Dense Quark Matter Research Articles

Effective repulsion in dense quark matter from nonperturbative gluon exchange

A moderately strong vector repulsion between quarks in dense quark matter is needed to explain how a quark core can support neutron stars heavier than two solar masses. We study this repulsion, parametrized by a four-fermion interaction with coupling g_V, in terms of non-perturbative gluon exchange in QCD in the Landau gauge. Matching the energy of quark matter, g_V n_q^2 (where n_q is the number density of quarks) with the quark exchange energy calculated in QCD with a gluon propagator parametrized by a finite gluon mass m_g and a frozen coupling alpha_s, at moderate quark densities, we find that gluon masses m_g in the range 200 - 600 MeV and alpha_s = 2 - 4 lead to a g_V consistent with neutron star phenomenology. Estimating the effects of quark masses and a color-flavor-locked (CFL) pairing gap, we find that g_V can be well approximated by a flavor-symmetric, decreasing function of density. We briefly discuss similar matchings for the isovector repulsion and for the pairing attraction.

Anyonic particle-vortex statistics and the nature of dense quark matter

We show that $\mathbb{Z}_3$-valued particle-vortex braiding phases are present in high density quark matter. Certain mesonic and baryonic excitations, in the presence of a superfluid vortex, have orbital angular momentum quantized in units of $\hbar/3$. Such non-local topological features can distinguish phases whose realizations of global symmetries, as probed by local order parameters, are identical. If $\mathbb{Z}_3$ braiding phases and angular momentum fractionalization are absent in lower density hadronic matter, as is widely expected, then the quark matter and hadronic matter regimes of dense QCD must be separated by at least one phase transition.

Charged pion condensation and duality in dense and hot chirally and isospin asymmetric quark matter in the framework of the NJL2 model

In this paper we investigate in the large-$N_c$ limit ($N_c$ is the number of colored quarks) the phase structure of a massless (1+1)-dimensional quark model with four-quark interaction and in the presence of baryon ($\mu_B$), isospin ($\mu_I$) and chiral isospin ($\mu_{I5}$) chemical potentials as well as at nonzero temperature. It is established that chiral isospin chemical potential leads to the generation of charged pion condensation (PC) in dense (nonzero baryon density) and chiral asymmetric quark matter for a wide range of isospin densities. It is shown that there exists a duality correspondence between the chiral symmetry breaking and the charged PC phenomena at any values of temperature even for very hot quark gluon plasma. Moreover, it is shown that charged PC phase with nonzero baryon density can be induced in the model at comparatively high temperatures. This opens up new possible physical systems, where it can be of importance, such as heavy ion collisions, just born neutron stars (proto-neutron stars), supernovas as well as neutron star mergers.

Phase transitions of cold and dense quark matter in an external magnetic field

In this work we study the effects of an external magnetic field in the competition of chiral and diquark order parameters in cold and dense quark matter, using a SU(2) version of the NJL model. We verify the influence of the magnetic field in the phase diagram, and perform a comparison of the results obtained using a Fermi-Dirac form factor regularization with ones obtained by using a method that makes a full separation of the finite magnetic contributions and the divergencies, the Magnetic Field Independent Regularization.

Anomaly-Induced Inhomogeneous Phase in Quark Matter without the Sign Problem

We demonstrate the existence of an anomaly-induced inhomogeneous phase in a class of vectorlike gauge theories without the sign problem, thus disproving the long-standing conjecture that the absence of the sign problem precludes spontaneous breaking of translational invariance. The presence of the phase in the two-color modification of quantum chromodynamics can be tested by an independent nonperturbative evaluation of the neutral pion decay constant as a function of an external magnetic field. Our results provide a benchmark for future lattice studies of inhomogeneous phases in dense quark matter.

