Contribution of the massive photon decay channel to neutrino cooling of neutron stars

We consider massive photon decay reactions via intermediate states of electron-electron-holes and proton-proton-holes into neutrino-antineutrino pairs in the course of neutron star cooling. These reactions may become operative in hot neutron stars in the region of proton pairing where the photon due to the Higgs-Meissner effect acquires an effective mass $m_{\gamma}$ that is small compared to the corresponding plasma frequency. The contribution of these reactions to neutrino emissivity is calculated; it varies with the temperature and the photon mass as $T^{3/2}m_{\gamma}^{7/2} e^{-m_{\gamma}/T}$ for $T < m_{\gamma}$. Estimates show that these processes appear as extra efficient cooling channels of neutron stars at temperatures $T \simeq (10^9-10^{10})$ K.