Neutrino Electric Charge in a Non-neutral Magnetized Plasma

Neutrinos can interact with photons in a thermal medium or an external electromagnetic field via the associated charged leptons (real or virtual). Neutrinos in a medium pick up an effective charge, which in the electroweak standard model originates from the vector type vertex of weak interaction. In a magnetized plasma, the axial vector part also start contributing to the effective charge of a neutrino dominantly to order for eB < m2, when B is the magnetic field.We conclude by inferring the magnetic field dependent contribution to the neutrino charge from the vector type vertex.