Next to leading order non Fermi liquid corrections to the neutrino emissivity and cooling of the neutron star

In this work we derive the expressions of the neutrino mean free path(MFP) and emissivity with non Fermi liquid corrections up to next to leading order(NLO) in degenerate quark matter. The calculation has been performed both for the absorption and scattering processes. Subsequently the role of these NLO corrections on the cooling of the neutron star has been demonstrated. The cooling curve shows moderate enhancement compared to the leading order(LO) non-Fermi liquid result. Although the overall correction to the MFP and emissivity are larger compared to the free Fermi gas, the cooling behavior does not alter significantly.