Chiral Restoration Research Articles

Reduction of pseudocritical temperatures of chiral restoration and deconfinement phase transitions in a magnetized PNJL model

We investigate the chiral restoration and deconfinement phase transitions under an external magnetic field in the frame of a Pauli-Villars regularized Polyakov loop extended Nambu-Jona-Lasinio model. A running Polyakov loop scale parameter T0(eB) is introduced to mimic the reaction of the gluon sector to the presence of magnetic fields. It is found that a decreasing T0(eB) with magnetic fields can realize the inverse magnetic catalysis phenomena of chiral condensates of u and d quarks, increase of Polyakov loop, and the reduction of pseudocritical temperatures of chiral restoration and deconfinement phase transitions. Published by the American Physical Society 2024

Parity doublet model for baryon octets: Ground states saturated by good diquarks and the role of bad diquarks for excited states

Parity doublet model is an effective chiral model that includes the chiral-variant and -invariant masses of baryons. The chiral-invariant mass has large impacts on the density dependence of models which can be constrained by neutron star observations. In the previous work, models of two flavors have been considered up to a few times nuclear saturation density, but in such dense regions it is also necessary to consider hyperons. With the chiral-invariant masses baryons can stay massive in extreme environments (e.g., neutron stars) where the chiral symmetry restoration takes place. In this work, we generalize the previous SU(2)L×SU(2)R parity models of nucleons to SU(3)L×SU(3)R models of the baryon octet within the linear realization of the chiral symmetry. The major problem in constructing such models has been too many candidates for the chiral representations of baryons. Motivated by the concepts of diquarks and the mended symmetry, we choose the (3L,3¯R)+(3¯L,3R), (3L,6R)+(6L,3R), and (1L,8R)+(8L,1R) representations and use quark diagrams to constrain the possible types of Yukawa interactions. The masses of the baryon octets for positive and negative baryons up to the first excitations are successfully reproduced. As expected from the diquark considerations, the ground-state baryons are well dominated by (3L,3¯R)+(3¯L,3R) and (1L,8R)+(8L,1R) representations, while the excited states require (3L,6R)+(6L,3R) representations. Important applications of our model are the chiral restoration for strange quarks at large density and the continuity of diquarks from hadronic to quark matter. We also address the problem of large Yukawa couplings which are enhanced in three-flavor construction. Published by the American Physical Society 2024

Effects of tensor spin polarization on the chiral restoration and deconfinement phase transitions

Effects of tensor spin polarization (TSP) on the chiral restoration and deconfinement phase transitions are studied in Polyakov loop extended Nambu–Jona-Lasinio (PNJL) model. For chiral phase transition, the higher the polarized degree of quark-antiquark pairs under the strong magnetic field, the higher the phase transition temperature. The TSP corrects the position of the critical end point. The small impact of TSP on the phase transition temperature is found for the deconfinement phase transition. On the other hand, we divide the phase space into three ranges based on the phase diagram obtained from the PNJL model: the confinement phase with chiral symmetry broken, the deconfinement phase with restored chiral symmetry, and the confinement phase with restored chiral symmetry (quarkyonic phase). It is found that TSP has only a very small effect on the anisotropic pressure in the deconfined phase with chiral symmetry restored and the quarkyonic phase, but it has a very strong effect on the anisotropic pressure in the confined phase with chiral symmetry broken. This is because TSP is closely related to chiral symmetry. The restoration of chiral symmetry means the dissociation of spin polarization condensate. Published by the American Physical Society 2024

Chiral symmetry restoration at finite temperature in a model with manifest confinement

Multiple lattice evidences support the existence of a confining but chirally symmetric regime of QCD above the chiral symmetry restoration crossover at Tch≃155 MeV. This regime is characterised by an approximate chiral spin symmetry of the partition function, which is a symmetry of the colour charge and the confining electric part of the QCD Lagrangian. It is traditionally believed that confinement should automatically induce spontaneous breaking of chiral symmetry, which would preclude the existence of a confining but chirally symmetric regime of QCD at high temperatures. We employ a well-known solvable quark model for QCD in 3+1 dimensions that is chirally symmetric and manifestly confining and argue that while confinement indeed induces dynamical breaking of chiral symmetry at T=0, a chiral restoration phase transition takes place at some critical temperature Tch. Above this temperature, the spectrum of the model consists of chirally symmetric hadrons with approximate chiral spin symmetry.

