Neutrino-Electron Interactions in External Active Media

Abstract

An intense electromagnetic field makes possible the processes which are forbidden in a vacuum such as the neutrino decay into the $W^+$ boson and a charged lepton, $\nu \rightarrow \ell ^{-} W^{+} \, (\ell = e, \mu , \tau )$ and the production of a lepton pair by neutrino, $\nu \rightarrow \nu \ell ^{-} \ell ^{+}$. In this chapter, we present in details the technique of calculations of the neutrino-electron processes in external active media. We consider mainly the two processes. The first one, which is possible in an intense external electromagnetic field and in the case of sufficiently high neutrino energy, is the decay $\nu \rightarrow e^{-} W^{+}$. The second process is the electron–positron pair production by a neutrino $\nu \rightarrow \nu + e^{-} + e^{+}$. We present the procedure of calculation of the process probability in the case of a strong magnetic field, when an electron and a positron are created in the ground Landau level, and in the crossed field limit. We calculate also the four-vector of the mean values of the neutrino energy and momentum losses due to the process $\nu \rightarrow \nu + e^- + e^+$, which could be essential in astrophysical applications. The process of the electron–positron pair production by neutrino in a strong magnetic field, if one more component of the external active medium which is dense plasma is taken into account, should be suppressed by the Fermi—Dirac statistical factors. In this chapter, we also consider the electron–positron plasma influence on the process $\nu \rightarrow \nu + e^- + e^+$, and take into consideration the crossed neutrino-electron processes. We also try to apply the results obtained to the well-known problem of large kick velocities of pulsars born in supernova explosions.