Quark Matter Phase Research Articles

Equations of State of different phases of dense quark matter

Compact stars with significant high densities in their interiors can give rise to quark deconfined phases that can open a window for the study of strongly interacting dense nuclear matter. Recent observations on the mass of two pulsars, PSR J1614-2230 and PSR J0348+0432, have posed a great restriction on their composition, since their equations of state must be hard enough to support masses of about at least two solar masses. The onset of quarks tends to soften the equation of state, but due to their strong interactions, different phases can be realized with new parameters that affect the corresponding equations of state and ultimately the mass-radius relationships. In this paper I will review how the equation of state of dense quark matter is affected by the physical characteristics of the phases that can take place at different baryonic densities with and without the presence of a magnetic field, as well as their connection with the corresponding mass-radius relationship, which can be derived by using different models.

The stifness of the supranuclear equation of state (once again)

We revisit the present status of the stiffness of the supranuclear equations of state, particularly the solutions that increase the stiffness in the presence of hyperons, the putative transition to a quark matter phase and the robustness of massive compact star observations.

Constant entropy hybrid stars: a first approximation of cooling evolution

We aim to study the possibility of a hadron-quark phase transition in the interior of neutron stars, taking into account different schematic evolutionary stages at finite temperature. We also discuss the strange quark matter stability in the quark matter phase. Furthermore, we aim to analyze the astrophysical properties of hot and cold hybrid stars, considering the constraint on maximum mass given by the pulsars J1614-2230 and J0348+0432. We have developed a computational code to construct semi-analytical hybrid equations of state at fixed entropy per baryon and to obtain different families of hybrid stars. An analytical approximation of the Field Correlator Method is developed for the quark matter equation of state. For the hadronic equation of state we use a table based on the relativistic mean field theory, without hyperons. We solved the relativistic structure equations of hydrostatic equilibrium and mass conservation for hybrid star configurations. For the different equations of state obtained, we calculated the stability window for the strange quark matter, lepton abundances, temperature profiles and contours profiles for the maximum mass star depending on the parameters of the Field Correlator Method. We also computed the mass-radius and gravitational mass-baryonic mass relationships for different hybrid star families. We have analyzed different stages of hot hybrid stars as a first approximation of the cooling evolution of neutron stars with quark matter cores. We obtain cold hybrid stars with maximum masses $\geq 2 M_\odot$ for different combinations of the Field Correlator Method parameters. In addition, our study based on the gravitational mass - baryonic mass plane shows a late phase transition between hadronic and quark matter during the proto-hybrid star evolution, in contrast with previous studies of proto-neutron stars.

Dissipationless Hall current in dense quark matter in a magnetic field

We show the realization of axion electrodynamics within the Dual Chiral Density Wave phase of dense quark matter in the presence of a magnetic field. The system exhibits an anomalous dissipationless Hall current perpendicular to the magnetic field and an anomalous electric charge density. Connection to topological insulators and 3D optical lattices, as well as possible implications for heavy-ion collisions and neutron stars are outlined.

Landau damping of gluons in the two-flavor color superconducting Fulde-Ferrell phase

We clarify aspects of gluon propagation in the two-flavor crystalline color superconducting phase of quark matter by analyzing the screening and Landau damping of gluons in the two-flavor Fulde-Ferrell (FF) phase. The paired quarks in the FF phase feature gapless excitations and therefore lead to Debye screening of the longitudinal \(t^{1}\), \(t^{2}\), and \(t^{3}\) gluons and Landau damping of transverse \(t^{1}\), \(t^{2}\), and \(t^{3}\) gluons. This is a marked difference from the 2SC phase where both of these are unscreened. The transverse \(t^{1}\), \(t^{2}\), and \(t^{3}\) gluons are long ranged in the zero energy limit and hence the interaction mediated by these is the most important mechanism for the scattering of the paired quarks. Therefore they play an important role in determining their transport properties.

New dynamic critical phenomena in nuclear and quark superfluids

We study the dynamic critical phenomena near the possible high-density QCD critical point inside the superfluid phase of nuclear and quark matter. We find that this critical point belongs to a new dynamic universality class beyond the conventional classification by Hohenberg and Halperin. We show that the speed of the superfluid phonon vanishes at the critical point and that the dynamic critical index is $z \approx 2$.

Stability of superfluid vortices in dense quark matter

Superfluid vortices in the color-flavor-locked (CFL) phase of dense quark matter are known to be energetically disfavored relative to well-separated triplets of "semi-superfluid" color flux tubes. However, the short-range interaction (metastable versus unstable) has not been established. In this paper we perform numerical calculations using the effective theory of the condensate field, mapping the regions in the parameter space of coupling constants where the vortices are metastable versus unstable. For the case of zero gauge coupling we analytically identify a candidate for the unstable mode, and show that it agrees well with the results of the numerical calculations. We find that in the region of the parameter space that seems likely to correspond to real-world CFL quark matter the vortices are unstable, indicating that if such matter exists in neutron star cores it is very likely to contain semi-superfluid color flux tubes rather than superfluid vortices.