Exploring quantum entanglement in chiral symmetry partial restoration with 1+1 string model

Within the confining color flux tube picture, we assess the color electric field generated by quark-antiquark pairs within the framework of the Schwinger model and estimate its impact on the chiral condensate. We observe differences in the distribution of the color flux tube generated by quark-antiquark pairs at different separation distances, leading to discrepancies in the partial restoration of chiral symmetry. Furthermore, we suggest incorporating the color magnetic field in the calculation of chiral condensate, leading to quantum entanglement effects, and proceed to compute the entanglement entropy. We observe that the entanglement entropy increases with the distance of the color source (the separation distance between quark and anti-quark), and the magnitude of the color electric field and chiral condensate restoration after spatial integration also increases with the distance of the color source. Then, we try to provide a qualitative explanation for the existence of these phenomena.

Fluctuations near the liquid-gas and chiral phase transitions in hadronic matter

We investigate the fluctuations of the net-baryon number density in dense hadronic matter. Chiral dynamics is modeled via the parity doublet Lagrangian, and the mean-field approximation is employed to account for chiral criticality. We focus on the qualitative properties and systematics of the second-order susceptibility of the net-baryon number density for individual positive- and negative-parity nucleons whose masses become degenerate at the chiral restoration. It is shown that the second-order susceptibility of the positive-parity state can become negative when the chiral symmetry is restored, as a natural consequence of the unique relationship of the mass to the order parameter. Moreover, we find that such negative fluctuations are indicative of approaching the critical point on the chiral phase boundary. Our results may have consequences for the interpretation of the experimental data on net-proton fluctuations in heavy-ion collisions.

Chiral Restoration of Nucleons in Neutron Star Matter: Studies Based on a Parity Doublet Model

We review the chiral variant and invariant components of nucleon masses and the consequence of their existence on the chiral restoration in extreme conditions, particularly in neutron star matter. We consider a model of linear realization of chiral symmetry with the nucleon parity doublet structure that permits the chiral invariant mass, m0, for positive and negative parity nucleons. The nuclear matter is constructed with the parity doublet nucleon model coupled to scalar fields σ, vector fields (ω,ρ), and mesons with strangeness through the U(1)A anomaly. In models with a large m0, the nucleon mass is insensitive to the medium, and the nuclear saturation properties can be reproduced without demanding strong couplings of the nucleons to the scalar fields σ and vector fields ω. We confront the resulting nuclear equations of state with nuclear constraints and neutron star observations and delineate the chiral invariant mass and effective interactions. To further examine the nuclear equations of state beyond the saturation density, we supplement quark models to set the boundary conditions from the high-density side. The quark models are constrained by the two-solar-mass conditions, and such constraints are transferred to nuclear models through the causality and thermodynamic stability conditions. We also calculate various condensates and the matter composition from nuclear to quark matter in a unified matter by constructing a generating functional that interpolates the nuclear and quark matter with external fields. Two types of chiral restoration are discussed: one due to the positive scalar charges of nucleons and the other triggered by the evolution of the Dirac sea. We found that the U(1)A anomaly softens equations of state from low to high density.

Effect of anomalous magnetic moment on the chiral transition at zero temperature in a strong magnetic field

The effect of the anomalous magnetic moment (AMM) on the chiral restoration is investigated at zero temperature in the strong magnetic fields with the vacuum magnetic regularization scheme. It is shown that the chiral restoration diagram sensitively depends on the AMM in the ultrastrong magnetic fields. In our work, the parameterization of AMM is employed as proportional to the square of the chiral condensate. The critical chemical potential is found to decrease linearly by the increasing coefficient in the AMM scale. At a smaller scale of the AMM, the critical chemical potential could go down and then grow up as the magnetic field increases. But at a larger scale, the magnetic catalysis on the critical chemical potential would not happen anymore.

