Wave packet description of Majorana neutrino oscillations in a magnetic field

TL;DR

This work analyzes Majorana neutrinos with transition magnetic moments propagating in strong magnetic fields using the wave-packet formalism. It provides an analytic solution of the modified Dirac equation for a two-flavor system and derives oscillation probabilities that incorporate decoherence from wave-packet separation. Key results include the oscillation length $L_{osc} = 2π / √(ω_{vac}^2 + ω_B^2)$ and the coherence length $L_{coh} = 2√2 σ_x / Δv(p_0)$, with the limits $ω_{vac} ≫ ω_B$ reproducing vacuum-like coherence and $ω_{vac} ≪ ω_B$ yielding $L_{coh} ∝ p_0^3$. These findings suggest measurable decoherence effects in environments like supernovae where magnetic fields are extreme, and provide a framework for incorporating magnetic-field effects into Majorana neutrino oscillations for future studies including matter interactions.

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 ($ω_{vac} \gg ω_B$), while it is proportional to the cube of the average neutrino momentum if ($ω_{vac} \ll ω_B$). We show that the decoherence effect may appear during neutrino propagation in a magnetic field of supernova.

Figures (1)

• Figure 1: Coherence and oscillations lengths for Majorana neutrino oscillations in a magnetic field as functions of neutrino energy assuming $\sigma_x = 10^{-12}$ cm. Left: $B= 10^{12}$ Gauss. Right: $B= 10^{11}$ Gauss.