We study the implications of the spontaneous and explicit Z(3) center symmetry breaking for the Polyakov loop susceptibilities. To this end, ratios of the susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop are computed within an effective model using a color group integration scheme. We show that the essential features of the lattice QCD results of these ratios can be successfully captured by the effective approach. Furthermore we discuss a novel scaling relation in one of these ratios involving the explicit breaking field, volume, and temperature.
We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge theory using the Symanzik improved gauge action on different-sized lattices. The longitudinal and transverse fluctu- ations of the Polyakov loop, as well as, that of its absolute value are considered. We analyze their properties in relation to the confinement-deconfinement phase transition. We also present results based on simulations of (2+1)-flavor QCD on 32^3 x 8 lattice using Highly Improved Staggered Quark (HISQ) action by the HotQCD collaboration. The influences of fermions on the Polyakov loop fluctuations are di…
We consider the $(2+1)$ flavor Polyakov Quark Meson Model and study the effect of including fermion vacuum fluctuations on the thermodynamics and phase diagram. The resulting model predictions are compared to the recent QCD lattice simulations by the HotQCD and Wuppertal-Budapest collaborations. The variation of the thermodynamic quantities across the phase transition region becomes smoother. This results in better agreement with the lattice data. Depending on the value of the mass of the sigma meson, including the vacuum term results in either pushing the critical end point into higher values…
We investigate correlations of the Polyakov loop fluctuations with eigenmodes of the lattice Dirac operator. Their analytic relations are derived on the temporally odd-number size lattice with the normal non-twisted periodic boundary condition for the link-variables. We find that the low-lying Dirac modes yield negligible contributions to the Polyakov loop fluctuations. This property is confirmed to be valid in confined and deconfined phase by numerical simulations in SU(3) quenched QCD. These results indicate that there is no direct, one-to-one correspondence between confinement and chiral sy…
The behavior of the quark condensates at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu--Jona-Lasinio model with Polyakov loop (PNJL) and its extension, the so-called entangled PNJL model (EPNJL). A comparison with recent lattice QCD data is performed and it is shown that at $T=0$ MeV the light quark condensates are in quantitative agreement. At finite temperature, although there is an overall reasonable agreement with several lattice results, it is shown that in the lattice calculations the effect due to the electr…
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…
In the present work, we analyse the effects of an external magnetic field on the chiral critical temperature $T_c$ of strongly interacting matter. In doing this, we can characterize the magnetic properties of the quantum chromodynamics (QCD) strong interacting matter, the quark-gluon plasma (QGP). We investigate this in the framework of the SU(3) Polyakov linear sigma-model (PLSM). To this end, we implement two approaches representing two systems, in which the Polyakov-loop potential added to PLMS either renormalized or non-normalized. The effects of Landau quantization on the strongly interac…
We explore the thermodynamics and phase structure of the Polyakov loop-extended two flavor chiral quark--meson (PQM) model beyond the mean-field approximation at imaginary chemical potential. Our approach is based on the functional renormalization group (FRG) method. At finite temperature and imaginary chemical potential, we solve the renormalization group flow equation for a scale-dependent thermodynamic potential in the presence of the gluonic background field. We determine behavior of order parameters of the PQM model in the FRG approach and compute the phase diagram. We compare our FRG res…
A model for particle production at the deconfining phase transition in QCD is developed, as the semi-classical decay of a condensate for the Polyakov loop. In such a model, generically particle production, as measured on an event-by-event basis, exhibits significant deviations from statistical behavior.
We explore the NJL model with Polyakov loops for a system of three colors and two flavors within the mean-field approximation, where both chiral symmetry and confinement are taken into account. We focus on the phase structure of the model and study the chiral and Polyakov loop susceptibilities.
We report the first model study of the net charge fluctuations in terms of D-measure within the framework of the Polyakov-Nambu-Jona-Lasinio model. Net charge fluctuation is estimated from the charge susceptibility evaluated using PNJL model. A parameterization of the freeze-out curve has been used to obtain D as a function of sqrt(s). We have discussed our results vis-a-vis recent experimental findings from ALICE collaboration.
