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

TL;DR

The paper develops a quantum-field-theory framework for Dirac neutrino oscillations in external fields, using dressed propagators and Dyson equations to account for matter potentials and magnetic-field interactions. In matter, the QFT treatment recovers the standard MSW-like oscillation behavior, while in a magnetic field it yields the spin-flavor precession with a leading QM-like term and a small additional QFT correction arising from a quantum term in the propagators. A central Dirac-specific point is that right-handed neutrinos are not observable in SM detectors, which modifies the observable channels compared to Majorana neutrinos. Overall, the work demonstrates that nonperturbative external-field effects can be handled consistently within QFT and provides explicit expressions for matrix elements and transition probabilities for Dirac neutrinos in two-field scenarios.

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.

Figures (2)

• Figure 1: The schematic illustration of the process corresponding to the $S$-matrix element in Eq. (\ref{['eq:Smatr']}). The broad neutrino line means that these particles interact with an external field while propagating from a source to a detector.
• Figure 2: The Feynman diagrams contributing to the dressed propagators $\Sigma_{ab}$ of Dirac mass eigenstates which take into account both diagonal and nondiagonal interactions with background matter. Thin lines correspond to the propagators $S_{a}$ in Eq. (\ref{['eq:propdiagur']}) in which only diagonal interaction with matter is accounted for. The same diagrams represent $\Sigma_{ab}$ for Dirac neutrinos with a transition magnetic moment in a magnetic field. In a magnetic case, we replace $G\to V_{\mathrm{B}}=\mu(\bm{\Sigma}\mathbf{B})$. Then, thin lines stand for the vacuum propagators in Eq. (\ref{['eq:Dirpropvac']}).