Chiral Restoration Research Articles

Light quarks at finite temperature: chiral restoration and the fate of the $$U(1)_A$$ symmetry

We review recent results on the role of light quark states within the QCD phase diagram. In particular, we will discuss how the combined use of theoretical techniques such as Effective Theories, Unitarization and Ward Identities helps to shed light on several important issues regarding chiral symmetry restoration, building bridges with recent lattice analyses. Special attention will be paid to the role of chiral and $U(1)_A$ partners in the interplay between those symmetries, which is crucial to properly understand the transition pattern. Light scalar mesons at finite temperature will be shown to be responsible for the description of susceptibilities encoding chiral and $U(1)_A$ restoration properties.

Cold magnetized quark matter at finite density in a nonlocal chiral quark model

We study the behavior of two-flavor dense quark matter under the influence of an external magnetic field in the framework of a nonlocal chiral quark model with separable interactions. The nonlocality is incorporated in the model by using a Gaussian form factor. It is found that for low and moderate values of magnetic field there is a decrease of the critical chiral restoration chemical potential $$\mu _c$$ , i.e. an inverse magnetic catalysis effect is observed. For larger values of eB the behavior of $$\mu _c$$ becomes more or less flat, depending on the parametrization. Within the considered parametrization range we do not find a significant growth of the critical chemical potential for large magnetic fields, as occurs in the case of the local NJL model.

Clear correlation between monopoles and the chiral condensate in SU(3) QCD

We study spontaneous chiral-symmetry breaking in SU(3) QCD in terms of the dual superconductor picture for quark confinement in the maximally Abelian (MA) gauge, using lattice QCD Monte Carlo simulations with four different lattices of $16^4$, $24^4$, $24^3\times 6$ at $\beta=6.0$ (i.e., the spacing $a \simeq$ 0.1 fm), and $32^4$ at $\beta=6.2$ (i.e., $a \simeq$ 0.075 fm), at the quenched level. First, in the confinement phase, we find Abelian dominance and monopole dominance in the MA gauge for the chiral condensate in the chiral limit,using the two different methods of i) the Banks-Casher relation with the Dirac eigenvalue density and ii) finite quark-mass calculations with the quark propagator and its chiral extrapolation. In the high-temperature deconfined phase, the chiral restoration is observed also for the Abelian and the monopole sectors. Second, we investigate local correlation between the chiral condensate and monopoles, which topologically appear in the MA gauge. We find that the chiral condensate locally takes a quite large value near monopoles. As an interesting possibility, the strong magnetic field around monopoles is responsible to chiral symmetry breaking in QCD, similarly to the magnetic catalysis.

Deconfining phase boundary of rapidly rotating hot and dense matter and analysis of moment of inertia

We discuss the effect of rapid rotation on the phase diagram of hadronic matter. The energy dispersion relation is shifted by an effective chemical potential induced by rotation. This suggests that rotation should lower the critical temperature of chiral restoration, but it is still controversial how the deconfinement temperature should change as a function of angular velocity. We adopt the hadron resonance gas model as an approach free from fitting parameters. We identify the deconfinement from the thermodynamic behavior and find that rotation decreases the deconfinement temperature. We also discuss the spatial inhomogeneity of the pressure and give a semi-quantitative estimate of the moment of inertia.

Dual meson condensates in the Polyakov-loop enhanced linear sigma model

The extent to which the dual meson condensates obtained in the Polyakov-loop enhanced linear sigma model can indicate deconfining transition is investigated by imposing the twisted boundary conditions. The influence of the improved unquenching effect, the dependence on the glue potential parametrization, and the role of the fermion vacuum contribution are focused on at the mean field level. At zero density, the rapid rise of the dual sigma condensate with $T$ is confirmed, which is more sensitive to the chiral transition than the increase of the Polyakov loop. For finite isospin chemical potential ${\ensuremath{\mu}}_{I}>{m}_{\ensuremath{\pi}}/2$, the dual sigma condensate shows abnormal thermal behavior which decreases with $T$ below the melting temperature ${T}_{c}^{{I}_{3}}$ of pion superfluidity. In contrast, the dual pion condensate always increases with $T$, with the maximum slope located at ${T}_{c}^{{I}_{3}}$ rather than ${T}_{c}^{P}$, as determined by the Polyakov loop. The dual vector meson condensate for ${\ensuremath{\mu}}_{I}>{m}_{\ensuremath{\pi}}/2$ is also more sensitive to the chiral restoration when considering the fermion vacuum contribution. The study suggests that the dual condensates calculated in this model are not appropriate indicators of deconfinement due to some limitations and uncertainty.

