Flavor Quark Matter Research Articles

Strange quark star and the parameter space of the quasi-particle model

The properties of strange quark stars are studied within the quasi-particle model. Taking into account chemical equilibrium and charge neutrality, the equation of state (EOS) of -flavor quark matter is obtained. We illustrate the parameter spaces with constraints from two aspects: one is based on the astronomical results of PSR and GW 170 817 , and the other is based on the constraints proposed from the theoretical study of a compact star that the EOS must ensure the tidal deformability and support a maximum mass above . It is found that neither type of constraints can restrict the parameter space of the quasi-particle model in a reliable region and thus we conclude that the low mass compact star cannot be a strange quark star.

Surface tension of hot and dense quark matter under strong magnetic fields

We study the surface tension of hot, highly magnetized three flavor quark matter droplets, focusing specifically on the thermodynamic conditions prevailing in neutron stars, hot lepton rich protoneutron stars and neutron star mergers. We explore the role of temperature, baryon number density, trapped neutrinos, droplet size and magnetic fields within the multiple reflection expansion formalism (MRE), assuming that astrophysical quark matter can be described as a mixture of free Fermi gases composed by quarks $u$, $d$, $s$, electrons and neutrinos, in chemical equilibrium under weak interactions. We find that the total surface tension is rather unaffected by the size of the drop, but is quite sensitive to the effect of baryon number density, temperature, trapped neutrinos and magnetic fields (specially above $eB \sim 5 \times 10^{-3} \mathrm{GeV}^2$). Surface tensions parallel and transverse to the magnetic field span values up to $\sim$ 25 MeV/fm$^2$. For $T \lesssim 100$ MeV the surface tension is a decreasing function of temperature but above 100 MeV it increases monotonically with $T$. Finally, we discuss some astrophysical consequences of our results.

Multiple critical endpoints in magnetized three flavor quark matter

The magnetized phase diagram for three-flavor quark matter is studied within the Polyakov extended Nambu--Jona-Lasinio model. The order parameters are analyzed with special emphasis on the strange quark condensate. We show that the presence of an external magnetic field induces several critical endpoints (CEPs) in the strange sector, which arise due to the multiple phase transitions that the strange quark undergoes. The spinodal and binodal regions of the phase transitions are shown to increase with external magnetic field strength. The influence of strong magnetic fields on the isentropic trajectories around the several CEPs is analyzed. A focusing effect is observed on the region towards the CEPs that are related with the strange quark phase transitions. Compared to the chiral transitions, the deconfinement transition turns out to be less sensitive to the external magnetic field and the crossover nature is preserved over the whole phase diagram.

A comparative study on two different approaches of bulk viscosity in the Polyakov–Nambu–Jona-Lasinio model

We have gone through a comparative study on two different kinds of bulk viscosity expressions by using a common dynamical model. The Polyakov–Nambu–Jona-Lasinio (PNJL) model in the realm of mean-field approximation, including up to eight quark interactions for 2+1 flavor quark matter, is treated for this common dynamics. We have probed the numerical equivalence as well as discrepancy of two different expressions for bulk viscosity at vanishing quark chemical potential. Our estimation of bulk viscosity to entropy density ratio follows a decreasing trend with temperature, which is observed in most of the earlier investigations. We have also extended our estimation for finite values of quark chemical potential.

Surface tension of highly magnetized degenerate quark matter

We study the surface tension of highly magnetized three flavor quark matter within the formalism of multiple reflection expansion (MRE). Quark matter is described as a mixture of free Fermi gases composed by quarks $u$, $d$, $s$ and electrons, in chemical equilibrium under weak interactions. Due to the presence of strong magnetic fields the particles' transverse motion is quantized into Landau levels, and the surface tension has a different value in the parallel and transverse directions with respect to the magnetic field. We calculate the transverse and longitudinal surface tension for different values of the magnetic field and for quark matter drops with different sizes, from a few fm to the bulk limit. For baryon number densities between $2-10$ times the nuclear saturation density, the surface tension falls in the range $2 - 20$ MeV /fm$^{2}$. The largest contribution comes from strange quarks which have a surface tension an order of magnitude larger than the one for $u$ or $d$ quarks and more than two orders of magnitude larger than for electrons. Our results show that the total surface tension is quite insensitive to the size of the drop. We also find that the surface tensions in the transverse and parallel directions are almost unaffected by the magnetic field if $eB$ is below $\sim 5 \times 10^{-3} $ GeV$^2$. Nevertheless, for higher values of $eB$, there is a significant increase in the parallel surface tension and a significant decrease in the transverse one with respect to the unmagnetized case.

