Weak magnetism effects in the direct Urca processes in cooling neutron stars

In the mean field approximation, we study the effects of weak magnetism and pseudoscalar interaction in the neutrino energy losses caused by the direct Urca processes on relativistic nucleons in the degenerate baryon matter. Our formula for the neutrino energy losses incorporates the effects of nucleon recoil, parity violation, weak magnetism, and pseudoscalar interaction. For numerical testing of our formula, we use a self-consistent relativistic model of the multicomponent baryon matter. We found that the effects of weak magnetism approximately double the neutrino emissivity, while the pseudoscalar interaction slightly suppresses the energy losses, approximately by 10%.