Quantum field theory treatment of the neutrino spin-flavor precession in a magnetic field

Abstract

We study the spin-flavor precession of neutrinos in a magnetic field within the quantum field theory approach in which neutrinos are virtual particles. Neutrinos are taken to be Majorana particles having a nonzero transition magnetic moment. We derive the dressed propagators of the neutrino mass eigenstates exactly accounting for the magnetic field contribution. The matrix element and the transition probability for the spin-flavor precession are obtained in the approximation of the forwardly scattered charged leptons. The leading term in the transition probability is shown to coincide with the result of the standard quantum mechanical description of neutrino oscillations. We also discuss the quantum field theory contributions to the neutrino dressed propagators and demonstrate that these contributions result in a small correction to the transition probability. The case of charged leptons with arbitrary energies is considered.

Figures (2)

• Figure 1: The schematic Feynman diagram for the reaction $l_{\beta}^{-}+N\to\text{neutrinos}\to l_{\alpha}^{+}+\tilde{N}'$. The arrows over fermionic lines, $l_\beta^-$, $l_\alpha^+$, and neutrinos, show the flow of the lepton number. Since we do not care about the details of the nuclear transformations in the source and the detector, the arrows over nuclear lines, $N$, $\tilde{N}$, $N'$, and $\tilde{N}'$, can signify the baryon number flow. The neutrino line has two counter-directional arrows since we deal with the Majorana particles which violate the lepton number. The time flows from left to right. Moreover, the neutrino line is broad since the mass eigenstates interact with a magnetic field [see Eq. (\ref{['eq:Weyeqsys']})]. Note that we take into account the magnetic interaction exactly (see Sec. \ref{['sec:PROPB']}).
• Figure 2: Feynman diagrams corresponding to Eq. (\ref{['eq:Dysser']}). 4D Fourier images of the bare propagators $-\mathrm{i}S_{a\mathrm{R,L}}$, given in Eqs. \ref{['eq:SL']} and \ref{['eq:SR']}, are depicted by thin solid lines BerLifPit82. The broad solid lines correspond to the dressed propagators $-\mathrm{i}\Sigma_{ab}$. The potential of the magnetic interaction is $V=\mathrm{i}\mu(\bm{\sigma}\mathbf{B})$.