Chiral Phase Diagram Research Articles

Influence of dynamical screening of four-quarks interaction on the chiral phase diagram

Influence of dynamical screening of four-quarks interaction on the chiral phase diagram

Non-extensive effects on the QCD equation of state and fluctuations of conserved charges within Polyakov quark meson model

The influence of non-extensive Tsallis statistics on the hadron phase structure has been investigated using the Polyakov-quark-meson (PQM) model. The analysis examines the non-extensive effects on the temperature dependence of PQM order parameters, thermodynamic quantities related to the quantum chromodynamics (QCD) equation of state, and fluctuations of conserved charges at varying chemical potentials. The results show that non-extensive effects have the most significant deviations near the crossover region. The pseudo-critical temperature T χ (μ B ) is not a universal constant and decreases with increasing non-extensive q parameter. The chiral phase diagram of the PQM model indicates a decrease in the behavior of the (T χ − μ B ) plane with increasing non-extensive q parameter. The PQM model exhibits good qualitative agreement with lattice QCD calculations. Moreover, these findings suggest the existence of a Tsallis limit, which serves as an alternative to the Stefan–Boltzmann limit for the massless ideal gas. The critical endpoint exhibits lower temperature but higher chemical potential with increasing non-extensive q parameter. Overall, this study highlights the importance of non-extensive Tsallis statistics in characterizing the quark-hadron phase structure of the PQM model and contributes to a deeper understanding of non-extensive effects in the quark-hadron phase transition.

Chiral symmetry breaking and phase diagram of dual chiral density wave in a rotating quark matter

Chiral symmetry breaking and phase diagram of dual chiral density wave in a rotating quark matter

Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model* *Supported by the National Natural Science Foundation of China (12005192) and the Project funded by China Postdoctoral Science Foundation (2020M672255, 2020TQ0287)

In this paper, a version of the Polyakov-Nambu-Jona-Lasinio (PNJL) model based on nonextensive statistical mechanics is presented. This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs (BG) statistics to a dimensionless nonextensivity parameter q. Thus, when q tends to 1, it returns to the BG case. Within the nonextensive PNJL model, we found that as q increases, the location of the critical end point (CEP) exhibits non-monotonic behavior. That is, for , CEP moves in the direction of lower temperature and larger quark chemical potential. However, for , CEP turns to move in the direction of lower temperature and lower quark chemical potential. In addition, we studied the moments of the net-baryon number distribution, that is, variance (), skewness (S), and kurtosis (κ). Our results are generally consistent with the latest experimental data reported, especially for , when q is set to .

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.

Nonextensive effects on QCD chiral phase transition with a chiral chemical potential* *Supported by the National Natural Science Foundation of China (12005192) and the Project funded by China Postdoctoral Science Foundation (2020M672255, 2020TQ0287)

In this study, we investigate the QCD chiral phase diagram in the presence of a chiral chemical potential based on nonextensive statistical mechanics. A feature of this new statistic is a dimensionless nonextensivity parameter q, which summarizes all possible effects violating the assumptions of Boltzmann-Gibbs (BG) statistics (when , it returns to the BG case). Within the nonextensive Polyakov-Nambu-Jona-Lasinio model, we find that as increases, the critical end point (CEP) in the plane continues to in the plane, and nonextensive effects have a significant impact on the evolution from the CEP to . Generally, with an increase in q, both the CEP and move in the direction of a lower temperature T and larger chemical potential μ (). In addition, we find that chiral charge density generally increases with T, μ, , and q. Our study may provide useful hints about lattice QCD and relativistic heavy-ion collision experiments.

Chiral Asymmetry and Phase Diagram of the Two-Color QCD

Chiral Asymmetry and Phase Diagram of the Two-Color QCD

Experimental investigation of chiral melting phase diagrams in high-pressure CO2 containing organic modifiers

A measurement method suitable to investigate the melting behavior of solid mixtures in a high-pressure, co-solvent–modified CO2 atmosphere was developed, using a variable volume, high-pressure view-cell. The solid sample is added after loading the organic solvents and pressurizing the cell with CO2. Investigation of the melting behavior was done by a first-and-last melting point method at 16 MPa pressure. The melting point depression depended on the organic modifier (being acetonitrile or the 7:3 mixture of cyclohexane and isopropyl acetate). Adding acetonitrile in 2% to the carbon dioxide atmosphere shifted the chiral melting phase diagram of 3-chloromandelic acid by approx. 8–10 °C compared to the values measured earlier in pure carbon dioxide at the same pressure. The eutectic composition of the racemic compound remained unchanged (around 70–75% ee), which is comparable to the limiting composition observed in our earlier antisolvent recrystallization results aiming the enantiomeric purification of the model molecule.

