omega_B$), while it is proportional to the cube of the average neutrino momentum if ($\omega_{vac} \ll \omega_B$). We show that the decoherence effect may appear during neutrino propagation in a magnetic field of supernova.