Polyakov Quark Meson Research Articles

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.

Phase structure of the on-shell parametrized 2+1 flavor Polyakov quark-meson model

Augmenting the improved chiral effective potential of the on-shell renormalized 2+1 flavor quark-meson (RQM) model with the Polyakov-loop potential that accounts for the deconfinement transition, we get the quantum chromodynamics (QCD)-like framework of the renormalized Polyakov quark-meson (RPQM) model. When the divergent quark one-loop vacuum term is included in the effective potential of the quark-meson (QM) model, its tree-level parameters, or the parameters fixed by the use of meson curvature masses, become inconsistent as the curvature masses involve the self-energy evaluations at zero momentum. Using the modified minimal subtraction method, the consistent chiral effective potential for the RQM model has been calculated after relating the counterterms in the on-shell scheme to those in the MS¯ scheme and finding the relations between the renormalized parameters of both the schemes where the physical (pole) masses of the π, K, η, and η′ pseudoscalar mesons and the scalar σ meson, the pion and kaon decay constants, have been put into the relation of the running couplings and mass parameter. Using the RPQM model and the PQM model with different forms for the Polyakov-loop potentials in the presence or the absence of the quark backreaction, we have computed and compared the effect of the consistent quark one-loop correction and the quark backreaction on the scaled chiral order parameter, the QCD phase diagrams, and the different thermodynamic quantities. The results have been compared with the 2+1 flavor lattice QCD data from the Wuppertal-Budapest Collaboration [ 73, ] and the HotQCD Collaboration []. Published by the American Physical Society 2024

Quark matter properties and fluctuations of conserved charges in (2+1)-flavored quark model * *Supported by the DST-SERB, Government of India for funding of research project (CRG/2019/000096)

In this study, the susceptibilities of conserved charges, baryon number, charge number, and strangeness number at zero and low values of chemical potential are presented. Taylor series expansion was used to obtain results for the three-flavor Polyakov quark meson (PQM) model and the Polyakov loop extended chiral quark mean-field (PCQMF) model. Mean-field approximation was used to study quark matter with the inclusion of the isospin chemical potential, as well as the vector interactions. The effects of isospin chemical potential and vector-interactions on phase diagrams were analyzed. A comparative analysis of the two models was completed. Fluctuations of the conserved charges were enhanced in the transition temperature regime and hence provided information about the critical end point (CEP). Susceptibilities of conserved quantities were calculated by using the Taylor series method. Enhancement of fluctuations in the transition temperature neighborhood provided a clear signature of a quantum chromodynamics (QCD) critical-point.

Analytical solution of surface tension of quark-hadron phase transition

By using the finite temperature field theory, the one-loop effective potential and the dynamics of the quantum chromodynamics deconfinement phase transition in the framework of Friedberg-Lee model are studied at finite temperature and density. Our results show that there is a first-order deconfinement phase transition for the full phase diagram, and the critical temperature is about 119.8 MeV for a zero chemical potential whereas the critical chemical is around 256.4 MeV when the temperature is fixed at <i>T</i> = 50 MeV. Moreover, in the thin-wall approximation, we investigate the dynamics of a strong first-order quark-hadron transition via homogeneous bubble nucleation in the Friedberg-Lee model. Under an appropriate boundary condition, the equation of motion for the <inline-formula><tex-math id="M3">\begin{document}$ \sigma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M3.png"/></alternatives></inline-formula> field is solved, then the evolutions of the bubble critical configuration with radius <inline-formula><tex-math id="M4">\begin{document}$ r $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M4.png"/></alternatives></inline-formula> at different temperatures and densities are calculated. The surface tension, the typical radius of the critical bubble and the shift in the coarse-grained free energy each as a function of temperature and chemical potential are obtained. In order to gain the reliability and advantages of the thin-wall approximation, our analytical results based on the thin-wall approximation are compared with those obtained by the exact numerical method accordingly. Finally, some consequences and possible applications of our results in the quark meson model and Polyakov quark meson model are also presented in the end of this paper.

