Normal Quark Matter Research Articles

Quark matter supported wormhole in third order Lovelock gravity

It is generally believed that wormholes are supported by exotic matter violating Null Energy Condition (NEC). However, various studies of wormhole geometries under Lovelock theories of gravity have reported existence of wormhole supported by matter satisfying NEC. Being inspired by these results, we explore the possibility of the existence of wormhole supported by normal quark matter in third order Lovelock gravity theory. Well known MIT Bag Model Equation of state is chosen for describing the quark matter. Taking physically acceptable approximations, we solve the field equations for shape function which satisfies flare out condition. The residual of the approximate solution is studied for accuracy and found to be acceptable.

A new class of hybrid EoS with multiple critical endpoints for simulations of supernovae, neutron stars and their mergers

We introduce a family of equations of state (EoS) for hybrid neutron star (NS) matter that is obtained by a two-zone parabolic interpolation between a soft hadronic EoS at low densities and a stiff quark matter EoS with color superconductivity at high densities within a finite region of baryonic chemical potentials mu _B^h< mu _B < mu _B^q. We consider two scenarios corresponding to a cross-over and a strong first-order transition between quark and hadron phases considered at finite and zero temperatures. This allows us to analyze the effects of finite entropy on the EoS and mass-radius relation of NS. We demonstrate that the formation of a color superconducting state of quark matter drives the evolution of matter in supernovae explosions under the condition of entropy conservation to higher temperatures than in the case of deconfinement to normal quark matter. Within the presented hybrid EoS scenario, regions of the QCD phase diagram may be accessible to supernovae and NS mergers that can be reached also in terrestrial experiments with relativistic heavy ion collisions.

Chiral phase transitions of helical matter

We study the thermodynamics of helical matter, namely quark matter in which a net helicity, $n_H$, is in equilibrium. Interactions are modeled by the renormalized quark-meson model with two flavors of quarks. Helical density is described within the grand-canonical ensemble formalism via a chemical potential, $\mu_H$. We study the transitions from the normal quark matter and hadron gas to the helical matter, drawing the phase diagram at zero temperature. We study the restoration of chiral symmetry at finite temperature and show that the net helical density softens the transition, moving the critical endpoint to lower temperature and higher baryon chemical potential. Finally, we discuss briefly the effect of a rigid rotation on the helical matter, in particular on the fluctuations of $n_H$, and show that these are enhanced by the rotation.

Ginzburg–Landau Free Energy of Crystalline Color Superconductors: A Matrix Formalism from Solid-State Physics**Supported by the National Natural Science Foundation of China under Grant No. 11335005 and the Ministry of Science and Technology under Grant Nos. 2013CB922000 and 2014CB845400, and by the US Department of Energy Topical Collaboration “Neutrinos and Nucleosynthesis in Hot and Dense Matter”

The Ginzburg–Landau (GL) free energy of crystalline color superconductors is important for understanding the nature of the phase transition to the normal quark matter and predicting the preferred crystal structure. So far the GL free energy at zero temperature has only been evaluated up to the sixth order in the condensate. To give quantitative reliable predictions we need to evaluate the higher-order terms. In this work, we present a new derivation of the GL free energy by using the discrete Bloch representation of the fermion field. This derivation introduces a simple matrix formalism without any momentum constraint, which may enable us to calculate the GL free energy to arbitrary order by using a computer.

Wormhole geometries supported by quark matter at ultra-high densities

A fundamental ingredient in wormhole physics is the presence of exotic matter, which involves the violation of the null energy condition (NEC). In this context, we investigate the possibility that wormholes could be supported by quark matter at extreme densities. Theoretical and experimental investigations of the structure of baryons show that strange quark matter, consisting of the u, d and s quarks, is the most energetically favorable state of baryonic matter. Moreover, at ultra-high densities, quark matter may exist in a variety of superconducting states, namely, the Color–Flavor-Locked (CFL) phase. Motivated by these theoretical models, we explore the conditions under which wormhole geometries may be supported by the equations of state (EOS) considered in the theoretical investigations of quark–gluon interactions. For the description of the normal quark matter, we adopt the Massachusetts Institute of Technology (MIT) bag model EOS, while the color superconducting quark phases are described by a first-order approximation of the free energy. By assuming specific forms for the bag and gap functions, several wormhole models are obtained for both normal and superconducting quark matter. The effects of the presence of an electrical charge are also taken into account.