Holographic quark matter with color superconductivity and a stiff equation of state for compact stars

We present a holographic model of QCD with a first order chiral restoration phase transition with chemical potential, mu. The first order behaviour follows from allowing a discontinuity in the dual description as the quarks are integrated out below their constituent mass. The model predicts a deconfined yet massive quark phase at intermediate densities (350 MeV< mu <500 MeV), above the nuclear density phase, which has a very stiff equation of state and a speed of sound close to one. We also include a holographic description of a colour superconducting condensate in the chirally restored vacuum and study the resulting equation of state. They provides a well behaved first order transition from the deconfined massive quark phase at very high density (mu>500 MeV). We solve the Tolman-Oppenheimer-Volkoff equations with the resulting equations of state and find stable hybrid stars with quark cores. We compute the tidal deformability for these hybrid stars and show they are consistent with LIGO/Virgo data on a neutron star collision. Our holographic model shows that quark matter could be present at the core of such compact stars.

Strong-Interaction Matter under Extreme Conditions from Chiral Quark Models with Nonlocal Separable Interactions

We review the current status of the research on effective nonlocal NJL-like chiral quark models with separable interactions, focusing on the application of this approach to the description of the properties of hadronic and quark matter under extreme conditions. The analysis includes the predictions for various hadron properties in vacuum, as well as the study of the features of deconfinement and chiral restoration phase transitions for systems at finite temperature and/or density. We also address other related subjects, such as the study of phase transitions for imaginary chemical potentials, the possible existence of inhomogeneous phase regions, the presence of color superconductivity, the effects produced by strong external magnetic fields and the application to the description of compact stellar objects.

Non‐local chiral quark model at finite chemical potential in the presence of an intense magnetic field

AbstractWe study the behavior of two‐flavor dense quark matter under the influence of an external magnetic field B in the framework of an extended Nambu‐Jona‐Lasinio model with non‐local and separable interactions. This non‐locality is incorporated in the model by using a Gaussian form factor. We find that within this model there is a decrease of the critical chiral restoration chemical potential for a rather wide range of increasing magnetic fields.

Inverse catalysis effect of the quark anomalous magnetic moment to chiral restoration and deconfinement phase transitions

The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions under magnetic fields is investigated in a Pauli-Villars regularized Polyakov-extended Nambu--Jona-Lasinio model. A linear-in-$B$ term for quark anomalous magnetic moment is introduced to the Lagrangian density of our model, and it plays the role of inverse catalysis to the phase transitions. With fixed magnetic field, the critical temperature decreases with quark AMM. When fixing quark AMM, the critical temperature increases with magnetic field for a small quark AMM, but decreases with magnetic field for a large quark AMM. The critical temperature of chiral restoration and deconfinement phase transitions is determined by the two competing factors, the catalysis effect of magnetic field and inverse catalysis of quark anomalous magnetic moment.

Magnetized hot and dense quark matter in the Polyakov Nambu–Jona–Lasinio model

In a strong magnetic field, the hot dense quark matter is investigated in the Polyakov Nambu–Jona–Lasinio model. The value of a traced Polyakov loop is found as a nonmonotonous function of the chemical potential at lower magnetic fields and as a monotonous increasing function at high magnetic fields. The decreasing pseudocritical temperatures for the chiral restoration and the deconfinement crossover are reproduced by a temperature-and-magnetic-field-dependent coupling constant to reflect the inverse magnetic catalysis. Furthermore, the deconfined but chiral broken phase can be observed in the split region of the Tχ and Tϕ.

Chiral perturbation theory for nonzero chiral imbalance

We construct the most general low-energy effective lagrangian including local parity violating terms parametrized by an axial chemical potential or chiral imbalance μ5, up to mathcal{O}left({p}^4right) order in the chiral expansion for two light flavours. For that purpose, we work within the Chiral Perturbation Theory framework where only pseudo-NGB fields are included, following the external source method. The mathcal{O}left({p}^2right) lagrangian is only modified by constant terms, while the mathcal{O}left({p}^4right) one includes new terms proportional to {mu}_5^2 and new low-energy constants (LEC), which are renormalized and related to particular observables. In particular, we analyze the corrections to the pion dispersion relation and observables related to the vacuum energy density, namely the light quark condensate, the chiral and topological susceptibilities and the chiral charge density, providing numerical determinations of the new LEC when possible. In particular, we explore the dependence of the chiral restoration temperature Tc with μ5. An increasing Tc(μ5) is consistent with our fits to lattice data of the ChPT-based expressions. Although lattice uncertainties are still large and translate into the new LEC determination, a consistent physical description of those observables emerges from our present work, providing a theoretically robust model-independent framework for further study of physical systems where parity-breaking effects may be relevant, such as heavy-ion collisions.