Impacts of the U(1)A anomaly on nuclear and neutron star equation of state based on a parity doublet model

We examine the role of the $\mathrm{U}{(1)}_{A}$ anomaly in a parity doublet model of nucleons which include the chiral variant and invariant masses. Our model expresses the $\mathrm{U}{(1)}_{A}$ anomaly by the Kobayashi-Maskawa-'t Hooft (KMT) interaction in the mesonic sector. After examining the roles of the KMT term in vacuum, we discuss its impacts on nuclear equations of state (EOS). The $\mathrm{U}{(1)}_{A}$ anomaly increases the masses of the ${\ensuremath{\eta}}^{\ensuremath{'}}$ and $\ensuremath{\sigma}$ mesons and enhances the chiral symmetry breaking. Also, the $\mathrm{U}{(1)}_{A}$ anomaly enlarges the energy difference between chiral symmetric and symmetry broken vacuum; in turn, the chiral restoration at high density adds a larger energy density (often referred as a bag constant) to EOSs than in the case without the anomaly, leading to softer EOSs. Including these $\mathrm{U}{(1)}_{A}$ effects, we update the previously constructed unified equations of state that interpolate the nucleonic EOS at ${n}_{B}\ensuremath{\le}2{n}_{0}$ (${n}_{0}=0.16\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$; nuclear saturation density) and quark EOS at ${n}_{B}\ensuremath{\ge}5{n}_{0}$. The unified EOS is confronted with the observational constraints on the masses and radii of neutron stars. The softening of EOSs associated with the $U$(1) anomaly reduces the overall radii, relaxing the previous constraint on the chiral invariant mass ${m}_{0}$. Including the attractive nonlinear $\ensuremath{\rho}\text{\ensuremath{-}}\ensuremath{\omega}$ coupling for the reduced slope parameter in the symmetry energy, our new estimate is $400\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}\ensuremath{\le}{m}_{0}\ensuremath{\le}700\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, with ${m}_{0}$ smaller than our previous estimate by $\ensuremath{\approx}$200 MeV.

The role of Debye mass in the chiral crossover in a strong magnetic field

In this paper, the Debye mass of quarks is investigated in the Nambu–Jona-Lasinio model at zero and nonzero chemical potentials. In a uniform plasma, the Debye mass usually behaves as a monotonous increasing function of the temperature, the chemical potential and the magnetic field. At the fixed coupling interaction G, we find that the magnetic catalysis (MC) on the occurrence of the chiral restoration could be revealed by the susceptibility of the Debye mass dm D /dT at low chemical potential and by the quantity Tdm D /dT in the region of moderate densities. However, the inverse MC is realized under a thermomagnetic coupling constant G(B, T) by the behavior of the Debye mass at both zero and nonzero chemical potentials.

Light mesons and phase structures in μ B -T-eB and μ I -T-eB spaces * *Supported by the National Natural Science Foundation of China (11775165)

Light mesons are investigated in and spaces using a two-flavor NJL model and used to determine chiral symmetry restoration and the pion superfluid phase transition. In space, during the chiral symmetry restoration process, the mass of the pseudo-Goldstone mode increases, with sudden jumps. At the critical end point, the meson exhibits a sharp but continuous mass increase, with a sudden mass jump at the Mott transition. In the nearby first order chiral phase transition region, we observe two mass jumps, one induced by the Mott transition and the other by the quark mass jump. The mass of the Higgs mode σ first decreases and then increases with chiral symmetry restoration, only showing a jump at the first order chiral phase transition. We plot a chiral phase diagram in terms of the change in quark mass, the Mott transition of the pseudo-Goldstone mode , and the minimum mass of the Higgs mode σ. Owing to explicit breaking of chiral symmetry in the physical case, the chiral restoration phase boundaries on the plane from the order parameter side and meson side are different. The and σ mass jumps will be helpful to the experimental search for the chiral phase diagram and critical end point. On the plane, the competition between the pion superfluid phase transition and chiral symmetry restoration under magnetic fields is studied in terms of the Goldstone mode and pseudo-Goldstone mode . In contrast to the two mass jumps of in the first order chiral phase transition region, the meson displays several mass jumps in the chiral crossover region. At the critical end point, also has sharp but continuous mass change, with a mass jump at the Mott transition. The isospin symmetry is strict, and the pion superfluid phase transition is uniquely determined by the massless Goldstone mode . The separation of chiral restoration and the pion superfluid phase boundaries is enhanced by the external magnetic field.

