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Non-Fermi-Liquid Specific Heat of Normal Degenerate Quark Matter

We compute the low-temperature behavior of the specific heat of normal (non-color-superconducting) degenerate quark matter as well as that of an ultradegenerate electron gas. Long-range magnetic interactions lead to non-Fermi-liquid behavior with an anomalous leading $T\ln T^{-1}$ term. Depending on the thermodynamic potential used as starting point, this effect appears as a consequence of the logarithmic singularity in the fermion self-energy at the Fermi surface or directly as a contribution from the only weakly screened quasistatic magnetic gauge bosons. We show that a calculation of Boyanovsky and de Vega claiming the absence of a leading $T\ln T^{-1}$ term missed it by omitting vector boson contributions to the internal energy. Using a formulation which collects all nonanalytic contributions in bosonic ring diagrams, we systematically calculate corrections beyond the well-known leading-log approximation. The higher-order terms of the low-temperature expansion turn out to also involve fractional powers $T^{(3+2n)/3}$ and we explicitly determine their coefficients up to and including order $T^{7/3}$ as well as the subsequent logarithmically enhanced term $T^3 \ln (c/T)$. We derive also a hard-dense-loop resummed expression which contains the infinite series of anomalous terms to leading order in the coupling and which we evaluate numerically. At low temperatures, the resulting deviation of the specific heat from its value in naive perturbation theory is significant in the case of strongly coupled normal quark matter and thus of potential relevance for the cooling rates of (proto-)neutron stars with a quark matter component.