Camouflage of the Phase Transition to Quark Matter in Neutron Stars

Abstract It has been known for some time that compact stars containing quark matter can masquerade as neutron stars in the range of measured mass and radius, making it difficult to draw firm conclusions on the phases of matter present inside the star. Using the vector-enhanced Bag model (vBag), we examine mass–radius and mass–compactness relations with Maxwell and Gibbs construction for hybrid stars with transitions from nuclear matter to two- or three-flavor quark matter, including sequential transitions. Not only can stable hybrid stars with either two- or three-flavor quark matter mimic neutron stars (the traditional masquerade), it also appears difficult to distinguish two-flavor from three-flavor quark matter, even in cases where a phase transition can be said to have occurred, such as in the presence of a distinct kink in the mass–radius relation. Furthermore, allowing for sequential flavor transitions, we find that the transition into an unstable branch can be caused by either a transition from nuclear to unstable quark matter or the sequential transition from nuclear to stable but “masquerading” two-flavor to unstable three-flavor quark matter. Addressing chiral restoration as well as quark deconfinement in a model of the phase transition, as the vBag does, adds further flexibility to the high-density equation of state, motivating caution in using even high-precision M–R data to draw firm conclusions on the nature of phases and phase transitions in neutron stars.

Spin polarization and chiral condensation in a ( 2+1 )-flavor Nambu–Jona-Lasinio model at finite temperature and baryon chemical potential

We investigate the ferromagnetic (spin polarization) condensation in (2+1) flavor Nambu Jona-Lasinio(NJL) model with non-zero current quark masses at finite temperature and density which may be relevant in the context of neutron stars. The spin polarization condensation arises due to a tensor type interaction which may be generated due to non-perturbative effects in Quantum Chromodynamics(QCD). In this investigation we have shown the interplay between chiral condensate and spin polarization condensation for different values of tensor coupling. Spin polarization in the case of 2+1 flavor is different from two flavor case because of additional F$_8$ condensate associated with $\lambda_8^f$ flavor generator. We find a non-zero value of the two spin condensates in the chirally restored phase. Beyond a certain temperature the spin polarization condensates vanish for rather large quark chemical potentials. The spin condensates affect the chiral phase transition, quark masses, and the quark dispersion relation. The spin polarization condensate appears only in the chiral restored phase for light quarks. For large enough tensor couplings, it is observed that the spin polarization condensate acts as a catalyst for chiral symmetry restoration. Thermodynamic behavior of $F_3$ and $F_8$ are found to be different and they affect the quark masses differently.

Properties of vector and axial-vector mesons in a nonlocal SU(2) PNJL model

We study the features of a SU(2) Polyakov-Nambu-Jona-Lasinio model that includes wave function renormalization and nonlocal vector interactions. Within this framework we analyze, among other properties, the masses, width and decay constants of light vector and axial-vector mesons at finite temperature. Then we obtain the corresponding phase diagram in a finite density scenario, after characterizing the deconfinement and chiral restoration transitions.

Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the UA(1) Symmetry

The temperature (T) dependence of the axion mass is predicted for T ′ s up to ∼ 2.3 × the chiral restoration temperature of QCD. The axion is related to the U A ( 1 ) anomaly. The squared axion mass m a ( T ) 2 is, modulo the presently undetermined scale of spontaneous breaking of Peccei–Quinn symmetry f a (squared), equal to QCD topological susceptibility χ ( T ) for all T. We obtain χ ( T ) by using quark condensates calculated in two effective Dyson–Schwinger models of nonperturbative QCD. They exhibit the correct chiral behavior, including the dynamical breaking of chiral symmetry and its restoration at high T. This is reflected in the U A ( 1 ) symmetry breaking and restoration through χ ( T ) . In our previous studies, such χ ( T ) yields the T-dependence of the U A ( 1 ) -anomaly-influenced masses of η ′ and η mesons consistent with experiment. This in turn supports our prediction for the T-dependence of the axion mass. Another support is a rather good agreement with the pertinent lattice results. This agreement is not spoiled by our varying u and d quark mass parameters out of the isospin limit.

Study of center and chiral symmetry realization in thermal N=1 super Yang-Mills theory using the gradient flow

The realization of center and chiral symmetries in $\mathcal{N}=1$ super Yang-Mills theory (SYM) is investigated on a four-dimensional Euclidean lattice by means of Monte Carlo methods. At zero temperature this theory is expected to confine external fundamental charges and to have a non-vanishing gaugino condensate, which breaks the non-anomalous Z$_{2\textrm{N}_{c}}$ chiral symmetry. In previous studies at finite temperatures, the phase transitions corresponding to deconfinement and chiral restoration were observed to occur at roughly the same critical temperature for SU(2) gauge group. We find further evidences for this observation from new measurements at smaller lattice spacings using the fermion gradient flow, and we discuss the agreement of our findings with conjectures from superstring theory. The implementation of the gradient flow technique allows us also to estimate, for the first time, the condensate at zero temperatures and zero gaugino mass with Wilson fermions.