Isentropic evolution of the matter in heavy-ion collisions and the search for the critical endpoint

We study the isentropic evolution of the matter produced in relativistic heavy-ion collisions for various values of the entropy-per-baryon ratio of interest for the ongoing and future experimental searches for the critical endpoint (CEP) in the QCD phase diagram: these includes the current beam-energy-scan (BES) program at RHIC and the fixed-target collisions foreseen for the near future at various facilities. We describe the hot-dense matter through two different effective Lagrangians: the PNJL (Polyakov–Nambu–Jona–Lasinio) and the PQM (Polyakov-quark-meson) models. We focus on quantities expected to have a direct experimental relevance: the speed of sound, responsible for the collective acceleration of the fireball, and the generalized susceptibilities, connected to the cumulants of the distributions of conserved charges. In principle they should affect the momentum spectra and the event-by-event fluctuations of the yields of identified particles. Taking realistic values for the initial temperature and the entropy-per-baryon ratio we study the temporal evolution of the above quantities looking for differences along isentropic trajectories covering different regions of the QCD phase diagram, passing far or close to the CEP or even intersecting the first-order critical line.

Influence of Finite Volume Effect on the Polyakov Quark–Meson Model

In the current work, we study the influence of a finite volume on 2 + 1 S U ( 3 ) Polyakov Quark–Meson model (PQM) order parameters, (fluctuations) correlations of conserved charges and the quark–hadron phase boundary. Our study of the PQM model order parameters and the (fluctuations) correlations of conserved charges indicates a sizable shift of the quark–hadron phase boundary to higher values of baryon chemical potential ( μ B ) and temperature (T) for decreasing the system volume. The detailed study of such effect could have important implications for the extraction of the (fluctuations) correlations of conserved charges of the QCD phase diagram from heavy ion data.

Roberge–Weiss phase transition and QCD phase diagram in the (2 + 1) flavor Polyakov quark meson model

The Roberge–Weiss (RW) phase transition of (2 + 1) flavor QCD at imaginary quark chemical potentials [Formula: see text] is investigated by employing the Polyakov loop extended Quark Meson model (PQM), where [Formula: see text] is temperature, and [Formula: see text] is a dimensionless chemical potential. We calculate some thermodynamic quantities and draw the phase diagram. This work can be considered as a supplement of studying the RW transition by using the effective model.

Calculations of shear, bulk viscosities and electrical conductivity in the Polyakov-quark–meson model

We have calculated different transport coefficients such as shear, bulk viscosities and electrical conductivity of quark and hadronic matter within the framework of a 2 flavor Polyakov-quark–meson model. For constant thermal widths of quarks and mesons, the temperature dependence of different transport coefficients reveals the thermodynamical phase space structure and their qualitative behavior are quite well in agreement with earlier works, based on other dynamical models. Besides the phase-space structure of quarks and mesons, their thermal width also have explicit temperature dependence. This dependence has been obtained here from the imaginary part of their respective self-energies at finite temperature. Due to the threshold conditions of their self energies, only some limited temperature regions of quark and hadronic phase are relevant for our numerical estimation of transport coefficients, which are grossly in agreement with some of the earlier results. An interesting outcome of the present analysis is that the quark relaxation time due to quark–meson loops can develop perfect fluid nature within a specific temperature range.

Nucleon properties in the Polyakov quark-meson model

We study the nucleon as a nontopological soliton in a quark medium as well as in a nucleon medium in terms of the Polyakov quark meson (PQM) model with two flavors at finite temperature and density. The constituent quark masses evolving with the temperature at various baryon chemical potentials are calculated and the equations of motion are solved according to the proper boundary conditions. The PQM model predicts an increasing size of the nucleon and a reduction of the nucleon mass in both hot environment. However, the phase structure is different from each other in quark and nucleon mediums. There is a crossover in the low-density region and a first-order phase transition in the high-density region in quark medium, whereas there exists a crossover characterized by the overlap of the nucleons in nucleon medium.

Transport coefficients in the Polyakov quark meson coupling model: A relaxation time approximation

We compute the transport coefficients, namely, the coefficients of shear and bulk viscosities as well as thermal conductivity for hot and dense matter. The calculations are performed within the Polyakov quark meson model. The estimation of the transport coefficients is made using the Boltzmann kinetic equation within the relaxation time approximation. The energy dependent relaxation time is estimated from meson meson scattering, quark meson scattering and quark quark scattering within the model. In our calculations, the shear viscosity to entropy ratio and the coefficient of thermal conductivity show a minimum at the critical temperature, while the ratio of bulk viscosity to entropy density exhibits a peak at this transition point.The effect of confinement modelled through a Polyakov loop potential plays an important role in the estimation of these dissipative coefficients both below and above the critical temperature.

