The lowest order electromagnetic radiative corrections to electron-positron annihilation into neutrino and antineutrino and to neutrino scattering by electrons are calculated. The pair annihilation corrections are used to calculate the radiative corrections to stellar neutrino luminosities in the temperature range in which the zero order process gives the dominant contribution. The corrections to the neutrino-electron scattering cross section are those relevant to a proposed experiment detecting scattered electrons with more than a minimum recoil energy whether or not a bremsstrahlung photon is emitted.
The results depend logarithmically on an ultraviolet cut-off in the same way as does the lowest order vacuum polarization diagram of electrodynamics. When the cut-off is taken to be on the order of the nucleon mass the luminosity is enhanced by as much as 10 percent belowT ~ 10⁹ °K and depressed by ~1 percent for T > 10⁹ °K.The scattering cross section is depressed by ~4 percent for the incident neutrino energies ~8 - 14 MeV of the proposed experiment.
A characteristic distance, the neutrino charge radius, is associated with a charge distribution of the neutrino and depends on the cut-off. With the cut-off at the nucleon mass the charge radius of the electron neutrino is estimated to be two orders of magnitude smaller than the experimental limit. The possible effects of a charge radius larger than the estimate are also considered. It is found that interference between the electromagnetic and weak couplings could depress both the non-relativistic stellar luminosity and the scattering cross section, but that if the scattering cross section is found to be as large as expected' the luminosity must be also.
