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

TL;DR

This paper develops a quantum field theory framework to analyze Dirac neutrino oscillations in external fields, addressing complexities in propagator calculations and deriving interaction probabilities.

Contribution

It introduces a QFT-based method for Dirac neutrino oscillations in external fields, including matter and magnetic interactions, with novel regularization techniques and probability calculations.

Findings

Derived matrix elements and probabilities for Dirac neutrinos in external fields.

Identified differences between Dirac and Majorana neutrino treatments.

Provided small QFT corrections to quantum mechanical predictions.

Abstract

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.