QUARK MATTER SYMMETRY ENERGY AND QUARK STARS

We extend the confined-density-dependent-mass (CDDM) model to include isospin dependence of the equivalent quark mass. Within the confined-isospin-density-dependent-mass (CIDDM) model, we study the quark matter symmetry energy, the stability of strange quark matter, and the properties of quark stars. We find that including isospin dependence of the equivalent quark mass can significantly influence the quark matter symmetry energy as well as the properties of strange quark matter and quark stars. While the recently discovered large mass pulsars PSR J1614-2230 and PSR J0348+0432 with masses around $2M_{\odot}$ cannot be quark stars within the CDDM model, they can be well described by quark stars in the CIDDM model. In particular, our results indicate that the two-flavor $u$-$d$ quark matter symmetry energy should be at least about twice that of a free quark gas or normal quark matter within conventional Nambu-Jona-Lasinio model in order to describe the PSR J1614-2230 and PSR J0348+0432 as quark stars.

Evaluating the phase diagram at finite isospin and baryon chemical potentials in the Nambu–Jona-Lasinio model

We study the phase diagram of two-flavor dense QCD at finite isospin and baryon chemical potentials in the framework of the Nambu--Jona-Lasinio model. We focus on the case with arbitrary isospin chemical potential ${\ensuremath{\mu}}_{\mathrm{I}}$ and small baryon chemical potential ${\ensuremath{\mu}}_{\mathrm{B}}\ensuremath{\le}{\ensuremath{\mu}}_{\mathrm{B}}^{\ensuremath{\chi}}$ where ${\ensuremath{\mu}}_{\mathrm{B}}^{\ensuremath{\chi}}$ is the critical chemical potential for the first-order chiral phase transition to happen at ${\ensuremath{\mu}}_{\mathrm{I}}=0$. The ${\ensuremath{\mu}}_{\mathrm{I}}\ensuremath{-}{\ensuremath{\mu}}_{\mathrm{B}}$ phase diagram shows a rich phase structure since the system undergoes a crossover from a Bose-Einstein condensate of charged pions to a BCS superfluid with condensed quark-antiquark Cooper pairs when ${\ensuremath{\mu}}_{\mathrm{I}}$ increases at ${\ensuremath{\mu}}_{\mathrm{B}}=0$, and a nonzero baryon chemical potential serves as a mismatch between the pairing species. We observe a gapless pion condensation phase near the quadruple point $({\ensuremath{\mu}}_{\mathrm{I}},{\ensuremath{\mu}}_{\mathrm{B}})=({m}_{\ensuremath{\pi}},{M}_{\mathrm{N}}\ensuremath{-}1.5{m}_{\ensuremath{\pi}})$ where ${m}_{\ensuremath{\pi}}$, ${M}_{\mathrm{N}}$ are the vacuum masses of pions and nucleons, respectively. The first-order chiral phase transition becomes a smooth crossover when ${\ensuremath{\mu}}_{\mathrm{I}}&gt;0.82{m}_{\ensuremath{\pi}}$. At very large isospin chemical potential, ${\ensuremath{\mu}}_{\mathrm{I}}&gt;6.36{m}_{\ensuremath{\pi}}$, an inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell superfluid phase, appears in a window of ${\ensuremath{\mu}}_{\mathrm{B}}$, which should in principle exist for arbitrary large ${\ensuremath{\mu}}_{\mathrm{I}}$. Between the gapless and the Larkin-Ovchinnikov-Fulde-Ferrell phases, the pion superfluid phase and the normal quark matter phase are connected by a first-order phase transition. In the normal phase above the superfluid domain, we find that charged pions are still bound states even though ${\ensuremath{\mu}}_{\mathrm{I}}$ becomes very large, which is quite different from that at finite temperature. Our phase diagram is in good agreement with that found in imbalanced cold atom systems.

Hadron-quark phase transition at nonzero isospin density: The effect of quark pairing

We compute the mixed phase of nuclear matter and 2SC matter for different temperatures and proton fractions. After showing that the symmetry energy of the 2SC phase is, to a good approximation, three times larger than the one of the normal quark phase, we discuss and compare all the properties of the mixed phase with a 2SC component or a normal quark matter component. In particular, the local isospin densities of the nuclear and the quark component and the stiffness of the mixed phase are significantly different whether the 2SC phase or the normal quark phase are considered. If a strong diquark pairing is adopted for the 2SC phase, there is a possibility to eventually enter in the nuclear matter 2SC matter mixed phase in low energy heavy ions collisions experiments. Possible observables able to discern between the formation of the 2SC phase or the normal quark phase are finally discussed.

Gauge dynamics in the PNJL model: Color neutrality and Casimir scaling

We discuss a gauge-invariant prescription to take the mean-field approximation self-consistently in the PNJL model (Nambu–Jona-Lasinio model with the Polyakov loop). We first address the problem of non-vanishing color density in normal quark matter, which is an artifact arising from gauge-fixed treatment of the Polyakov loop mean-fields. We then confirm that the gauge average incorporated in our prescription resolves this problem and ensures color neutrality. We point out that the proposed method has an advantage in computing the expectation value of any function of the Polyakov loop matrix. We discuss the Casimir scaling as an immediate application of the method.