Chiral magnetic properties of QCD phase-diagram

The QCD phase-diagram is studied, at finite magnetic field. Our calculations are based on the QCD effective model, the SU(3) Polyakov linear-sigma model (PLSM), in which the chiral symmetry is integrated in the hadron phase and in the parton phase, the up-, down- and strange-quark degrees of freedom are incorporated besides the inclusion of Polyakov loop potentials in the pure gauge limit, which are motivated by various underlying QCD symmetries. The Landau quantization and the magnetic catalysis are implemented. The response of the QCD matter to an external magnetic field such as magnetization, magnetic susceptibility and permeability has been estimated. We conclude that the parton phase has higher values of magnetization, magnetic susceptibility, and permeability relative to the hadron phase. Depending on the contributions to the Landau levels, we conclude that the chiral magnetic field enhances the chiral quark condensates and hence the chiral QCD phase-diagram, i.e. the hadron-parton phase-transition likely takes place, at lower critical temperatures and chemical potentials.

Effect of momentum anisotropy on quark matter in the quark-meson model * *Supported by the National Natural Science Foundation of China (11935007) and the Fundamental Research Funds for the Central Universities (2020CXZZ107)

We investigate the chiral phase structure of quark matter with spheroidal momentum-space anisotropy specified by one anisotropy parameter in the 2+1 flavor quark-meson model. We find that the chiral phase diagram and the location of the critical endpoint (CEP) are significantly affected by the value of . With an increase in , the CEP is shifted to lower temperatures and higher quark chemical potentials. In addition, the temperature of the CEP is more sensitive to the anisotropy parameter than the corresponding quark chemical potential, which is the opposite to that from the finite system volume effect. The effects of the momentum anisotropy on the thermodynamic properties and scalar (pseudoscalar) meson masses are also studied at the vanishing quark chemical potential. The numerical results reveal that an increase in can hinder the restoration of chiral symmetry. We also find that shear viscosity and electrical conductivity decrease as increases. However, the bulk viscosity exhibits a significant non-trivial behavior with in the entire temperature domain of interest.

Chiral transition and the chiral charge density of the hot and dense QCD matter.

We study the chirally imbalanced hot and dense strongly interacting matter by means of the Dyson-Schwinger equations (DSEs). The chiral phase diagram is studied in the presence of chiral chemical potential μ5. The chiral quark condensate leftlangle overline{psi}psi rightrangle is obtained with the Cornwall-Jackiw-Tomboulis (CJT) effective action in concert with the Rainbow truncation. Catalysis effect of dynamical chiral symmetry breaking (DCSB) by μ5 is observed. We examine with two popular gluon models and consistency is found within the DSE approach, as well as in comparison with lattice QCD. The critical end point (CEP) location (μE, TE ) shifts toward larger TE but constant μE as μ5 increases. A technique is then introduced to compute the chiral charge density n5 from the fully dressed quark propagator. We find the n5 generally increases with temperature T , quark number chemical potential μ and μ5. Since the chiral magnetic effect (CME) is typically investigated with peripheral collisions, we also investigate the finite size effect on n5 and find an increase in n5 with smaller system size.

Octet meson spectra and chiral phase diagram in the improved soft-wall AdS/QCD model

We give a further study on chiral phase diagram in the improved soft-wall AdS/QCD model with $2+1$ flavors. The equations of motion for the octet pseudoscalar, vector and axial-vector mesons are derived to compute the octet meson spectra and relevant decay constants, by which the model parameters are determined. The chemical potential effects on thermal transition of chiral condensate are investigated, which enables us to obtain the chiral phase diagram in the $\mu-T$ plane. We find that the critical end point linking the crossover transition with the first-order phase transition still exists and locates at $(\mu_B, T_c) \simeq (390 \MeV, 145 \MeV)$, which along with the crossover line are consistent with lattice result and experimental analysis from relativistic heavy ion collisions.

Thermodynamic properties of light mesons and phase transition in an extended SU(2) NJL model

In this work, we study the temperature and chemical potential dependence of the masses of sigma and pion mesons as well as the quark condensate by using a SU(2) flavor version of the Nambu–Jona–Lassino model, introducing a prescription that mimics confinement. We have found that as the temperature increases, the mass of sigma shifts down, while the pion mass remains almost constant. On the other hand, the quark condensate decreases as the temperature and chemical potential increases. We have also analyzed the temperature and chemical potential dependence of the spectral function of the sigma meson, from which we observe at low values of T and [Formula: see text] an absence of a peak. Furthermore, as the Mott temperature is reached, its value increases abruptly and a distinct peak emerges, which is related with the dissociation of the sigma. For the case of [Formula: see text], the Mott dissociation is exhibited about the temperature of 189 MeV. We have also obtained the chiral phase diagram and the meson dissociation for different values of [Formula: see text]. From these results, we can state a relation between chiral symmetry restoration and Mott dissociation.

