Quantum field theory treatment of the spin-flavor precession of Dirac neutrinos with diagonal magnetic moments

Abstract

We apply the quantum field theory (QFT) approach to describe the spin-flavor precession of Dirac neutrinos. The magnetic moments matrix of these neutrinos is taken to be diagonal in the mass basis. Neutrino mass eigenstates are considered to be virtual particles in the QFT approach. The neutrino contribution to the matrix element of the overall process, which includes the emission, the propagation and the detection of neutrinos, is contained in the propagators of massive neutrinos. Using the recently derived propagator of a massive neutrino, which exactly accounts for the magnetic moment interaction, we derive the transition probability of the process $ν_{e\mathrm{L}}\toν_{μ\mathrm{L}}$ under the influence of a magnetic field. The result is compared with the prediction of the standard quantum mechanical (QM) approach. We briefly discuss the possibility to derive the QFT corrections to the QM expressions.