Neutrino Charge in a Magnetized Media

Abstract

In the presence of a thermal medium or an external electro-magnetic field, neutrinos can interact with photon, mediated by the corresponding charged leptons (real or virtual). The effect of a medium or an electromagnetic field is two-fold—to induce an effective νγ vertex and to modify the dispersion relations of all the particles involved to render the processes kinematically viable. It has already been noted that, in a medium, neutrinos acquire an effective charge, which in the standard model of electroweak interaction comes from the vector type vertex of weak interaction. On the other hand, in a magnetized plasma, the axial vector part also starts contributing to the effective charge of a neutrino. This contribution corresponding to the axial vector part in the interaction Lagrangian is denoted as the axial polarisation tensor. In this note, we outline the calculation of the axial polarization tensor to odd and even powers in eB. We further show its gauge invariance properties. Finally, we infer upon the zero external momentum limit of this axial polarisation tensor.

Keywords

• neutrino
• finite temperature field theory
• magnetic field
• Schwinger proper time representation