  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.