Strange quark chiral phase transition in hot2+1-flavor magnetized quark matter

Using the Polyakov--Nambu--Jona-Lasinio model the strange quark chiral phase transition and the effect of its current mass on a hot magnetized three flavor quark matter at zero chemical potential is investigated. The impact of the 't Hooft mixing term on the restoration of the chiral symmetry on the light and strange sectors is studied and the critical temperature dependence on the magnetic field strength of the chiral strange transition is analyzed. It is shown that the s quark is much less sensitive to the magnetic field than the light quarks. Due to the 't Hooft term, it has a strong influence on the light quarks at all temperatures for small magnetic fields and for temperatures close to the transition temperature at zero magnetic field and above for strong magnetic fields. In particular, the large mass of the s quark makes the chiral transition of the light sector smoother and shifted to larger temperatures. A scalar coupling that weakens when the magnetic field increases will originate an inverse magnetic catalysis also in the s quark and smoothen the signature of the crossover on thermodynamical quantities such as the sound velocities or the specific heat.

Surface tension of magnetized quark matter

The surface tension of quark matter plays a crucial role for the possibility of quark matter nucleation during the formation of compact stellar objects and also for the existence of a mixed phase within hybrid stars. However, despite its importance, this quantity does not have a well established numerical value. Some early estimates have predicted that, at zero temperature, the value falls within the wide range $\gamma_0\approx10-300{\rm\ MeV/fm^2}$ but, very recently, different model applications have reduced these numerical values to fall within the range $\gamma_0\approx5-30{\rm\ MeV/fm^2}$ which would favor the phase conversion process as well as the appearance of a mixed phase in hybrid stars. In magnetars one should also account for the presence of very high magnetic fields which may reach up to about $ eB\approx 3-30\, m_\pi^2$ ($B \approx 10^{19}-10^{20} \,G$) at the core of the star so that it may also be important to analyze how the presence of a magnetic field affects the surface tension. With this aim we consider magnetized two flavor quark matter, described by the Nambu--Jona-Lasinio model. We show that although the surface tension oscillates around its B=0 value, when $0 < eB \lesssim 10 \, m_\pi^2$, it only reaches values which are still relatively small. For $eB \approx 5\, m_\pi^2$ the B=0 surface tension value drops by about 30% while for $eB \gtrsim 10\, m_\pi^2$ it quickly raises with the field intensity so that the phase conversion and the presence of a mixed phase should be suppressed if extremely high fields are present. We also investigate how thermal effects influence the surface tension for magnetized quark matter.

Chiral transition within effective quark models under magnetic fields

We consider the simplest versions of the Nambu--Jona-Lasinio (NJL) model and the Linear Sigma Model (LSM), in the Mean Field Approximation (MFA), in order to analyze hot and dense two flavor quark matter subject to strong magnetic fields. We pay especial attention to the case of a finite chemical potential, which has not yet been fully explored. Our results, for the NJL model, are in qualitative agreement with other recent applications showing that, for stronger fields, the first order segment of the transition line increases with the magnetic strength while the coexistence chemical potential value, at low temperatures, decreases. In the present work, one of the most important results is related to the analysis of how these features affect the phase coexistence region in the $T-\rho_B$ plane. We find that the coexistence boundary oscillates around the B=0 value for magnetic fields of the order $eB \lesssim 9.5\, m_\pi^2$ which can be understood by investigating the filling of Landau levels at vanishing temperature. So far, most investigations have been concerned with the effects of the magnetic field over the $T-\mu$ plane only while other thermodynamical quantities such as the adiabats, the quark number susceptibility, the interaction measure and the latent heat have been neglected. Here, we take a step towards filling this gap by investigating the influence of a magnetic field over these quantities. Finally, we argue that a naive application of the MFA does not seem to be appropriate to treat the LSM in the presence of magnetic fields.

Rigid Crystalline Color Superconducting Quark Matter

Cold three flavor quark matter at large (but not asymptotically large) densities may exist in a crystalline color superconducting phase. These phases are characterized by a gap parameter Δ that varies periodically in space, forming a crystal structure. A Ginzburg-Landau expansion in Δ shows that two crystal structures based on cubic symetry are particularly favorable, and may be the ground state of matter at densities present in neutron star cores. By deriving the effective action for the phonon fields that describe spaceand time-dependent fluctuations of the crystal structure formed by Δ, one can obtain its shear modulus. Within a Ginzburg-Landau approximation, we find shear moduli which are 20 to 1000 times larger than those of neutron star crusts. This phase of matter is thus more rigid than any known material in the universe, but at the same time the crystalline color superconducting phase is also superfluid. These properties raise the possibility that the presence of this phase within neutron stars may have distinct implications for their phenomenology. For example, (some) pulsar glitches may originate in crystalline superconducting neutron star cores.