Charged Pion Condensation in Dense Quark Matter: Nambu–Jona-Lasinio Model Study

In this short review we tried to give an outline of investigations of charged pion condensation (PC) in dense baryonic (quark) matter in the framework of effective Nambu–Jona-Lasinio (NJL)-type models. The possibility of charged PC phase in dense quark matter with isospin asymmetry is investigated. First, it is demonstrated that this phase can be realized in the framework of massless NJL model. However, the existence of this phase is enormously fragile to the values of current quark mass and we show that charged PC phase is forbidden in electrically neutral dense quark matter with β -equilibrium when current quark masses are close to their physical value of 5.5 MeV. Nevertheless, then it is shown that in real physical systems there could be conditions promoting the appearance of charged PC phenomenon in dense quark matter; specifically, it was shown that if one takes into consideration the fact that system can have finite size, then a dense charged PC phase can be realized there. It was also demonstrated that the possibility of inhomogeneous pion condensate might allow this phase to appear. In addition, more recently it was revealed that there is another interesting factor that can induce a charged PC phase in dense quark matter even without isospin imbalance. It is a chiral imbalance of the system (non-zero difference between densities of left- and right-handed quarks). These results can be interesting in heavy ion collision experiments, where it is expected to get high baryon densities. It is of interest also in the context of neutron stars, where quark matter might be realized in the core and very high baryon and isospin densities are attained.

Dualities and inhomogeneous phases in dense quark matter with chiral and isospin imbalances in the framework of effective model

It has been shown in [15, 70] in the framework of Nambu-Jona-Lasinio model with the assumption of spatially homogeneous condensates that in the large-Nc limit (Nc is the number of quark colours) there exist three dual symmetries of the thermodynamic potential, which describes dense quark matter with chiral and isospin imbalances. The main duality is between the chiral symmetry breaking and the charged pion condensation phenomena. There have been a lot of studies and hints that the ground state could be characterized by spatially inhomogeneous condensates, so the question arises if duality is a rather deep property of the phase structure or just accidental property in the homogeneous case. In this paper we have shown that even if the phase diagram contains phases with spatially inhomogeneous condensates, it still possesses the property of this main duality. Two other dual symmetries are not realized in the theory if it is investigated within an inhomogeneous approach to a ground state. Based on various previously studied aspects of the QCD phase diagram of dense isospin asymmetric matter with possible inhomogeneous condensates, in the present paper a unified picture and full phase diagram of dense quark matter with isospin imbalance have been assembled. Acting on this diagram by a dual transformation, we obtained, in the framework of an approach with spatially inhomogeneous condensates and without any calculations, a full phase diagram of chirally asymmetric dense medium. This example shows that the duality is not just entertaining mathematical property but an instrument with very high predictivity power. The obtained phase diagram is quite rich and contains various spatially inhomogeneous phases.

Lattice study of static quark-antiquark interactions in dense quark matter

In this paper we study the interactions among a static quark-antiquark pair in the presence of dense two-color quark matter with lattice simulation. To this end we compute Polyakov line correlation functions and determine the renormalized color averaged, color singlet and color triplet grand potentials. The color singlet grand potential allows us to elucidate the number of quarks induced by a static quark antiquark source, as well as the internal energy of such a pair in dense quark matter. We furthermore determine the screening length, which in the confinement phase is synonymous with the string breaking distance. The screening length is a decreasing function of baryon density, due to the possibility to break the interquark string via a scalar diquark condensate at high density. We also study the large distance properties of the color singlet grand potential i a dense medium and find that it is well described by a simple Debye screening formula, parameterized by a Debye mass and an effective coupling constant. The latter is of order of unity, i.e. even at large density two-color quark matter is a strongly correlated system.

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.

Chiral symmetry breaking, color superconductivity, and equation of state for magnetized strange quark matter

We investigate the vacuum structure of dense quark matter in strong magnetic fields at finite temperature and densities in a 3 flavor Nambu Jona Lasinio (NJL) model including the Kobayashi-Maskawa-t'Hooft (KMT) determinant term using a variational method. The method uses an explicit structure for the `ground' state in terms of quark-antiquark condensates as well as diquark condensates. The mass gap equations and the superconducting gap equations are solved self consistently and are used to compute the thermodynamic potential along with the charge neutrality conditions. We also derive the equation of state for the charge neutral strange quark matter in the presence of strong magnetic fields which could be relevant for neutron stars.

Towards a holographic quark-hadron continuity

We study dense nuclear and quark matter within a single microscopic approach, namely the holographic Sakai-Sugimoto model. Nuclear matter is described via instantons in the bulk, and we show that instanton interactions are crucial for a continuous connection of chirally broken and chirally symmetric phases. The continuous path from nuclear to quark matter includes metastable and unstable stationary points of the potential, while the actual chiral phase transition remains of first order, as in earlier approximations. We show that the model parameters can be chosen to reproduce low-density properties of nuclear matter and observe a non-monotonic behavior of the speed of sound as a function of the baryon chemical potential, as suggested by constraints from QCD and astrophysics.

