Embedding Vacuum Fluctuations in the Dirac Equation: On the Neutrino Electric Millicharge and Magnetic Moment

An extension of the Dirac equation for an initially massless particle carrying an electric charge, assumed to be embedded via minimal coupling into an external fluctuating electromagnetic four-potential of the vacuum, is suggested. We conjecture that appropriate averages of the four-vector can lead to observable quantities, such as a particle mass in its rest frame. The conditions on the potential mean values to become gauge-invariant are obtained. The mass is found to be proportional to the magnitude of the charge times the associated mean Lorentz scalar of the four-potential, and the relation holds for both spacelike and timelike types of four-vectors. For the latter, the extended Dirac equation violates Lorentz covariance, but the violation can be argued to occur within a time scale allowed by the uncertainty principle. For larger times, the particle has acquired a mass and Lorentz covariance is restored. This mathematical scenario is applied to acquire estimates of the neutrino millicharge and magnetic moment, in good agreement with the present upper bounds obtained experimentally. The issue of unstable particle decay is considered by focusing, for illustration, on the main decay channels of the selected particles. From the lifetime of the τ lepton, a lower bound of the effective neutrino mass is predicted, which can be tested in future experiments.