Thermodynamics and the phase structure of the Polyakov loop-extended two flavor chiral quark-meson model (PQM) are explored. The analysis of the PQM model is based on the functional renormalization group (FRG) method. An appropriate truncation of the effective action with quarks coupled to background gluonic fields is introduced. Within this scheme, we derive the renormalization group flow equation for the scale-dependent thermodynamic potential at finite temperature and density in the presence of a symmetry breaking external field. The influence of fluctuations and of the background gluon fie…
We study the thermodynamics of QCD system under external magnetic field via the 2+1 flavor Polyakov-loop quark-meson model. To incorporate quantum and thermal fluctuations, the functional renormalization group approach is implemented in our work. Pressure, entropy density, magnetic susceptibility and other thermodynamic quantities are calculated and analyzed to investigate the effect of magnetic field on the QCD system. The calculated results are in reasonable agreement with lattice QCD simulations and perturbation theory. We then give an intuitive picture for the response of QCD system to the…
In order to come closer to a realistic model of high-energy collisions, we simulate SU(2) lattice gauge theory under fluctuating temperature. The fluctuations are Euler-Gamma distributed, leading to a canonical state maximizing the Renyi and Tsallis entropy formulas. We test the random lattice spacing method numerically on the Polyakov Loop expectation value. The critical coupling and presumably also the critical deconfinement temperature shifts about 30 per cent to higher values with a realistic degree of fluctuations.
We explore the influence of heavy quarks on the deconfinement phase transition in an effective model for gluons interacting with dynamical quarks in color SU(3). With decreasing quark mass, the strength of the explicit breaking of the Z(3) symmetry grows and the first-order transition ends in a critical endpoint. The nature of the critical endpoint is examined by studying the longitudinal and transverse fluctuations of the Polyakov loop, quantified by the corresponding susceptibilities. The longitudinal susceptibility is enhanced in the critical region, while the transverse susceptibility show…
We study SU(2) Yang-Mills theory at finite temperature in the framework of the functional renormalization group. We concentrate on the effective potential for the Polyakov loop which serves as an order parameter for confinement. In this first status report, we focus on the behaviour of the effective Polyakov-loop potential at high temperatures. In addition to the standard perturbative result, our findings provide information about the ``RG improved'' backreactions of Polyakov-loop fluctuations on the potential. We demonstrate that these fluctuations establish the convexity of the effective pot…
The baryon-number susceptibilities is correlated to the fluctuations obtained in experiments, we can theoretically calculate the susceptibility and compare it with the experimental fluctuations data. In this paper, we calculate the baryon-number susceptibilities from the Polyakov-loop-extended Nambu-Jona-Lasinio (PNJL) model, then compare them with the the heavy ion collision experimental fluctuation data and the results from other models, lattice QCD and the Dyson-Schwinger equations (DSEs) approach. Our results are in line with the experiment and very similar to the results of DSEs at experi…
We study order parameters for the confinement-deconfinement phase transition related to the Polyakov-loop variable. The functional renormalisation group is used to compute these order parameters in a unified, non-perturbative continuum approach. Our result for the expectation value of the traced Polyakov loop agrees quantitatively with the lattice result. Furthermore, we discuss how this order parameter differs from the standard continuum Polyakov loop. For temperatures close to the phase transition temperature there are significant deviations. We argue that these deviations are of crucial imp…
We investigate chiral and deconfinement transitions in the strong coupling lattice QCD for color SU(3). We combine the leading order Polyakov loop effective action of the strong coupling expansion and the next-to-next-to-leading order (1/g^4) fermionic effective action with one species of unrooted staggered fermion. Two approximation schemes are adopted to evaluate the Polyakov loop effects; a Haar measure method (no fluctuation from the mean field) and a Weiss mean-field method (with fluctuations). The Polyakov loop is found to suppress the chiral condensate and to reduce the chiral transitio…
We have estimated the susceptibilities of conserved charges for 2-flavor strongly interacting matter with varying system sizes, using the Polyakov loop enhanced Nambu Jona-Lasinio model. The susceptibilities for vanishing baryon densities are found to show a scaling with the system volume in the hadronic as well as partonic phase. This scaling breaks down for a temperature range of about 30-50 MeV around the cross-over region. Simultaneous measurements of the various susceptibilities may thus indicate how close to the cross-over region the freeze-out occurs for the fireball created in heavy-io…
Thermodynamics and the phase structure of the Polyakov loop-extended two flavors chiral quark--meson (PQM) model is explored beyond the mean-field approximation. The analysis of the PQM model is based on the functional renormalization group (FRG) method. We formulate and solve the renormalization group flow equation for the scale-dependent thermodynamic potential in the presence of the gluonic background field at finite temperature and density. We determine the phase diagram of the PQM model in the FRG approach and discuss its modification in comparison with the one obtained under the mean-fie…
In the current work, we study the influence of a finite volume on $2+1$ $SU(3)$ 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) …
In a recent publication we noticed that the Hamiltonian density for fluctuations around the 't Hooft-Polyakov monopole appeared to be non-Hermitian. Here we show that when this Hamiltonian density is integrated into the Hamiltonian all non-Hermitian terms give a vanishing total contribution.
