  In this work we have derived the expressions of the mean free path (MFP) and emissivity of the neutrinos by incorporating non-Fermi liquid (NFL) corrections upto next to leading order (NLO). We have shown how such corrections affect the cooling of the neutron star composed of quark matter core. 
Non-Fermi liquid correction to the neutrino mean free path and   emissivity in neutron star beyond the leading order