Neutrino emission due to Cooper pairing in neutron stars

Neutrino emission caused by Cooper pairing of baryons in neutron stars is recalculated by accurately taking into account for conservation of the vector weak current. The vector current contribution to the neutrino emissivity is found to be several orders of magnitude smaller than that obtained before by different authors. Therefore, the neutrino energy losses due to singlet-state pairing of baryons can in practice be neglected in simulations of neutron star cooling. This makes negligible the neutrino radiation from pairing of protons or hyperons. The neutrino radiation from triplet pairing takes place through axial weak currents. For these states, when the total momentum projection is $m_{j}=0$, the vanishing of the vector weak current contribution results in the suppression of the neutrino energy losses by about 25%. The neutrino emissivity due to triplet pairing with $| m_{j}| =2$ is suppressed by about a factor of 3, caused by the collective contribution of spin-density fluctuations in the condensate.