We investigate chiral and deconfinement transitions in the framework of the strong coupling lattice QCD for color SU(3) with one species of unrooted staggered fermion at finite temperature and quark chemical potential. We take account of the leading order Polyakov loop terms as well as the next-to-next-to-leading order (1/g^4) fermionic terms of the strong coupling expansion in the effective action. We investigate the Polyakov loop effects by comparing two approximation schemes, a Haar measure method (no fluctuation from the mean field) and a Weiss mean-field method (with fluctuations). The ef…
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.
A natural mechanism for finite temperature quark confinement arises via the coupling of the adjoint Polyakov loop to the chromomagnetic field. Lattice simulations and analytical results both support this hypothesis. Finite temperature SU(3) lattice simulations show that a large external coupling to the chromomagnetic field restores confinement at temperatures above the normal deconfining temperature. A one-loop calculation of the effective potential for SU(2) gluons in a background field shows that a constant chromomagnetic field can drive the Polyakov loop to confining behavior, and the Polya…
We study the physical mechanism of how an external magnetic field influences the QCD quark condensate. Two competing mechanisms are identified, both relying on the interaction between the magnetic field and the low quark modes. While the coupling to valence quarks enhances the condensate, the interaction with sea quarks suppresses it in the transition region. The latter `sea effect' acts by ordering the Polyakov loop and, thereby, reduces the number of small Dirac eigenmodes and the condensate. It is most effective around the transition temperature, where the Polyakov loop effective potential …
We investigate the QCD phase diagram at zero chemical potential and finite temperature in the presence of an external magnetic field within the three flavor Polyakov-Nambu-Jona-Lasinio and entangled Polyakov-Nambu-Jona-Lasinio models looking for the inverse magnetic catalysis. Two scenarios for a scalar coupling parameter dependent on the magnetic field intensity are considered. These dependencies of the coupling allow to reproduce qualitatively lattice QCD results for the quark condensates and for the Polyakov loop: due to the magnetic field the quark condensates are enhanced at low and high …
Study of finite volume number density fluctuations in the SU(3) Polyakov loop extended Nambu-Jona-Lasinio model for the search of the QCD Critical Point
We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss p…
We integrate out fast varying quantum fluctuations around static A_4 and A_i fields for the SU(N) gauge group. By assuming that the gluon fields are slowly varying but allowing for an arbitrary amplitude of A_4 we obtain two variants of the effective high-temperature theory for the Polyakov line. One is the effective action for the gauge-invariant eigenvalues of the Polyakov line, and it is explicitly Z(N) symmetric. The other is the effective action for the Polyakov line itself as an element of the SU(N). In this case the theory necessarily includes the spatial components A_i to ensure its ga…
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 $μ$, and $T$ plane in both the models PQMVT and PQM. The P…
Effects of external magnetic field on various properties of the quantum chromodynamics under extreme conditions of temperature and density have been analysed. To this end, we use SU(3) Polyakov linear sigma-model and assume that the external magnetic field eB adds some restrictions to the quarks energy due to the existence of free charges in the plasma phase. In doing this, we apply the Landau theory of quantization. This requires an additional temperature to drive the system through the chiral phase-transition. Accordingly, the dependence of the critical temperature of chiral and confinement …
We obtain the phase diagram of strong interactions in the presence of a magnetic field within the linear sigma model coupled to quarks and to the Polyakov loop, and show that the chiral and deconfinement lines can split. We also study the behavior of the chiral condensate in this magnetic environment and find an approximately linear dependence on the external field, in accordance with lattice data.