Inverse catalysis effect of the quark anomalous magnetic moment to chiral restoration and deconfinement phase transitions at finite baryon chemical potential

The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions in baryon chemical potential-temperature $(\mu_B-T)$ plane under magnetic fields is investigated in frame of a Pauli-Villars regularized PNJL model. It's found that the quark AMM plays the role of inverse catalysis to the phase transitions, and large quark AMM will change the magnetic catalysis phenomena of phase transitions to inverse magnetic catalysis in the whole $\mu_B-T$ plane. For a fixed magnetic field, the critical temperature $T_c$ and critical baryon chemical potential $\mu_B^c$ decreases with quark AMM. The stronger the magnetic field is, the inverse catalysis effect of AMM becomes more important. For a small AMM $\kappa=\kappa_1$, it shows the magnetic catalysis effect for critical temperature $T_c$ at vanishing $\mu_B$ with increasing magnetic field, and (inverse) magnetic catalysis effect for critical baryon chemical potential $\mu_B^c$ at vanishing $T$ under (weak) strong magnetic field. At finite $T$ and $\mu_B$, there exist some crossings of the phase transition lines with different magnetic field. For a large AMM $\kappa=\kappa_2$, we obtain the inverse magnetic catalysis effect in the whole $\mu_B-T$ plane, and no crossings of phase transition lines happen.

Roper-like singly heavy baryons in a chiral model

We investigate the Roper-like singly heavy baryons such as Λc(2765) and Ξc(2967) in a chiral model. Based on chiral symmetry of diquarks inside the baryons, we propose that the Roper-like baryons are mostly pentaquark states (Qqqqq¯ ) while the corresponding ground-state ones Λc(2286) and Ξc(2470) are three-quark states (Qqq). Besides, the mass spectrum of negative-parity Λc and Ξc which are heavy quark spin-singlet is predicted by the linear representation of chiral symmetry. We also derive a sum rule of the heavy baryon masses and an extended Goldberger-Treiman relation. In addition to them, we demonstrate the parity-partner structure of the Λc’s and Ξc’s by showing mass degeneracies of them at the chiral restoration point. We expect that the present investigation leads to a better understanding of the diquarks inside hadrons from the viewpoint of chiral symmetry.

Neutron star properties with careful parametrization in the vector and axial-vector meson extended linear sigma model

The existence of quark matter inside the cores of heavy neutron stars is a possibility which can be probed with modern astrophysical observations. We use a vector and axial-vector meson extended quark-meson model to describe quark matter in the core of neutron stars. We discover that an additional parameter constraint is necessary in the quark model to ensure chiral restoration at high densities. By investigating hybrid star sequences with various parameter sets, we show that low sigma meson masses are needed to fulfill the upper radius constraints and that the maximum mass of stable hybrid stars is only slightly dependent on the parameters of the crossover-type phase transition. Using this observation and results from recent astrophysical measurements, a constraint of $2.5<{g}_{V}<4.3$ is set for the constituent quark--vector meson coupling. The effect of a nonzero bag constant is also investigated, and we observe that its effect is small for values adopted in previous works.

Thermodynamics of PNJL model at zero temperature in a strong magnetic field

In this paper, the deconfinement and chiral restoration transitions in a strong magnetic field are realized at zero temperature in the Polyakov Nambu-Jona-Lasinio model. We provide the thermodynamic treatment to mimic the deconfinement phase transition at zero temperature together with the entangled scalar and vector interactions coupled with the Polyakov loop. The magnetic catalysis is found by a rising behavior of the critical chemical potential for the first-order deconfinement phase transition. While the magnetic catalysis on the chiral restoration could convert to inverse magnetic catalysis under the running coupling interaction ansatz. Furthermore, the stronger magnetic field makes the possible quarkyonic phase window to be enlarged under the running coupling interaction.

Nuclear Potentials Relevant to the Symmetry Energy in Chiral Models

We employ the extended Nambu-Jona-Lasinio (NJL), linear-σ models, and the density-dependent model with chiral limits to work out the mean fields and relevant properties of nuclear matter. To have the constraint from the data, we re-examine the Dirac optical potentials and symmetry potential based on the relativistic impulse approximation (RIA). Unlike the extended NJL and the density-dependent models with the chiral limit in terms of the vanishing scalar density, the extended linear-σ model with a sluggish changing scalar field loses the chiral limit at the high-density end. The various scalar fields can characterize the different Schrödinger-equivalent potentials and kinetic symmetry energy in the whole density region and the symmetry potential in the intermediate density region. The drop in the scalar field due to the chiral restoration results in a clear rise of the kinetic symmetry energy. The chiral limit in the models gives rise to the softening of the symmetry potential and thereof the symmetry energy at high densities.