Chiralspin Symmetry and Its Implications for QCD

In a local gauge-invariant theory with massless Dirac fermions, a symmetry of the Lorentz-invariant fermion charge is larger than a symmetry of the Lagrangian as a whole. While the Dirac Lagrangian exhibits only a chiral symmetry, the fermion charge operator is invariant under a larger symmetry group, S U ( 2 N F ) , that includes chiral transformations as well as S U ( 2 ) C S chiralspin transformations that mix the right- and left-handed components of fermions. Consequently, a symmetry of the electric interaction, which is driven by the charge density, is larger than a symmetry of the magnetic interaction and of the kinetic term. This allows separating in some situations electric and magnetic contributions. In particular, in QCD, the chromo-magnetic interaction contributes only to the near-zero modes of the Dirac operator, while confining chromo-electric interaction contributes to all modes. At high temperatures, above the chiral restoration crossover, QCD exhibits approximate S U ( 2 ) C S and S U ( 2 N F ) symmetries that are incompatible with free deconfined quarks. Consequently, elementary objects in QCD in this regime are quarks with a definite chirality bound by the chromo-electric field, without the chromo-magnetic effects. In this regime, QCD can be described as a stringy fluid.

Roberge-Weiss endpoint and chiral symmetry restoration in Nf=2+1 QCD

We investigate the fate of the Roberge-Weiss endpoint transition and its connection with the restoration of chiral symmetry as the chiral limit of $N_f = 2+1$ QCD is approached. We adopt a stout staggered discretization on lattices with $N_t = 4$ sites in the temporal direction; the chiral limit is approached maintaining a constant physical value of the strange-to-light mass ratio and exploring three different light quark masses, corresponding to pseudo-Goldstone pion masses $m_\pi \simeq 100, 70$ and 50 MeV around the transition. A finite size scaling analysis provides evidence that the transition remains second order, in the 3D Ising universality class, in all the explored mass range. The residual chiral symmetry of the staggered action also allows us to investigate the relation between the Roberge-Weiss endpoint transition and the chiral restoration transition as the chiral limit is approached: our results, including the critical scaling of the chiral condensate, are consistent with a coincidence of the two transitions in the chiral limit; however we are not able to discern the symmetry controlling the critical behavior, because the critical indexes relevant to the scaling of the chiral condensate are very close to each other for the two possible universality classes (3D Ising or O(2)).

Nonquenching of gA in nuclei, Landau-Migdal fixed-point theory, and emergence of scale symmetry in dense baryonic matter

How the axial coupling constant $g_A$ in nuclear Gamow-Teller transitions described in shell model gets "quenched" to a universal constant close to 1 can be explained by nuclear correlations in Fermi-liquid fixed point theory using a scale-symmetric chiral Lagrangian supplemented with hidden local symmetric vector mesons. Contrary to what one might naively suspect -- and has been discussed in some circles, there is no fundamental quenching at nuclear matter density due to QCD condensates. When the density of many-body systems treated with the same Lagrangian increases beyond the density $n=n_{1/2}\gsim 2n_0$ (where $n_0$ is the normal nuclear matter density) at which skyrmions representing baryons fractionize to half-skyrmions, with the $\rho$ meson driven toward the vector manifestation fixed point and a scalar meson $\sigma$ driven to the dilaton-limit fixed point with the nucleons parity-doubled, the dense matter supports the "pseudo-conformal" sound velocity for $n\gsim n_{1/2}$ while the trace of the energy momentum tensor remains non-vanishing. A plausible interpretation is that this signals the emergence of scale symmetry not explicitly present or hidden in QCD in the vacuum. The fundamental constant $g_A$, unaffected by QCD condensates for $n< n_{1/2}$, does go to 1 as the dilaton-limit fixed point is approached before arriving at chiral restoration, but it is not directly related to the "quenched $g_A$" in nuclei which can be explained as a Fermi-liquid fixed point quantity. The mechanism that produces a precocious pseudo-conformal sound velocity is expected to impact on the tidal deformability $\Lambda$ in gravity waves from coalescing neutron stars.

Holographic description of color superconductivity

The difficulty of describing the gauge dependent bi-quark condensate in the QCD colour superconducting phase has made it hard to construct a holographic dual of the state. To side step this problem, we argue that near the chiral restoration transition in the temperature-chemical potential plane, the strongly coupled gluons are likely completely gapped so that the colour quantum numbers of the quarks can be thought of below that gap as global indices. A standard AdS-superconductor model can then be used to analyze the fermionic gap formation. We investigate the role of four-fermion interactions, which might be used to include the gapped QCD interactions, on the vacuum and metastable vacua of the model. It turns out to be easiest to simply relate the standard interaction of the holographic superconductor to the strength of the gapped gluons. The result is a holographic description of the QCD colour superconducting phase diagram. We take a first look at how quark mass enters and causes a transition between the colour flavour locked phase and the 2SC phase.