Firstly we qualitatively analyze the formation of the dip and peak structures of the kurtosis $κσ^2$ of net baryon number fluctuation along imagined freeze-out lines and discuss the signature of the existence of the QCD critical end point (CEP) in the Nambu--Jona-Lasinio (NJL) model, Polyakov-NJL (PNJL) model as well as $μ$-dependent PNJL($μ$ PNJL) model with different parameter sets, and then we apply a realistic PNJL model with parameters fixed by lattice data at zero chemical potential, and quantitatively investigate its $κσ^2$ along the real freeze-out line extracted from experiments. The …
The Polyakov loop extended Nambu and Jona-Lasinio model (PNJL model) in a mean field framework shows astonishingly good agreement with lattice QCD calculations which needs to be better understood. The present work reports on further developments concerning both Polyakov loop and mesonic fluctuations beyond mean field approximation. Corrections beyond mean field are of special interest for the thermal expectation values of the Polyakov loop $Φ$ and its conjugate $Φ^*$, which differ once the quark chemical potential is non-zero. Mesonic fluctuations are also considered with emphasis on the role …
We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature T-chi and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at T-chi is shown to be supported by finite temperature lattice calculations.
We analyze the consequences of the inclusion of the gluonic Polyakov loop in chiral quark models at finite temperature. Specifically, the low-energy effective chiral Lagrangian from two such quark models is computed. The tree level vacuum energy density, quark condensate, pion decay constant and Gasser-Leutwyler coefficients are found to acquire a temperature dependence. This dependence is, however, exponentially small for temperatures below the mass gap in the full unquenched calculation. The introduction of the Polyakov loop and its quantum fluctuations is essential to achieve this result an…
At very high temperatures Yang--Mills theories can be described through perturbation theory. At the tree level the time components of the gluon fields decouple and yield a dimensionally reduced theory. The expectation value of the Polyakov loop then assumes values of the Z(N) center group. At intermediate temperatures, however, this is not true anymore. The time dependence shows up in loops. In a recent work we integrated out fast varying quantum fluctuations around background A_i and static A_4 fields. We assumed that these fields are slowly varying but that the amplitude of A_4 is arbitrary.…
We propose a physical mechanism for inverse magnetic catalysis, the suppression of the chiral condensate by an external magnetic field in QCD around the critical temperature. We show that this effect, seen in lattice simulations, is a result of how the sea quarks react to the magnetic field. We find that the suppression of the condensate happens because the quark determinant can suppress low quark modes by ordering the Polyakov loop. This mechanism is particularly efficient around $T_c$ where the Polyakov loop effective potential is flat and the determinant can have a significant ordering effe…
The QCD phase diagram at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu--Jona-Lasinio (NJL) model and the NJL model with the Polyakov loop (PNJL). A scalar coupling parameter dependent on the magnetic field intensity is considered. The scalar coupling has been fitted so that the lattice QCD pseudocritical chiral transition temperatures are reproduced and in the limit of large magnetic field decreases with the inverse of the magnetic field intensity. This dependence of the coupling allows to reproduce the lattice QCD…
We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for the Wilson line which includes a "fuzzy" bag term to generate non-perturbative fluctuations. The effective potential for the Polyakov loop is extracted from the simulations including all modes of the loop as well as for cooled configuration where the hard modes have been ave…
In an extension of the Nambu-Jona-Lasinio model where the quarks interact with the temporal gluon field, represented by the Polyakov loop, we explore the relation between the deconfinement and chiral phase transitions. The effect of Polyakov loop dynamics on thermodynamic quantities, on the phase structure at finite temperature and baryon density and on various susceptibilities is presented. Particular emphasis is put on the behavior and properties of the fluctuations of the (approximate) order parameters and their dependence on temperature and net--quark number density. We also discuss how th…
Fluctuations of baryon, charge and strangeness have been investigated in Polyakov loop enhanced Nambu--Jona-Lasinio model. Multiple reflection expansion method has been incorporated to include the surface and curvature energy along with the system volume. The results of different fluctuations are then compared with the available experimental data from the heavy ion collision.
