Quantum field theory treatment of oscillations of Dirac neutrinos in external fields

We study neutrino oscillations in external fields using the approach based on the quantum field theory (QFT). Neutrinos are virtual particles in this formalism. Neutrino mass eigenstates are supposed to be Dirac fermions. We consider two cases of external fields: the neutrino electroweak interaction with background matter and the interaction with an external magnetic field owing to the presence of the transition magnetic moment. The formalism used involves the dressed propagators of mass eigenstates in external fields. In the matter case, finding of these propagators for Dirac neutrinos has certain difficulties compared to the Majorana particles considered previously. These difficulties are overcome by regularizing the effective potential of the neutrino interaction with matter. The QFT formalism application to the spin-flavor precession also encounters certain peculiarities in the Dirac case compared to the Majorana one. They are related to the observability of right polarized Dirac neutrinos. We derive the matrix elements and the probabilities for Dirac neutrinos interacting with both types of external fields. In case of the spin-flavor precession, we obtain the small QFT contribution to the probabilities in addition to the prediction of the quantum mechanical approach.

💡 Research Summary

The paper presents a comprehensive quantum‑field‑theoretic (QFT) framework for describing oscillations of Dirac neutrinos in external environments, specifically (i) a background of ordinary matter and (ii) an external magnetic field coupled through a transition magnetic moment. The authors begin by recalling that neutrino flavor oscillations arise from mixing between two active flavors (ν_e, ν_μ) with a vacuum mixing angle θ, and they treat the mass eigenstates ψ_a (a = 1, 2) as Dirac fields with masses m_a. In the QFT picture neutrinos are virtual particles propagating between a source and a detector; the S‑matrix element for the whole process contains the Fourier transform of the neutrino propagator Σ_{ab}(p) = ∫d⁴x e^{ip·(x−y)}⟨0|T