Z(3) metastable states in a Polyakov quark meson model

We study the existence of Z(3) metastable states in the presence of the dynamical quarks within the ambit of Polyakov quark meson (PQM) model. Within the parameters of the model, it is seen that for temperatures $T_m$ greater than the chiral transition temperature $T_c$, Z(3) metastable states exist ( $T_{m} \sim 310$ MeV at zero chemical potential). At finite chemical potential $T_m$ is larger than the same at vanishing chemical potential. We also observe a shift of ($\sim 5^\circ$) in the phase of the metastable vacua at zero chemical potential. The energy density difference between true and Z(3) metastable vacua is very large in this model. This indicates a strong explicit symmetry breaking effect due to quarks in PQM model. We compare this explicit symmetry breaking in PQM model with small explicit symmetry breaking as a linear term in Polyakov loop added to the Polyakov loop potential. We also study about the possibility of domain growth in a quenched transition to QGP in relativistic heavy ion collisions.

Phase Diagram and Isentropic Curves from the Vector Meson Extended Polyakov Quark Meson Model

In the framework of the $N_f = 2+1$ flavor (axial)vector meson extended Polyakov quark meson model we investigate the QCD phase diagram at finite temperature and density. We use a $\chi^2$ minimization procedure to parameterize the model based on tree\,-\,level decay widths and vacuum scalar and pseudoscalar curvature masses which incorporate the contribution of the constituent quarks. Using a hybrid approximation (mesons at tree level, fermions at one\,-\,loop level) for the grand potential we determine the phase boundary both on the $\mu_B-T$ and $\rho-T$ planes. We also determine the location of the critical end point of the phase diagram. Moreover by calculating the pressure and other thermodynamical quantities derived from it, we determine a set of isentropic curves in the crossover region. We show that the curves behave very similarly as their counterparts obtained from the lattice in the crossover regime.

Chiral Phase Transition Scenarios from the Vector Meson Extended Polyakov Quark Meson Model

Chiral phase transition is investigated in an SU(3)L SU(3)R symmetric vector meson extended linear sigma model with additional constituent quarks and Polyakov loops (extended Polyakov quark meson model). The parameterization of the Lagrangian is done at zero temperature in a hybrid approach, where the mesons are treated at tree-level, while the constituent quarks at 1-loop level. The temperature and baryochemical potential dependence of the two assumed scalar condensates are calculated from the hybrid 1-loop level equations of states. The order of the phase transition along the T = 0 and B = 0 axes are determined for various parameterization scenarios. We

Thermodynamics of [formula omitted]-flavor strongly interacting matter at nonzero isospin

We investigate the phase structure of strongly interacting matter at non-vanishing isospin before the onset of pion condensation in the framework of the unquenched Polyakov–Quark-Meson model with 2+1 quark flavors. We show results for the order parameters and all relevant thermodynamic quantities. In particular, we obtain a moderate change of the pressure with isospin at vanishing baryon chemical potential, whereas the chiral condensate decreases more appreciably. We compare the effective model to recent lattice data for the decrease of the pseudo-critical temperature with the isospin chemical potential. We also demonstrate the major role played by the value of the pion mass in the curvature of the transition line, and the need for lattice results with a physical pion mass. Limitations of the model at nonzero chemical potential are also discussed.

Fluctuations and correlations of conserved charges in the (2+1) Polyakov quark meson model

We consider the $(2+1)$ flavor Polyakov Quark Meson Model and study the fluctuations (correlations) of conserved charges upto sixth (fourth) order. Comparison is made with lattice data wherever available and overall good qualitative agreement is found, more so for the case of the normalised susceptibilities. The model predictions for the ratio of susceptibilities go to that of an ideal gas of hadrons as in Hadron Resonance Gas Model at low temperatures while at high temperature the values are close to that of an ideal gas of massless quarks. Our study provides a strong basis for the use of PQM as an effective model to understand the topology of the QCD phase diagram.

