The Specific Heat of Normal, Degenerate Quark Matter: Non-Fermi Liquid Corrections

In normal degenerate quark matter, the exchange of dynamically screened transverse gluons introduces infrared divergences in the quark self-energies that lead to the breakdown of the Fermi liquid description. If the core of neutron stars are composed of quark matter with a normal component, cooling by direct quark Urca processes may be modified by non-Fermi liquid corrections. We find that while the quasiparticle density of states is finite and non-zero at the Fermi surface, its frequency derivative diverges and results in non-Fermi liquid corrections to the specific heat of the normal, degenerate component of quark matter. We study these non-perturbative non-Fermi liquid corrections to the specific heat and the temperature dependence of the chemical potential and show that these lead to a reduction of the specific heat.