The electric charge of neutrinos and plasmon decay

By using both thermal field theory and a somewhat more intuitive method, we define the electric charge as well as the charge radius of neutrinos propagating inside a plasma. We show that electron neutrinos acquire a charge radius of order $\sim 6.5 \times 10^{-16}$ cm, regardless of the properties of the medium. Then, we compute the rate of plasmon decay which such an electric charge or a charge radius implies. Taking into account the relativistic effects of the degenerate electron gas, we compare our results to various approximations as well as to recent calculations and determine the regimes where the electric charge or the charge radius does mediate the decay of plasmons. Finally, we discuss the stellar limits on any anomalous charge radius of neutrinos.