The properties of cold and dense quark matter have been the subject of extensive investigation, especially in the last decade. Unfortunately, we still lack of a complete understanding of the properties of matter in these conditions. One possibility is that quark matter is in a color superconducting phase which is characterized by the formation of a diquark condensate. We review some of the basic concepts of color superconductivity and some of the aspects of this phase of matter which are relevant for compact stars. Since quarks have color, flavor as well as spin degrees of freedom many different color superconducting phases can be realized. At asymptotic densities QCD predicts that the color flavor locked phase is favored. At lower densities where the QCD coupling constant is large, perturbative methods cannot be applied and one has to rely on some effective model, eventually trying to constrain such a model with experimental observations. The picture is complicated by the requirement that matter in the interior of compact stars is in weak equilibrium and neutral. These conditions and the (possible) large value of the strange quark mass conspire to separate the Fermi momenta of quarks with different flavors, rendering homogenous superconducting phases unstable. One of the aims of this presentation is to introduce non-experts in the field to some of the basic ideas of color superconductivity and to some of its open problems.
We investigate modification of the dilepton production rate by the diquark fluctuations that form well-developed collective modes near the critical temperature of color superconductivity. Through the analysis of the photon self-energy called the Aslamasov-Larkin, Maki-Thompson and density of states terms in the theory of metalic superconductivity, it is shown that the collective mode in the diquark channel affects the photon self-energy significantly and thereby gives rise to an anomalous enhacement of the dilepton production rate in the low invariant-mass region.
We investigate the effects of isospin asymmetry on the competition between color-superconductivity and inhomogeneous chiral symmetry breaking in dense two-flavor quark matter using an extended Nambu--Jona-Lasinio model. We confirm the appearance of a coexistence window where chiral symmetry is inhomogeneously broken and a nonzero spatially homogeneous diquark gap is present, consistently with previous works, and show that such a phase survives at nonzero isospin chemical potentials. We also discuss how the model phase structure becomes modified as large isospin asymmetries are considered.
The color superconductivity was studied with an adaptation of the Nambu and Jona-Lasinio model (NJL). This one was coupled to a Polyakov loop, to form the PNJL model. A $μ$-dependent Polyakov loop potential was considered. An objective of the presented works was to describe the analytical calculations required to establish the equations to be solved, in all of the treated cases. They concerned the normal quark phase, the 2-flavor color-superconducting and the color-flavor-locked phases, in an SU(3)f X SU(3)c description. The calculations were performed according to the temperature T, the chemi…