Chiral phase transition and QCD phase diagram from AdS/QCD

We study the chemical potential effects on the chiral phase transition in a simply improved soft-wall AdS/QCD model, which can realize consistently the properties of linear confinement and spontaneous chiral symmetry breaking. The $\mu-T$ phase diagrams with both zero and physical quark masses have been obtained from this model. For the case of physical quark mass, the chiral transition has a crossover behavior at low chemical potential. With the increase of the chemical potential $\mu$, the critical temperature $T_c$ descends towards zero, and the crossover transition turns into a first-order one at some intermediate value of $\mu$, which implies that a critical end point naturally exists in this improved soft-wall model. All these features agree with our current perspective on the QCD phase diagram.

Chiral phase diagram of strongly interacting matter at finite volume

Chiral phase diagram of strongly interacting matter at finite volume

Phase structure of NJL model with weak renormalization group

We analyze the chiral phase structure of the Nambu–Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V(σ;t) is given as a partial differential equation, where σ:=ψ¯ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V(σ;t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

Chiral Thermodynamics in a Finite Box

Finite-volume modifications of the two-flavor chiral phase diagram are investigated within an effective quark-meson model in various mean-field approximations. The role of vacuum fluctuations and boundary conditions, their influence on higher cumulants and signatures of a possible pseudo-critical endpoint are amplified with smaller volumes.

On SU(3) Effective Models and Chiral Phase Transition

Sensitivity of Polyakov Nambu-Jona-Lasinio (PNJL) model and Polyakov linear sigma-model (PLSM) has been utilized in studying QCD phase-diagram. From quasi-particle model (QPM) a gluonic sector is integrated into LSM. The hadron resonance gas (HRG) model is used in calculating the thermal and dense dependence of quark-antiquark condensate. We review these four models with respect to their descriptions for the chiral phase transition. We analyze the chiral order parameter, normalized net-strange condensate, and chiral phase-diagram and compare the results with recent lattice calculations. We find that PLSM chiral boundary is located in upper band of the lattice QCD calculations and agree well with the freeze-out results deduced from various high-energy experiments and thermal models. Also, we find that the chiral temperature calculated from HRG is larger than that from PLSM. This is also larger than the freeze-out temperatures calculated in lattice QCD and deduced from experiments and thermal models. The corresponding temperature and chemical potential are very similar to that of PLSM. Although the results from PNJL and QLSM keep the same behavior, their chiral temperature is higher than that of PLSM and HRG. This might be interpreted due the very heavy quark masses implemented in both models.

Thermodynamics and higher order moments in SU(3) linear σ-model with gluonic quasiparticles

In the framework of the linear σ-model (LSM) with three quark flavors, the chiral phase diagram at finite temperature and density is investigated. For temperatures higher than the critical temperature (), we added to the LSM the gluonic sector from the quasi-particle model (QPM), which assumes that the interacting gluons in the strongly interacting matter, the quark–gluon plasma (QGP), are phenomenologically the same as non-interacting massive quasi-particles. The dependence of the chiral condensates of strange and non-strange quarks on the temperature and chemical potential is analyzed. Then, we calculate the thermodynamics in the new approach (using a combination of the LSM and the QPM). Confronting the results with those from recent lattice quantum chromodynamics simulations reveals an excellent agreement for almost all thermodynamic quantities. The dependences of the first-order and second-order moments of the particle multiplicity on the chemical potential at fixed temperature are studied. These investigations are implemented through characterizing the large fluctuations accompanying the chiral phase transition. The results for the first-order and second-order moments are compared with those from the (3) Polyakov linear σ-model (PLSM). Also, the resulting phase diagrams deduced in the PLSM and the LSM+QPM are compared with each other.

Non- 5 hermiticity fermions in two dimensions

We construct 2D non-$\gamma_{5}$hermiticity fermions based on the minimal doubling fermion. We investigate symmetries, reflection positivity, eigenvalue distribution and the number of poles for our fermions. As simple tests for application to the fermion, the Gross-Neveu model in two dimensions is studied using the non-$\gamma_{5}$hermiticity fermion. We draw the parity broken phase diagram, called Aoki phase and the chiral broken phase diagram for the model with an imaginary chemical potential.