Phase diagram of neutral quark matter: Self-consistent treatment of quark masses

Theoretical studies suggest that quark matter at suffi ciently high densities and suffi ciently low temperatures may be a color superconductor. (For a review on color superconductivity see for example, Ref. [1].) In nature such conditions appear in the central regions of neutron stars. Therefore it is possible that matter is color superconducting in the cores of these objects. In compact stars matter has to be neutral with respect to electric and color charges. It should also remain in β equilibrium. Taking these constraints into account may have a strong effect on the competition between different phases of deconfi ned quark matter at large densities [2, 3]. We studied locally neutral three-fl avor quark matter within the framework of a Nambu– Jona-Lasinio model [4]. In the analysis we take dynamically generated quark masses into account self-consistently. For each point in the plane of temperature T and quark chemical potential μ we have to compute nine quantities for each of the competing phases. These are the three constituent quark masses, Mu, Md, and Ms, the three gap parameters, ∆ud, ∆us, and ∆ds, which measure the diquark condensates, one electric and two color charge chemical potentials, μQ, μ3, and μ8, which are needed to ensure neutrality. These are obtained by solving a coupled set of six gap equations together with the three neutrality conditions. In Fig. 1 the resulting phase diagram of neutral quark matter is displayed in the T -μ plane. In principle there could be seven color superconducting phases (different combinations of non-vanishing ∆ab). We see that for our conditions only three appear as the ground state of neutral matter. These are the two-fl avor color superconductor (2SC) with ∆ud 6= 0 and∆us = ∆ds = 0, the color-fl avor locked phase (CFL) with ∆ud,∆us,∆ds 6= 0, and the uSC phase with ∆ud,∆us 6= 0 and∆ds = 0. In the region of small quark chemical potentials and not too high temperatures we fi nd a non-superconducting phase in which the approximate chiral symmetry is spontaneously broken and quarks have relatively large constituent quark masses (χSB). At intermediate quark chemical potentials and very low temperatures there is a chirally restored normal (non color superconducting) quark matter phase (NQ). In this region quark pairing is not possible because charge neutrality disfavors a 2SC-type pairing and