Michael Buballa

NJL-model analysis of dense quark matter

Abstract Investigations of deconfined quark matter within NJL-type models are reviewed, focusing on the regime of low temperatures and “moderate” densities, which is not accessible by perturbative QCD. Central issue is the interplay between chiral symmetry restoration and the formation of color superconducting phases. In order to lay a solid ground for this analysis, we begin with a rather detailed discussion of two- and three-flavor NJL models and their phase structure, neglecting the possibility of diquark pairing in a first step. An important aspect of this part is a comparison with the MIT bag model. The NJL model is also applied to investigate the possibility of absolutely stable strange quark matter. In the next step the formalism is extended to include diquark condensates. We discuss the role and mutual influence of several conventional and less conventional quark–antiquark and diquark condensates. As a particularly interesting example, we analyze a spin-1 diquark condensate as a possible pairing channel for those quarks which are left over from the standard spin-0 condensate. For three-flavor systems, we find that a self-consistent calculation of the strange quark mass, together with the diquark condensates, is crucial for a realistic description of the 2SC–CFL phase transition. We also study the effect of neutrality constraints which are of relevance for compact stars. Both, homogeneous and mixed, neutral phases are constructed. Although neutrality constraints generally tend to disfavor the 2SC phase we find that this phase is again stabilized by the large values of the dynamical strange quark mass which follow from the self-consistent treatment. Finally, we combine our solutions with existing hadronic equations of state to investigate the existence of quark matter cores in neutron stars.

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

We study the phase diagram of dense, locally neutral three-flavor quark matter within the framework of the Nambu\char21{}Jona-Lasinio model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagram in the plane of temperature and quark chemical potential is presented. The results for two qualitatively different regimes, intermediate and strong diquark coupling strength, are presented. It is shown that the role of gapless phases diminishes with increasing diquark coupling strength.

Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases

We investigate the role of the isoscalar-vector interaction and the dynamics of the Polyakov loop on inhomogeneous phases in the phase diagram of the two-flavor Nambu-Jona-Lasinio model. Thereby we concentrate on inhomogeneous phases with a one-dimensional modulation, explicitly domain-wall solitons and, for comparison, the chiral spiral. While the inclusion of the Polyakov loop merely leads to quantitative changes compared to the original Nambu-Jona-Lasinio model, the inclusion of a repulsive vector-channel interaction has significant qualitative effects: Whereas for homogeneous phases the first-order phase transition gets weakened and eventually turns into a second-order transition or a crossover, the domain of inhomogeneous phases is less affected. In particular the location of the Lifshitz point in terms of temperature and density is not modified. Consequently, the critical point disappears from the phase diagram and only a Lifshitz point (showing a different critical behavior) remains. In particular, susceptibilities remain finite.

Inhomogeneous chiral condensates

Abstract The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal’s pion condensation, but recently received new momentum through studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg–Landau analyses as well as in specific calculations, both within effective models and in Dyson–Schwinger or large- N c approaches to QCD. Questions about the most favored shape of the modulations and its dimension, and about the effects of nonzero isospin chemical potential, strange quarks, color superconductivity, and external magnetic fields on these inhomogeneous phases will be addressed as well.

Neutron stars and the transition to color superconducting quark matter

Abstract We explore the relevance of color superconductivity inside a possible quark matter core for the bulk properties of neutron stars. For the quark phase we use a Nambu–Jona-Lasinio (NJL) type model, extended to include diquark condensates. For the hadronic phase, a microscopic many-body model is adopted, with and without strangeness content. In our calculations, a sharp boundary is assumed between the hadronic and the quark phases. For NJL model parameters fitted to vacuum properties we find that no star with a pure quark core does exist. Nevertheless, the presence of color superconducting phases can lower the neutron star maximum mass substantially. In some cases, the transition to quark matter occurs only if color superconductivity is present. Once the quark phase is introduced, the value of the maximum mass stays in any case below the value of two solar masses.

Mixed phases of color superconducting quark matter

Abstract We examine electrically and color neutral quark matter in β -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.

Color–flavor unlocking and phase diagram with self-consistently determined strange-quark masses

Abstract The phase diagram of strongly interacting matter at nonzero temperature and baryon chemical potential is calculated within a three-flavor NJL-type quark model with realistic quark masses. The model exhibits spontaneous chiral symmetry breaking as well as diquark condensation in the two-flavor color-superconducting phase and in the color–flavor-locked phase. We investigate the color–flavor-unlocking phase transition, taking into account self-consistently calculated effective quark masses. We find that it is mainly triggered by a first-order phase transition with respect to the strange-quark mass. It takes place at much higher values of the chemical potential than the transition to the hadronic phase such that we find a relatively large region in the phase diagram where the two-flavor color-superconductor seems to be the most favored state.

Momentum dependence of the pion cloud for ϱ-mesons in nuclear matter

Abstract We extend hadronic models for ϱ -meson propagation in cold nuclear matter via coupling to in-medium pions to include finite three-momentum. Special care is taken to preserve gauge invariance. Consequences for photoabsorption on the proton and on nuclei as well as for the dilepton production in relativistic heavy-ion collisions are discussed.

Flavor-mixing effects on the QCD phase diagram at non-vanishing isospin chemical potential: one or two phase transitions?

Abstract We investigate effects of a fixed nonzero isospin chemical potential on the μ B – T phase diagram of strongly interacting matter using a Nambu–Jona-Lasinio-type four fermion interaction. We focus on the influence of a flavor-mixing interaction induced by instantons. We find that already for rather moderate values of the coupling strength in the flavor-mixing channel the recent findings of two separate phase transitions do not persist.

Modifications of the rho-meson from the virtual pion cloud in hot and dense matter

Abstract The modification of the ρ -meson self-energy due to the coupling to in-medium pions is calculated consistently at finite baryon density and temperature, keeping the full 3-momentum dependence in a gauge invariant way. As a function of nucleon density, the ρ -meson spectral function is strongly enhanced in the invariant mass region M≲650 MeV , while the maximum, i.e., the pole mass, is slightly shifted upwards. As a function of temperature, for fixed nucleon density, the imaginary part of the self-energy increases further due to Bose-enhancement. At the same time the mass shift from the real part becomes very large. As a consequence of these medium effects, the dilepton rate in the low-mass region M≲650 MeV increases strongly, while the peak at M≈770 MeV disappears.