We consider the massive Dirac neutrino electric charge and magnetic moment within the context of the standard model supplied with an SU(2)-singlet right-handed neutrino in an arbitrary $R_{\xi }$ gauge. Using the dimensional-regularization scheme we start with the calculations of the one-loop contributions to the neutrino electromagnetic vertex function exactly accounting for the neutrino mass. We examine the decomposition of the massive neutrino electromagnetic vertex function. It is found by means of direct calculations that the massive neutrino vertex function contains only the four form factors. Then we derive the closed integral expressions for different contributions to the neutrino electric form factor, electric charge, and magnetic moment. For several one-loop contributions to the neutrino charge and magnetic moment that were calculated previously with mistakes by the other authors, we find the correct results. We show that the electric charge for the massive neutrino is a gauge independent and vanishing parameter in the first two orders of the expansion over the neutrino mass parameter ${b=(m}_{\nu }{/M}_W{)}^2.$ From the obtained closed two-integral expression for a massive neutrino electric form factor it is also possible to derive the neutrino charge radius. In the particular choice of the ’t Hooft–Feynman gauge we also demonstrate that the neutrino charge is zero in all orders of expansion over b, i.e., for an arbitrary mass of neutrino. For each of the diagrams contributing to the neutrino magnetic moment, we obtain the expressions accounting for the leading (zeroth) and next-to-leading (first) order in b, where the gauge dependence is shown explicitly. Each of the contributions is finite and the sum of all contributions turns out to be gauge independent. Our calculations also enable us to obtain the neutrino magnetic moment in theoretical models that differ from each other by the values of particles’ masses, including the case of a very heavy neutrino. The general expression for the massive neutrino magnetic form factor is presented.

• Received 15 May 2003

DOI:https://doi.org/10.1103/PhysRevD.69.073001