Spin-one color superconductivity in compact stars?—an analysis within NJL-type models

We present results of a microscopic calculation using NJL-type model of possible spin-one pairings in two flavor quark matter for applications in compact star phenomenology. We focus on the color-spin locking phase (CSL) in which all quarks pair in a symmetric way, in which color and spin rotations are locked. The CSL condensate is particularly interesting for compact star applications since it is flavor symmetric and could easily satisfy charge neutrality. Moreover, the fact that in this phase all quarks are gapped might help to suppress the direct Urca process, consistent with cooling models. The order of magnitude of these small gaps (≃1 MeV) will not influence the EoS, but their also small critical temperatures (Tc≃800 keV) could be relevant in the late stages neutron star evolution, when the temperature falls below this value and a CSL quark core could form.

Meson Supercurrent State in High-Density QCD

The ground state of three flavor quark matter at asymptotically large density is believed to be the color-flavor-locked (CFL) phase. At nonasymptotic density the effect of the nonzero strange quark mass cannot be neglected. If the strange quark mass exceeds m(s) approximately m(u)(1/3)delta(2/3), the CFL state becomes unstable toward the formation of a neutral kaon condensate. Recently, several authors discovered that for m(s) approximately (2deltap(F))(1/2) the CFL state contains gapless fermions, and that the gapless modes lead to an instability in current-current correlation functions. Using an effective theory of the CFL state, we demonstrate that this instability can be resolved by the formation of a meson supercurrent, analogous to Migdal's p-wave pion condensate. This state has a nonzero meson current that is canceled by a backflow of gapless fermions.

Phase structure of two-flavor quark matter: Heterogeneous superconductors

We analyze the free energy of charge and color neutral 2-flavor quark matter within the BCS approximation. We consider both the homogeneous gapless superconducting phase and the heterogeneous mixed phase where normal and BCS superconducting phases coexist. We calculate the surface tension between normal and superconducting phases and use it to compare the free energies of the gapless and mixed phases. Our calculation, which retains only the leading order gradient contribution to the free energy, indicates that the mixed phase is energetically favored over an interesting range of densities of relevance to 2 flavor quark matter in neutron stars.

Single-flavor color superconductivity with color-sextet pairing

We analyze the color superconductivity of one massive flavor quark matter at moderate baryon density. First, we briefly review the framework of color superconductivity. Then, we suggest a mechanism which, within QCD, can lead to formation of a spin-zero color-sextet condensate. The most general form of the order parameter implies a complete breakdown of the SU (3) × U (1) symmetry. However, the conventional fermionic NJL-type description in the mean-field approximation seems to favor an enhanced O(3) symmetry of the ground state. This is ascribed to the use of the mean-field approximation and possible solutions are suggested.

Color superconductor with a color-sextet condensate

We analyze color superconductivity of one massive flavor quark matter at moderate baryon density with a spin-zero color-sextet condensate. The most general form of the order parameter implies complete breakdown of the SU(3)× U(1) symmetry. However, both the conventional fourth-order polynomial effective bosonic description and the fermionic NJL-type model in the mean-field approximation favor an enhanced O(3) symmetry of the ground state. We suggest two mechanisms how the complete symmetry breakdown could be achieved.

Color superconductor with a color-sextet condensate

We analyze color superconductivity of one massive flavor quark matter at moderate baryon density with a spin-zero color-sextet condensate. The most general Higgs-type ground-state expectation value of the order parameter implies complete breakdown of the SU(3)xU(1) symmetry. However, both the conventional fourth-order polynomial effective bosonic description, and the NJL-type fermionic description in the mean-field approximation favor an enhanced SO(3) symmetry of the ground state. We ascribe this finding to the failure of the mean-field approximation and propose that a more sophisticated technique is needed.

Coexistence of pion condensation and color superconductivity in two flavor quark matter

We show that the superconducting 2SC phase at high density and normal chiraly broken quark phase at low density is separated by the mixed non-uniform phase along the baryon density line.

Spatial structure of quark Cooper pairs in a color superconductor

Spatial structure of Cooper pairs with quantum numbers color 3^*, I=J=L=S=0 in ud 2 flavor quark matter is studied by solving the gap equation and calculating the coherence length in full momentum range without the weak coupling approximation. Although the gap at the Fermi surface and the coherence length depend on density weakly, the shape of the r-space pair wave function varies strongly with density. This result indicates that quark Cooper pairs become more bosonic at higher densities.

Quark core stars, quark stars and strange stars

A recent one flavor (zero temperature) quark matter equation of state is generalized to several flavors. It is shown that quarks undergo a first order phase transition. In addition, this equation of state depends on few parameters, one in the two flavor case, two in the three flavor case, and these parameters can be constrained by phenomenology. This equation of state is then applied to 1) the hadronquark transition in neutron stars and the determination of quark star stability, 2) the investigation of strange matter stability and possible strange star existence.