Mixed phases of color superconducting quark matter

We examine electrically and color neutral quark matter in beta-equilibrium focusing on the possibility of mixed phases between different color superconducting phases. To that end we apply the Gibbs criterion to ensure phase equilibrium and discuss the external conditions under which these mixed phases can occur. Neglecting surface and Coulomb effects we find a rich structure of different mixed phases with up to four components, including 2SC and CFL matter as well as more ``exotic'' components, like a phase with us- and ds-pairing but without ud-pairing. Preliminary estimates indicate, however, that the mixed phases become unstable if surface and Coulomb effects are included.Comment: 22 pages, 9 figures, v2: minor changes in the text, version to appear in Nucl. Phys.

Self-consistent parametrization of the two-flavor isotropic color-superconducting ground state

Lack of Lorentz invariance of QCD at finite quark chemical potential in general implies the need of Lorentz non-invariant condensates for the self-consistent description of the color-superconducting ground state. Moreover, the spontaneous breakdown of color SU(3) in this state naturally leads to the existence of SU(3) non-invariant non-superconducting expectation values. We illustrate these observations by analyzing the properties of an effective 2-flavor Nambu-Jona-Lasinio type Lagrangian and discuss the possibility of color-superconducting states with effectively gapless fermionic excitations. It turns out that the effect of condensates so far neglected can yield new interesting phenomena.Comment: 16 pages, 3 figure

A quark action for very coarse lattices

We investigate a tree-level O(a^3)-accurate action, D234c, on coarse lattices. For the improvement terms we use tadpole-improved coefficients, with the tadpole contribution measured by the mean link in Landau gauge. We measure the hadron spectrum for quark masses near that of the strange quark. We find that D234c shows much better rotational invariance than the Sheikholeslami-Wohlert action, and that mean-link tadpole improvement leads to smaller finite-lattice-spacing errors than plaquette tadpole improvement. We obtain accurate ratios of lattice spacings using a convenient ``Galilean quarkonium'' method. We explore the effects of possible O(alpha_s) changes to the improvement coefficients, and find that the two leading coefficients can be independently tuned: hadron masses are most sensitive to the clover coefficient, while hadron dispersion relations are most sensitive to the third derivative coefficient C_3. Preliminary non-perturbative tuning of these coefficients yields values that are consistent with the expected size of perturbative corrections.Comment: 22 pages, LaTe

Heating (Gapless) Color-Flavor Locked Quark Matter

We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature T and the strange quark mass Ms. At T=0, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where Ms^2/mu < 2 Delta, and the metallic gapless CFL phase, which occurs at larger Ms^2/mu. Here, mu is the chemical potential for quark number and Delta is the gap in the CFL phase. We find this distinction blurred at nonzero T, as the CFL phase undergoes an insulator-to-metal crossover when it is heated. We present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters Delta_1, Delta_2 and Delta_3 describing ds-pairing, us-pairing and ud-pairing respectively, go to zero in an NJL model. For small values of Ms^2/mu, we find that Delta_2 vanishes first, then Delta_1, then Delta_3. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger Ms^2/mu, we find that Delta_1 vanishes first, then Delta_2, then Delta_3. Hence, we find a "doubly critical'' point in the (Ms^2/mu,T)-plane at which two lines of second order phase transitions (Delta_1->0 and Delta_2->0) cross. Because we do not make any small-Ms approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of Ms that there are no strange quarks present.Comment: 24 pages; 22 figures; typos in labelling of Figs. 7, 20 correcte

Ginzburg-Landau approach to the three flavor LOFF phase of QCD

We explore, using a Ginzburg-Landau expansion of the free energy, the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors, using the NJL four-fermion coupling to mimic gluon interactions. We find that, below the point where the QCD homogeneous superconductive phases should give way to the normal phase, Cooper condensation of the pairs u-s and d-u is possible, but in the form of the inhomogeneous LOFF pairing.Comment: 8 pages, 4 figures. Eq. (20) corrected. As a consequence figures have been modified to show only the solution with parallel total momenta of the us, ud pairs, as the other configurations are suppressed. Main conclusions of the paper are unchange

Quark mass effects on the stability of hybrid stars

We perform a study of the possible existence of hybrid stars with color superconducting quark cores using a specific hadronic model in a combination with an NJL-type quark model. It is shown that the constituent mass of the non-strange quarks in vacuum is a very important parameter that controls the beginning of the hadron-quark phase transition. At relatively small values of the mass, the first quark phase that appears is the two-flavor color superconducting (2SC) phase which, at larger densities, is replaced by the color-flavor locked (CFL) phase. At large values of the mass, on the other hand, the phase transition goes from the hadronic phase directly into the CFL phase avoiding the 2SC phase. It appears, however, that the only stable hybrid stars obtained are those with the 2SC quark cores.Comment: 12 pages, 7 eps figures; v2: figures and table modified after correction of a minor numerical mistake, discussion clarified, references added, conclusions unchanged; version to appear in PL

Colour superconductivity in finite systems

In this paper we study the effect of finite size on the two-flavour colour superconducting state. As well as restricting the quarks to a box, we project onto states of good baryon number and onto colour singlets, these being necessary restrictions on any observable ``quark nuggets''. We find that whereas finite size alone has a significant effect for very small boxes, with the superconducting state often being destroyed, the effect of projection is to restore it again. The infinite-volume limit is a good approximation even for quite small systems.Comment: 14 pages RevTeX4, 12 eps figure

Color-Neutral Superconducting Quark Matter

We investigate the consequences of enforcing local color neutrality on the color superconducting phases of quark matter by utilizing the Nambu-Jona-Lasinio model supplemented by diquark and the t'Hooft six-fermion interactions. In neutrino free matter at zero temperature, color neutrality guarantees that the number densities of u, d, and s quarks in the Color-Flavor-Locked (CFL) phase will be equal even with physical current quark masses. Electric charge neutrality follows as a consequence and without the presence of electrons. In contrast, electric charge neutrality in the less symmetric 2-flavor superconducting (2SC) phase with ud pairing requires more electrons than the normal quark phase. The free energy density cost of enforcing color and electric charge neutrality in the CFL phase is lower than that in the 2SC phase, which favors the formation of the CFL phase. With increasing temperature and neutrino content, an unlocking transition occurs from the CFL phase to the 2SC phase with the order of the transition depending on the temperature, the quark and lepton number chemical potentials. The astrophysical implications of this rich structure in the phase diagram, including estimates of the effects from Goldstone bosons in the CFL phase, are discussed.Comment: 20 pages, 4 figures; version to appear in Phys. Rev.