Neutrino Pair Emission from Cooper Pair Breaking and Recombination in Superfluid Quark Matter

For the low energy Standard Model neutrino-matter interactions, we calculate neutrino pair ($\nu\bar\nu$) emissivites in superfluid quark matter. Just below the critical temperature, Cooper pairs continuously break and recombine, resulting in the emission of $\nu\bar \nu$ pairs with a rate that greatly exceeds the standard quark modified Urca and bremsstrahlung rates. At the same baryon density in baryonic and quark matter, the ratio of baryon to quark $\nu\bar\nu$ emissivites lies in the range 2-5 for the densities of interest in the long-term cooling of solar mass compact stars. We also find that in matter containing hyperons, $\nu\bar\nu$ emission can occur with hyperons of all species.