Probing the QCD phase structure with higher order baryon number susceptibilities within the NJL model * * Supported in part by the National Natural Science Foundation of China (11475085, 11535005, 11690030, 11575069, 11221504), and the MoST of China 973-Project ( 2015CB856901)

Conserved charge fluctuations can be used to probe the phase structure of strongly interacting nuclear matter in relativistic heavy-ion collisions. To obtain the characteristic signatures of the conserved charge fluctuations for the quantum chromodynamics (QCD) phase transition, we study the susceptibilities of dense quark matter up to eighth order in detail, using an effective QCD-based model. We studied two cases, one with the QCD critical end point (CEP) and one without owing to an additional vector interaction term. The higher order susceptibilities display rich structures near the CEP and show sign changes as well as large fluctuations. These can provide us information about the presence and location of the CEP. Furthermore, we find that the case without the CEP also shows a similar sign change pattern, but with a relatively smaller magnitude compared with the case with the CEP. Finally, we conclude that higher order susceptibilities of conserved charge can be used to probe the QCD phase structures in heavy-ion collisions.

Chiral imbalanced hot and dense quark matter: NJL analysis at the physical point and comparison with lattice QCD

Hot and dense quark matter with isospin and chiral imbalances is investigated in the framework of the (3+1)-dimensional Nambu–Jona-Lasinio model (NJL) in the large-N_c limit (N_c is the number of quark colors). Its phase structure is considered in terms of barion – mu _B, isospin – mu _I and chiral isospin – mu _{I5} chemical potentials. It is shown in the paper that (i) in the chiral limit there is a duality between chiral symmetry breaking (CSB) and charged pion condensation (PC) phenomena. (ii) At the physical point, i.e. at nonzero bare quark mass m_0, and temperature this duality relation is only approximate, although rather accurate. (iii) We have shown that the chiral isospin chemical potential mu _{I5} in dense quark matter generates charged pion condensation both at zero and nonzero m_0, and at mu _{I5}ne 0 this phase might be observed up to temperatures as high as 100 MeV. (iv) Pseudo-critical temperature of the chiral crossover transition rises in the NJL model with increasing mu _{I5}. (v) It has been found an agreement between particular sections of the phase diagram in the framework of NJL model and corresponding ones in lattice QCD simulations. Two different plots from different lattice simulations that are completely independent and are not connected at the first sight are in reality dual to each other, it means that lattice QCD simulations support the hypothesis that in real quark matter there exists the (approximate) duality between CSB and charged PC. Moreover, we can reverse the logic and we can predict the increase of pseudo-critical temperature with chiral chemical potential, the much debated effect recently, just by the duality notion, hence bolster confidence in this result (lattice QCD showed this feature for unphysically large pion mass) and put it on the considerably more solid ground.

Electric conductivity of hot and dense quark matter in a magnetic field with Landau level resummation via kinetic equations

I address microscopic calculations for the electric conductivity in quark matter under a magnetic field at finite temperature and chemical potentials. The problem of the lowest Landau level approximation is that the electric conductivity unphysically diverges due to phase space restriction. With several Landau levels taken into account, the electric conductivity quickly converges to reach qualitative agreement with observed behavior in condensed matter experiment.

Neutron stars and stellar mergers as a laboratory for dense QCD matter

Neutron star observations, including direct mass and radius measurements as well as the analysis of gravitational wave signals emitted by stellar mergers, provide valuable and unique insights into the properties of strongly interacting matter at high densities. In this proceedings contribution, I review recent efforts to systematically constrain the equation of state (EoS) of dense nuclear and quark matter using a combination of ab initio particle and nuclear physics calculations and astrophysical data. In particular, I discuss the constraints that the gravitational wave observation GW170817 has placed on the EoS, and comment on the future prospects of improving the accuracy, to which this quantity is known.

Regularization issues for a cold and dense quark matter model in β equilibrium

A regularization scheme that explicitly separates vacuum contributions from medium effects is applied to a Nambu--Jona-Lasinio model with diquark interactions and in $\beta-$equilibrium. We perform a comparison of this proposed scheme with the more traditional one, where no separation of vacuum and medium effects is done. Our results point to both qualitative and quantitative important differences between these two methods, in special regarding the phase structure of the model in the cold and dense nuclear matter case.