Cold quark matter phase diagram under strong magnetic fields within a generalized SU(2) NJL model

We study the effect of intense magnetic fields on the phase diagram of cold, strongly interacting matter within an extended version of the Nambu-Jona-Lasinio model that includes flavor mixing effects and vector interactions. Different values of the relevant model parameters in acceptable ranges are considered. Charge neutrality and beta equilibrium effects, which are specially relevant to the study of compact stars, are also taken into account. In this case the behavior of leptons is discussed.

Aharonov-Bohm phase in high density quark matter

Stable non-Abelian vortices, which are color magnetic flux tubes as well as superfluid vortices, are present in the color-flavor locked phase of dense quark matter with diquark condensations. We calculate the Aharanov-Bohm phases of charged particles, that is, electrons, muons, and color-flavor locked mesons made of tetraquarks around a non-Abelian vortex.

New class of hybrid EoS and Bayesian M - R data analysis

We explore systematically a new class of two-phase equations of state (EoS) for hybrid stars that is characterized by three main features : (1) stiffening of the nuclear EoS at supersaturation densities due to quark exchange effects (Pauli blocking) between hadrons, modelled by an excluded volume correction, (2) stiffening of the quark matter EoS at high densities due to multiquark interactions and (3) possibility for a strong first order phase transition with an early onset and large density jump. The third feature results from a Maxwell construction for the possible transition from the nuclear to a quark matter phase and its properties depend on the two parameters used for (1) and (2), respectively. Varying these two parameters one obtains a class of hybrid EoS that yields solutions of the Tolman-Oppenheimer-Volkoff (TOV) equations for sequences of hadronic and hybrid stars in the mass-radius diagram which cover the full range of patterns according to the Alford-Han-Prakash classification following which a hybrid star branch can be either absent, connected or disconnected with the hadronic one. The latter case often includes a tiny connected branch. The disconnected hybrid star branch, also called "third family", corresponds to high-mass twin stars characterized by the same gravitational mass but different radii. We perform a Bayesian analysis and demonstrate that the observation of such a pair of high-mass twin stars would have a sufficient discriminating power to favor hybrid EoS with a strong first order phase transition over alternative EoS.

Trajectory of the cosmic plasma through the quark matter phase diagram

Experimental studies of the quark-gluon plasma (QGP) focus on two, in practice distinct, regimes: one in which the baryonic chemical potential ${\ensuremath{\mu}}_{B}$ is essentially zero, the other in which it is of the same order of magnitude as the temperature. The cosmic QGP which dominates the early universe after reheating is normally assumed to be of the first kind, but recently it has been suggested that it might well be of the second: this is the case in the theory of ``little inflation.'' If that is so, then it becomes a pressing issue to fix the trajectory of the Universe, as it cools, through the quark matter phase diagram: in particular, one wishes to know where in that diagram the plasma epoch ends, so that the initial conditions of the hadronic epoch can be determined. Here we combine various tools from strongly coupled QGP theory (the latest lattice results, together with gauge-gravity duality) in order to constrain that trajectory, assuming that little inflation did occur.

Excluded volume effects in the hybrid star EoS

In this contribution, we outline a new 2-phase description of the quark-nuclear matter hybrid equation of state that takes into account effects of phase space occupation (excluded volume) in both, the hadronic and the quark matter phases. For the nuclear matter phase, the reduction of the available volume at increasing density leads to a stiffening, while for the quark matter phase a reduction of the effective string tension in the confining density functional is obtained. The deconfinement phase transition in the resulting hybrid equation of state is sensitive to both excluded volume effects. As an application, we consider matter under compact star constraints of electric neutrality and β-equilibrium. We obtain mass- radius relations for hybrid stars that fulfill the 2M⨀ constraint and exhibit the high-mass twin phenomenon. Both features depend sensitively on the excluded volume.

Towards a new quark-nuclear matter EoS for applications in astrophysics and heavy-ion collisions

The aim of our work is to develop a unified equation of state (EoS) for nuclear and quark matter for a wide range in temperature, density and isospin so that it becomes applicable for heavy-ion collisions as well as for the astrophysics of neutron stars, their mergers and supernova explosions. As a first step, we use improved EoS for the hadronic and quark matter phases and join them via Maxwell construction. We discuss the limitations of a 2-phase description and outline steps beyond it, towards the formulation of a unified quark-nuclear matter EoS on a more fundamental level by a cluster virial expansion.