Thermal Evolution of Strange Stars

ABSTRACTWe have investigated the thermal evolution of rotating strange stars with the deconfinement heating due to magnetic braking. We consider stars consisting of either normal quark matter or a color-flavor-locked phase. Combining deconfinement heating with magnetic-field decay, we find that the thermal evolution curves are identical to those from pulsar data, solving the problem of scarce data for old strange stars.

Neutrino emission from direct Urca processes in pion condensed quark matter

We study neutrino emission from direct Urca processes in pion condensed quark matter. In compact stars with high baryon density, the emission is dominated by the gapless modes of the pion condensation which leads to an enhanced emissivity. While for massless quarks the enhancement is not remarkable, the emissivity is significantly larger and the cooling of the condensed matter is considerably faster than that in normal quark matter when the mass difference between u and d quarks is sizable.

Larkin-Ovchinnikov-Fulde-Ferrell state in two-color quark matter

We explore the phase structure of two-color and two-flavor QCD in the space of the quark chemical potential ${\ensuremath{\mu}}_{\mathrm{q}}$ and the isospin chemical potential ${\ensuremath{\mu}}_{\mathrm{I}}$. Using a mean-field model we calculate the chiral and diquark condensates, $\ensuremath{\sigma}$ and $\ensuremath{\Delta}$, self-consistently. In weak coupling and in the chiral limit, we confirm the interval of the isospin chemical potential, $0.71{\ensuremath{\Delta}}_{0}&lt;{\ensuremath{\mu}}_{\mathrm{I}}&lt;0.75{\ensuremath{\Delta}}_{0}$, in which a single plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase is favored over isotropic superfluidity and normal quark matter. The LOFF window becomes slightly wider at high density. For stronger coupling with nonzero quark mass, which is relevant to currently available numerical simulations in lattice two-color QCD, the single plane-wave LOFF phase appears only at sufficiently high density. The prediction obtained for the LOFF region could be tested with lattice since we can prove that the present system is free from the fermion sign problem. We draw the energy landscape on which local minima corresponding to the isotropic superfluid phase and the LOFF phase and a local maximum corresponding to the gapless phase are manifest. Our results clearly illustrate the path from the unstable gapless phase down to the LOFF phase.

Phase diagram of quark matter in nonlocal chiral models under color and electric charge neutrality conditions

We consider the phase diagram of two-flavor quark matter under neutron star constraints for the case of two nonlocal, covariant quark models within the mean field approximation. In one of these models (Model I) the nonlocality arises from the regularization procedure, motivated by the instanton liquid model, whereas in the second one (Model II) a separable approximation of the one-gluon exchange interaction is applied. We find that Model II predicts a larger quark mass gap, and the corresponding critical temperature at µ = 0, Tc(0) ~ 140 MeV, is in better agreement with recent lattice QCD results than the prediction of the standard local NJL model, which exceeds 200 MeV. For both models we have considered various coupling strengths in the scalar diquark channel, showing that different low-temperature quark matter phases can occur at intermediate densities: a normal quark matter (NQM) phase, a superconducting quark matter (2SC) phase and a mixed 2SC-NQM phase. In most cases, a narrow gapless 2SC phase region is also obtained at finite temperatures.

Electrical Neutrality and Symmetry Restoring Phase Transitions at High Densityin a Two-Flavor Nambu–Jona-Lasinio Model

A general research on chiral symmetry restoring phase transitionsat zero temperature and finite chemical potentials under electricalneutrality condition has been conducted in a Nambu–Jona-Lasiniomodel to describe two-flavor normal quark matter. Depending on whetherm0/Λ, the ratio of dynamical quark mass in vacuum and the 3Dmomentum cutoff in the loop integrals, is less or greater than 0.413,the phase transition will be of the second or first order.A complete phase diagram of u quark chemical potential versus m0is given. With the electrical neutrality constraint, the region wherethe second order phase transition happens will be wider than the onewithout electrical neutrality limitation. The results also show that,for the value of m0/Λ from QCD phenomenology,the phase transition must be of the first order.

Phase transition from hadronic matter to quark matter

We study the phase transition from two-flavor nuclear matter to quark matter. A mean field model, constructed at the quark level, is used to give the equation of state for nuclear matter, while the equation of state for color superconducting quark matter is calculated within the NJL model. It is found that at low temperature, the phase transition from nuclear to color superconducting quark matter will take place when the density is of order $2.5{\ensuremath{\rho}}_{0}\text{--}5{\ensuremath{\rho}}_{0}$. At zero density, the quark phase will appear when the temperature is larger than about 148 MeV. Within the mean field treatment, the phase transition from nuclear matter to quark matter is always first order, whereas the transition between color superconducting quark matter and normal quark matter is second order.