Revisiting the phase structure of the Polyakov-quark-meson model in the presence of vacuum fermion fluctuation

We have considered the contribution of fermionic vacuum loop in the effective potential of Polyakov loop extended Quark Meson Model (PQM) for the two quark flavour case and explored the phase structure and thermodynamics of the resulting PQMVT model (Polyakov Quark Meson Model with Vacuum Term) in detail at non zero as well as zero chemical potential. The temperature variations of order parameters and their derivatives have been calculated and the phase diagram together with the location of critical end point (CEP) has been obtained in $\mu$, and $T$ plane in both the models PQMVT and PQM. The PQMVT model analysis has been compared with the calculations in PQM model in order to bring out the effect of fermionic vacuum term on the physical observables. We notice that the critical end point (CEP) which is located near the temperature axis at ($\mu=81.0$, $T = 167$ MeV) in the PQM model gets shifted close to the chemical potential axis at ($\mu_{CEP}=294.7$, $T_{CEP}=84.0$ MeV) in the PQMVT model calculations of the phase diagram. Since it emerges from a background of second order transition in the chiral limit of massless quarks, the crossover occurring at $\mu$ = 0 in PQMVT model for the realistic case of explicitly broken chiral symmetry, has been identified as quite a soft and smooth transition. We have presented and compared the results for temperature variations of thermodynamic observables at zero and different non-zero quark chemical potentials. It is noticed that the presence of fermionic vacuum term in the effective potential leads to a smoother and slower temperature variation of thermodynamic quantities.

Towards finite density QCD with Taylor expansions

Convergence properties of Taylor expansions of observables, which are also used in lattice QCD calculations at non-zero chemical potential, are analyzed in an effective Nf=2+1 flavor Polyakov quark–meson model. A recently developed algorithmic technique allows the calculation of higher-order Taylor expansion coefficients in functional approaches. This novel technique is for the first time applied to an effective Nf=2+1 flavor Polyakov quark–meson model and the findings are compared with the full model solution at finite densities. The results are used to discuss prospects for locating the QCD phase boundary and a possible critical endpoint in the phase diagram.

The phase structure of the Polyakov–quark–meson model beyond mean field

The Polyakov-extended quark–meson model (PQM) is investigated beyond mean-field. This represents an important step towards a fully dynamical QCD computation. Both the quantum fluctuations to the matter sector and the back-reaction of the matter fluctuations to the QCD Yang–Mills sector are included. Results on the chiral and confinement–deconfinement crossover/phase transition lines and the location of a possible critical endpoint are presented. Moreover, thermodynamic quantities such as the pressure and the quark density are discussed.

Thermodynamics of (2+1)-flavor QCD: Confronting models with lattice studies

The Polyakov-quark-meson (PQM) model, which combines chiral as well as deconfinement aspects of strongly interacting matter is introduced for three light quark flavors. An analysis of the chiral and deconfinement phase transition of the model and its thermodynamics at finite temperatures is given. Three different forms of the effective Polyakov loop potential are considered. The findings of the (2+1)-flavor model investigations are confronted to corresponding recent QCD lattice simulations of the RBC-Bielefeld, HotQCD and Wuppertal-Budapest collaborations. The influence of the heavier quark masses, which are used in the lattice calculations, is taken into account. In the transition region the bulk thermodynamics of the PQM model agrees well with the lattice data.

Meson masses and mixing angles in the2+1flavor Polyakov quark meson sigma model and symmetry restoration effects

The meson masses and mixing angles have been calculated for the scalar and pseudoscalar sector in the framework of the generalized $2+1$ flavor Polyakov loop augmented quark meson linear sigma model. We have given the results for two different forms of the effective Polyakov loop potential. The comparison of results with the existing calculations in the bare $2+1$ quark meson linear sigma model, shows that the restoration of chiral symmetry becomes sharper due to the influence of the Polyakov loop potential. We find that inclusion of the Polyakov loop in the quark meson linear sigma model together with the presence of axial anomaly, triggers an early and significant melting of the strange condensate. We have examined how the inclusion of the Polyakov loop qualitatively and quantitatively affects the convergence in the masses of the chiral partners in pseudoscalar ($\ensuremath{\pi}$, $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}$, $K$) and scalar ($\ensuremath{\sigma}$, ${a}_{0}$, ${f}_{0}$, $\ensuremath{\kappa}$) meson nonets as the temperature is varied on the reduced temperature scale. The role of ${U}_{A}(1)$ anomaly in determining the isoscalar masses and mixing angles for the pseudoscalar ($\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$) and scalar ($\ensuremath{\sigma}$ and ${f}_{0}$) meson complex, has also been investigated in the Polyakov loop augmented quark meson linear sigma model. The interplay of chiral symmetry restoration effects and the setting up of ${U}_{A}(1)$ restoration trend has been discussed and analyzed in the framework of the presented model calculations.