Variational approach to the inhomogeneous chiral phase in quark matter

The inhomogeneous chiral phase is discussed in QCD at finite temperature and/or density. We study the phase diagram on the density-temperature plane by taking into account the effect of the current mass by a variational method. It is demonstrated that our framework well describes the inhomogeneous phase over the whole phase region.

Mixed phase effects on high-mass twin stars

Recently it has been found that a certain class of hybrid star equations of state with a large latent heat (strong first order phase transition obtained by a Maxwell construction) between stiff hadronic hadronic and stiff quark matter phases allows for the appearance of a third family of compact stars (including "twins") at high mass of $\sim 2 M_\odot$. We investigate how robust this high-mass twin phenomenon is against a smoothing of the transition which would occur, e.g., due to pasta structures in the mixed phase. To this end we propose a simple construction of a pasta-like equation of state with a parameter that quantifies the degree of smoothing of the transition and could eventually be related to the surface tension of the pasta structures. It is interesting to note that the range of energy densities for the transition as well as the pressure at the onset of the transition of this class of hybrid star matter at zero temperature corresponds well to values of the same quantities found in finite temperature lattice QCD simulations for the 1 $\sigma$ region at the pseudocritical temperature $T_c=154 \pm 9$ MeV. The pattern of the speed of sound as a function of energy density is very different.

Phonons, pions, and quasi-long-range order in spatially modulated chiral condensates

We investigate low-energy fluctuations in the real kink crystal phase of dense quark matter within the Nambu--Jona-Lasinio model. The modulated chiral condensate breaks both the translational symmetry and chiral symmetry spontaneously, which leads to the appearance of phonons and pions that are dominant degrees of freedom in the infrared. Using the Ginzburg-Landau expansion near the Lifshitz point, we derive elastic free energies for phonons and pions in dependence on the temperature and chemical potential. We show that the one-dimensional modulation is destroyed by thermal fluctuations of phonons at nonzero temperature, and compute the exponent that characterizes the anisotropic algebraic decay of quasicondensate correlations at long distance. We also estimate finite-volume effects on the stability of the real kink crystal and briefly discuss the possibility of its existence in neutron stars.

Cold magnetized quark matter phase diagram within a generalized SU(2) NJL model

We study the effect of intense magnetic fields on the phase diagram of cold, strongly interacting matter within an extended version of the Nambu-Jona-Lasinio model that includes flavor-mixing effects and vector interactions. Different values of the relevant model parameters in acceptable ranges are considered. Charge neutrality and beta equilibrium effects, which are especially relevant to the study of compact stars, are also taken into account. In this case, the behavior of leptons is discussed.

Holography of Little Inflation

For several crucial microseconds of its early history, the Universe consisted of a Quark–Gluon Plasma. As it cooled during this era, it traced out a trajectory in the quark matter phase diagram. The form taken by this trajectory is not known with certainty, but is of great importance: it determines, for example, whether the cosmic plasma passed through a first-order phase change during the transition to the hadron era, as has recently been suggested by advocates of the “Little Inflation” model. Just before this transition, the plasma was strongly coupled and therefore can be studied by holographic techniques. We show that holography imposes a strong constraint (taking the form of a bound on the baryonic chemical potential relative to the temperature) on the domain through which the cosmic plasma could pass as it cooled, with important consequences for Little Inflation. In fact, we find that holography applied to Little Inflation implies that the cosmic plasma must have passed quite close to the quark matter critical point, and might therefore have been affected by the associated fluctuation phenomena.

Non-uniform Phases in a Three-flavour 't Hooft Extended Nambu--Jona-Lasinio Model

The possible existence of non-uniform phases in cold dense quark matter in the light quark sector ($u$, $d$ and $s$) is addressed using the Nambu-Jona--Lasinio Model extended to include flavour-mixing 't Hooft determinant. The effect of changes in the coupling strengths of the model is discussed. It is seen that the inclusion of the strange sector catalyses the appearance of these non-uniform phases extending the domain for their appearance.

Some recent progress on magnetic effects for non-Abelian vortices in color-flavor-locked quark matter

It is recently known that strong magnetic fields may lead to highly nontrivial effects on strongly interacting matter,including the color-flavor-locked phase of dense quark matter. Dense quark matter provides various kind of topological solitons such as vortices,domain walls,monopoles,kinks,boojums etc.,it is hence natural to expect that the magnetic field can also affect these topological solitons. In this mini-review,we update our recent progress on the studies of magnetic field effects in the color-flavor-locked quark matter. The particular emphasis is given on the non-Abelian vortices since they are the most fundamental string-like topological excitations under certain circumstance. Their relevant properties( e. g.,the profile function and the tension energy) and the magnetic-field dependence are investigated with the Ginzburg-Landau framework.