Neutral color-spin-locking phase in neutron stars

We present results for the spin-1 color-spin-locking (CSL) phase using a NJL-type model in two-flavor quark matter for compact stars applications. The CSL condensate is flavor symmetric and therefore charge and color neutrality can easily be satisfied. We find small energy gaps ⋍ 1 MeV, which make the CSL matter composition and the EoS not very different from the normal quark matter phase. We keep finite quark masses in our calculations and obtain no gapless modes that could have strong consequences in the late cooling of neutron stars. Finally, we show that the region of the phase diagram relevant for neutron star cores, when asymmetric flavor pairing is suppressed, could be covered by the CSL phase.

Fermionic Quasiparticles in QCD at High Baryon Density

We study fermionic quasi-particles in QCD at very high baryon density. In the normal quark matter phase unscreened magnetic gluon exchanges lead to non-Fermi liquid behavior. Non-Fermi liquid effects manifest themselves in low energy Green functions that depend on logarithms and fractional powers of energy. In the superfluid phase there is an energy gap for fermionic excitations. Quark mass effects can cause the energy gap to vanish. Gapless fermions in the color flavor locked phase cause an instability towards a state with a non-zero supercurrent.

Phase diagram of neutral quark matter in nonlocal chiral quark models

We consider the phase diagram of two-flavor quark matter under neutron star constraints for two nonlocal, covariant quark models within the mean-field approximation. In the first case (Model I) the nonlocality arises from the regularization procedure, motivated by the instanton liquid model, whereas in the second one (Model II) a separable approximation of the one-gluon exchange interaction is applied. We find that Model II predicts a larger quark mass gap and a chiral symmetry breaking (CSB) phase transition line which extends 15--20% further into the phase diagram spanned by temperature ($T$) and chemical potential ($\ensuremath{\mu}$). The corresponding critical temperature at $\ensuremath{\mu}=0$, ${T}_{c}(0)\ensuremath{\simeq}140\text{ }\text{ }\mathrm{MeV}$, is in better accordance to recent lattice QCD results than the prediction of the standard local NJL model, which exceeds 200 MeV. For both Model I and Model II we have considered various coupling strengths in the scalar diquark channel, showing that different low-temperature quark matter phases can occur at intermediate densities: a normal quark matter (NQM) phase, a two-flavor superconducting (2SC) quark matter phase and a mixed 2SC-NQM phase. Although in most cases there is also a gapless 2SC phase, this occurs in general in a small region at nonzero temperatures, thus its effect should be negligible for compact star applications.

γ-ray bursts and the QCD phase diagram

The quantum chromodynamics phase diagram shows the phase transitions that can take place in matter at different temperatures and densities. In this work we discuss the possibility that \ensuremath{\gamma}-ray bursts might result from a phase change in the interior of a neutron star and calculate the energy released in the conversion of a metastable star into a stable star. We consider several different initial and several different final configurations. Initial metastable stars are taken as hadronic, hybrid, and quark stars with unpaired quarks; possible stable stars are hybrid and quark stars, taken both with unpaired and paired phases to study the deconfinement phase transition and normal quark matter--superconducting quark matter phase transition within a large number of relativistic models used to describe compact stars. The models used for the hadron matter are the nonlinear Walecka model and the quark-meson coupling model with and without hyperons. For the quark matter we have used the MIT bag model, the bag model with paired quarks to which we refer as the color-flavor-locked phase model, and the Nambu--Jona-Lasinio model. Within this mechanism we obtain energies of the order of ${10}^{50}\ensuremath{-}{10}^{53}$ erg, accounting for both long and short \ensuremath{\gamma}-ray bursts.

COLOR SUPERCONDUCTIVITY AT MODERATE BARYON DENSITY

This article focuses on the two-flavor color superconducting phase at moderate baryon density. In order to simultaneously investigate the chiral phase transition and the color superconducting phase transition, the Nambu–Gorkov formalism is extended to treat the quark-antiquark and diquark condensates on an equal footing. The competition between the chiral condensate and the diquark condensate is analyzed. The cold dense charge neutral two-flavor quark system is investigated in detail. Under the local charge neutrality condition, the ground state of two-flavor quark matter is sensitive to the coupling strength in the diquark channel. When the diquark coupling strength is around the value obtained from the Fierz transformation or from fitting the vacuum bayron mass, the ground state of charge neutral two-flavor quark matter is in a thermal stable gapless 2SC (g2SC) phase. The unusual properties at zero as well as nonzero temperatures and the chromomagnetic properties of the g2SC phase are reviewed. Under the global charge neutrality condition, assuming the surface tension is negligible, the mixed phase composed of the regular 2SC phase and normal quark matter is more favorable than the g2SC phase. A hybrid nonstrange neutron star is constructed.