Possible ferromagnetism of dense quark matter

The cardinal focus of the present review is to investigate the possibility of the para-ferro phase transition of dense quark matter. For these, the calculation of the single-particle energies, ground state energy (GSE) densities, and spin susceptibility χ of degenerate quark matter with one gluon exchange interaction in terms of spin-dependent Landau parameters (LPs) have been presented. The expressions for the GSE and χ of cold and dense spin-polarized quark matter have been derived with corrections due to correlation. Furthermore, the magnetic properties of spin polarized quark matter have been discussed by evaluating the magnetization ⟨M⟩ and magnetic susceptibility χM in terms of LPs. Finally, the possibility of magnetic instability has been revealed by studying the density dependence of ⟨M⟩ and χM.

Dualities in dense quark matter with isospin, chiral, and chiral isospin imbalance in the framework of the large- Nc limit of the NJL4 model

In this paper, we investigate the phase structure of the dense quark matter in the presence of baryon ${\ensuremath{\mu}}_{B}$, isospin ${\ensuremath{\mu}}_{I}$, chiral ${\ensuremath{\mu}}_{5}$, and chiral isospin ${\ensuremath{\mu}}_{I5}$ chemical potentials in the framework of the Nambu--Jona-Lasinio model. We show that, in the large-${N}_{c}$ limit (${N}_{c}$ is the number of quark colors), there exist three duality correspondences in the model. The first duality is between the chiral symmetry breaking and the charged-pion condensation phenomena, and there are two new dualities that hold only for chiral symmetry breaking and charged-pion condensation phenomena separately. These dualities show that chiral symmetry breaking phenomenon does not feel the difference between chiral ${\ensuremath{\mu}}_{5}$ and chiral isospin ${\ensuremath{\mu}}_{I5}$ chemical potentials, and charged-pion condensation phenomenon does not feel the difference between isospin ${\ensuremath{\mu}}_{I}$ and chiral ${\ensuremath{\mu}}_{5}$ chemical potentials. We show that ${\ensuremath{\mu}}_{5}$ can generate charged-pion condensation, but this generation occurs at not so large baryon densities. In the case of both chiral imbalances (chiral ${\ensuremath{\mu}}_{5}$ and chiral isospin ${\ensuremath{\mu}}_{I5}$ chemical potentials), the phase portrait is rather rich, and we show that charged-pion condensation in dense quark matter takes up a large part of the phase diagram. Charged-pion condensation in dense quark matter happens even in the case of zero isospin imbalance and requires only chiral imbalances; this fact can be demonstrated with the use of one of the new dualities and this is only one example of when these dualities are of great use in exploring the phase diagram.

New color-magnetic defects in dense quark matter

Color-flavor locked (CFL) quark matter expels color-magnetic fields due to the Meissner effect. One of these fields carries an admixture of the ordinary abelian magnetic field and therefore flux tubes may form if CFL matter is exposed to a magnetic field, possibly in the interior of neutron stars or in quark stars. We employ a Ginzburg–Landau approach for three massless quark flavors, which takes into account the multi-component nature of color superconductivity. Based on the weak-coupling expressions for the Ginzburg–Landau parameters, we identify the regime where CFL is a type-II color superconductor and compute the radial profiles of different color-magnetic flux tubes. Among the configurations without baryon circulation we find a new solution that is energetically preferred over the flux tubes previously discussed in the literature in the parameter regime relevant for compact stars. Within the same setup, we also find a new defect in the 2SC phase, namely magnetic domain walls, which emerge naturally from the previously studied flux tubes if a more general ansatz for the order parameter is used. Color-magnetic defects in the interior of compact stars allow for sustained deformations of the star, potentially strong enough to produce detectable gravitational waves.

Electric Conductivity of Hot and Dense Quark Matter in a Magnetic Field with Landau Level Resummation via Kinetic Equations.

We compute the electric conductivity of quark matter at finite temperature T and a quark chemical potential μ under a magnetic field B beyond the lowest Landau level approximation. The electric conductivity transverse to B is dominated by the Hall conductivity σ_{H}. For the longitudinal conductivity σ_{∥}, we need to solve kinetic equations. Then, we numerically find that σ_{∥} has only a mild dependence on μ and the quark mass m_{q}. Moreover, σ_{∥} first decreases and then linearly increases as a function of B, leading to an intermediate B region that looks consistent with the experimental signature for the chiral magnetic effect. We also point out that σ_{∥} at a nonzero B remains within the range of the lattice-QCD estimate at B=0.