Chiral restoration of strange baryons

We review the results of a phenomenological model for cold and dense nuclear matter exhibiting a chiral phase transition. The idea is to model the quark-hadron phase transition under neutron star conditions within a single model, but without adding quark degrees of freedom by hand. To this end, strangeness is included in the form of hyperonic degrees of freedom, whose light counterparts provide the strangeness in the chirally restored phase. In the future, the model can be used for instance to compute the surface tension at the (first-order) chiral phase transition and to study the possible existence of inhomogeneous phases.

Chiral condensates for neutron stars in hadron-quark crossover: From a parity doublet nucleon model to a Nambu–Jona-Lasinio quark model

We study the chiral condensates in neutron star matter from nuclear to quark matter domain. We describe nuclear matter with a parity doublet model (PDM), quark matter with the Nambu--Jona-Lasino (NJL) model, and a matter at the intermediate density by interpolating nuclear and quark matter equations of state. The model parameters are constrained by nuclear physics and neutron star observations. Various condensates in the interpolated domain are estimated from the chemical potential dependence of the condensates at the boundaries of the interpolation. The use of the PDM with substantial chiral invariant mass ($m_0 \gtrsim 500$ MeV, which is favored by the neutron star observations) predicts the mild chiral restoration, and the significant chiral condensate remains to baryon density $n_B \sim 2-3n_0$ ($n_0\simeq 0.16\,{\rm fm}^{-3}$: nuclear saturation density), smoothly approaching the NJL predictions for the color-flavor-locked phase at $n_B \gtrsim 5n_0$. The same method is applied to estimate diquark condensates, number densities of up-, down- and strange-quarks, and the lepton fraction. In our descriptions the chiral restoration in the interpolated domain proceeds with two conceptually distinct chiral restoration effects; the first is associated with the positive scalar density in a nucleon, relevant in dilute regime, and the other primarily arises from the modification of the quark Dirac sea, which is triggered by the growth of the quark Fermi sea. We discuss several qualitative conjectures to interpolate the microphysics in nuclear and quark matter.

Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions: Topological Structure of Dense Matter

We review a new development on the possible direct connection between the topological structure of the Nf=1 baryon as a FQH droplet and that of the Nf≥2 baryons (such as nucleons and hyperons) as skyrmions. This development suggests a possible “domain-wall (DW)” structure of compressed baryonic matter at high density expected to be found in the core of massive compact stars. Our theoretical framework is anchored on an effective nuclear effective field theory that incorporates two symmetries either hidden in the vacuum in QCD or emergent from strong nuclear correlations. It presents a basically different, hitherto undiscovered structure of nuclear matter at low as well as high densities. Hidden “genuine dilaton (GD)” symmetry and hidden local symmetry (HLS) gauge-equivalent at low density to nonlinear sigma model capturing chiral symmetry, put together in nuclear effective field theory, are seen to play an increasingly important role in providing hadron–quark duality in baryonic matter. It is argued that the FQH droplets could actually figure essentially in the properties of the vector mesons endowed with HLS near chiral restoration. This strongly motivates incorporating both symmetries in formulating “first-principles” approaches to nuclear dynamics encompassing from the nuclear matter density to the highest density stable in the Universe.

Fluctuations and phases in baryonic matter

The phase structure of baryonic matter is investigated with focus on the role of fluctuations beyond the mean-field approximation. The prototype test case studied is the chiral nucleon-meson model, with added comments on the chiral quark-meson model. Applications to nuclear matter include the liquid-gas phase transition. Extensions to high baryon densities are performed for both nuclear and neutron matter. The role of vacuum fluctuations is systematically explored. It is pointed out that such fluctuations tend to stabilize the hadronic phase characterized by spontaneously broken chiral symmetry, shifting the chiral restoration transition to very high densities. This stabilization effect is shown to be further enhanced by additional dynamical fluctuations treated with functional renormalisation group methods.