We study how the charge neutrality affects the phase structure of three-flavor PNJL model. We point out that, within the conventional PNJL model at finite density the color neutrality is missing because the Wilson line serves as an external ``colored'' field coupled to dynamical quarks. In this paper we heuristically assume that the model may still be applicable. To get color neutrality one has then to allow non vanishing color chemical potentials. We study how the quark matter phase diagram in $(T,m_s^2/μ)$-plane is affected by imposing neutrality and by including the Polyakov loop dynamics. …
Finite temperature compact electrodynamics in (2+1) dimensions is studied in the presence of external electromagnetic fields. The deconfinement temperature is found to be insensitive to the external fields. This result corroborates our observation that external fields create additional small--size magnetic dipoles from the vacuum which do not spoil the confining properties of the model at low temperature. However, the Polyakov loop is not an order parameter of confinement. It can vanish in deconfinement in the presence of external field. This does not mean the restoration of confinement for ce…
We study the effect of quantum and thermal fluctuations as well as the mass dependence of the phase structure of QCD at finite temperature and density within a dynamical Polyakov-loop--extended quark-meson model. The glue dynamics is simulated by the Polyakov-loop potential, also including the back-coupling of the matter sector to the glue dynamics. In the chiral limit, the chiral phase transition at large chemical potential and low temperature splits into two transition branches. For non-vanishing pion masses the chiral transition at small chemical potential changes from a phase transition to…
We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature $T_χ$ and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behavior of Polyakov loop susceptibilities at $T_χ$ is shown to be supported by finite temperature lattice calculations.
We apply a Monte-Carlo method to the two flavor Polyakov loop extended Nambu and Jona-Lasinio (PNJL) model. In such a way we can go beyond mean field calculations introducing fluctuations of the fields. We study the impact of fluctuations on the thermodynamics of the model. We calculate the second derivatives of the thermodynamic grand canonical partition function with respect to the chemical potential and present a comparison with lattice data also for flavor non-diagonal susceptibilities.
We discuss the influence of fluctuations on thermodynamics near the chiral phase transition within Polyakov loop extended quark--meson model based on the functional renormalization group (FRG) method. We include the gluon fields in the FRG flow equation self-consistently on the mean-field level. We focus on the properties of the phase diagram and net-baryon number fluctuations.
We present results for the (color)magnetic and (color)electric screening masses of the Quark-Gluon Plasma in the presence of an external magnetic field. The screening masses are extracted from the correlators of Polyakov loops, determined by lattice QCD simulations at the physical point. We explore temperatures in the range $200\,\mathrm{MeV}\lesssim T\lesssim 330\,\mathrm{MeV}$ and magnetic field intensities up to $|e|B \sim 1.3\,\mathrm{GeV}^2$. We find that both screening masses are increasing functions of the magnetic field and that the dependence on $B$ becomes weaker for larger temperatu…
Recent consensus on the $N_f=2+1$ equation of state at vanishing chemical potential from different lattice-QCD groups has spoiled the previous agreement with the outcome from the mean-field Polyakov-Nambu-Jona-Lasinio model. In this letter we review the thermodynamics of the PNJL model introducing two important aspects needed to describe the pressure computed in the lattice QCD. First, we consider the thermodynamics of the model beyond the mean-field approach to include pseudoscalar and scalar mesonic-like fluctuations into the grand-canonical potential. This accounts for the hadronic pressure…
Comparing critical regions in Polyakov-quark-meson models: Effects of flavor (two versus 2+1) under on-shell renormalization, and on-shell versus curvature-mass parameter fixing for the two-flavor case
University of Allahabad（阿拉哈巴德大学）；Acharya Narendra Deo Kisan P.G. College（阿查里亚·纳伦德拉·迪奥农民研究生学院）；Maa Pateswari University（玛雅·帕特什瓦里大学）
We study two-color QCD in an external magnetic backround at finite temperature using the Polyakov-loop extended two-flavor two-color NJL model. At T=0, the chiral condensate is calculated and it is found to increase as a function of the magnetic field $B$. In the chiral limit the deconfinement transition lies below the chiral transition for nonzero magnetic fields $B$. At the physical point, the two transitions seem to coincide for field strengths up to $|qB|\approx 5m_π^2$ whereafter they split. The splitting between the two increases as a function of $B$ in both the chiral limit and at the p…
The entanglement extended Polyakov--Nambu--Jona-Lasinio model at zero chemical potential in the presence of an external magnetic field is studied. The effect of the entanglement parametrization is analyzed, in particular, on the pseudocritical transition temperatures and on the thermodynamical properties of the model. The model predicts that the coincidence or not of both chiral and deconfinement transition temperatures, in the presence of an external magnetic field, depends on the entanglement parametrization chosen.
