We formulate the Polyakov-Nambu-Jona-Lasinio (PNJL) model in 0+1 dimensions. The thermodynamics captured by the partition function yields a bulk pressure, as well as quark susceptibilities versus temperature that are similar to the ones in 3+1 dimensions. Around the transition temperature the behavior in the pressure and quark susceptibilities follows from the interplay between the lowest Matsubara frequency and the Polyakov line. The reduction to the lowest Matsubara frequency yields a matrix Model. In the presence of the Polyakov line the UV part of the Dirac spectrum features oscillations when close to the transition temperature.
Quark number susceptibilities at finite quark chemical potential are investigated in the framework of the Polyakov-loop-extended Nambu Jona-Lasinio (PNJL) model. A detailed comparison is performed between the available lattice data, extrapolated using a Taylor expansion around vanishing chemical potential, and PNJL results consistently obtained from a Taylor series truncated at the same order. The validity of the Taylor expansion is then examined through a comparison between the full and truncated PNJL model calculations.
An improved version of the PNJL model is used to calculate various thermodynamical quantities, {\it viz.}, quark number susceptibility, isospin susceptibility, specific heat, speed of sound and conformal measure. Comparison with Lattice data is found to be encouraging.
The Monte-Carlo method is applied to the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. This leads beyond the saddle-point approximation in a mean-field calculation and introduces fluctuations around the mean fields. We study the impact of fluctuations on the thermodynamics of the model, both in the case of pure gauge theory and including two quark flavors. In the two-flavor case, we calculate the second-order Taylor expansion coefficients of the thermodynamic grand canonical partition function with respect to the quark chemical potential and present a comparison with extrapolations …
We present some results pertaining quantities which are regarded as good indicators of the pseudo-critical temperatures for the deconfinement and partial chiral restoration transitions using a polynomial form for the Polyakov potential part and an extended version of the NJL model which includes 6 and 8 quark interaction terms. Some comparisons with results from the lattice formulation of QCD (lQCD) are performed and results for the location of the critical endoint in the phase diagram are also presented. It is shown that the comparison with lQCD results favors a moderately strong OZI-violatin…
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 have investigated the fluctuations and the higher order susceptibilities of quark number, isospin number, electric charge and strangeness at vanishing chemical potential for 2+1 flavor Polyakov loop extended Nambu--Jona-Lasinio model. The calculations are performed for the bound effective potential in the quark sector requiring up to eight quark interaction terms. These have been contrasted to the lattice results which currently have somewhat heavier quarks in the light flavor sector. The results show sufficient qualitative agreement. For comparison we also present the results obtained with…
We present the Taylor expansion coefficients of the pressure in quark number chemical potential $μ_0=μ_B / 3=μ_u=μ_d$, for the strongly interacting matter as described by the PNJL model for two light degenerate flavours of quarks u and d. The expansion has been done upto eighth order in $μ_0$, and the results are consistent with recent estimates from Lattice. We have further obtained the specific heat $C_V$, squared speed of sound $v_s^2$ and the conformal measure $\cC$.
The magnetic susceptibility of the QCD vacuum is analyzed in the framework of a nonlocal SU(3) Polyakov-Nambu-Jona-Lasinio model. Considering two different model parametrizations, we estimate the values of the $u$ and $s$-quark tensor coefficients and magnetic susceptibilities and then we extend the analysis to finite temperature systems. Our numerical results are compared to those obtained in other theoretical approaches and in lattice QCD calculations.
We have extended the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavours to include the isospin chemical potential ($μ_I$). All the diagonal and mixed derivatives of pressure with respect to the quark number (proportional to baryon number) chemical potential ($μ_0$) and isospin chemical potential upto sixth order have been extracted at $μ_0 = μ_I = 0$. These derivatives give the generalized susceptibilities with respect to quark and isospin numbers. Similar estimates for the flavour diagonal and off-diagonal susceptibilities are also presented. Comparison to Lattice QCD (LQCD)…
We extend the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavours by including the effect of the SU(3) measure with a Van der Monde (VdM) term. This ensures that the Polyakov loop always remains in the domain [0,1]. The pressure, energy density, specific heat, speed of sound and conformal measure show small or negligible effects from this term. However various quark number and isospin susceptibilities are all found to approach their respective ideal gas limits around 2 $T_c$. We compare our methods with other similar approaches in PNJL model and also present a quantitative com…
The QCD transition from a hadronic to a quark-gluon plasma phase is a cross-over at vanishing/small baryo-chemical potential, while at higher chemical potentials it is argued that it becomes of first order, ending with a critical end-point. The present goal is the determination of the critical line and, possibly, the recognition of the critical endpoint. For this purpose, the effective model (Nambu-Jona-Lasinio model with Polyakov Loop) with 2+1 flavours is used. In Mean Field Approximation it is possible to obtain all thermodynamic quantities (pressure, entropy, energy and quark density) and …
We calculate the 2nd and 4th order quark number susceptibilities at zero baryochemical potential, using a PNJL approach and an approach which includes, in a single model, quark and hadronic degrees of freedom. We observe that the susceptibilities are very sensitive to possible quark-quark vector interactions. Compared to lattice data our results suggest that above $T_c$ any mean field type of repulsive vector interaction can be excluded from model calculations. Below $T_c$ our results show only very weak sensitivity on the strength of the quark and hadronic vector interaction. The best descrip…
Finite-Size Effects on the Critical End Point of Magnetized Quark Matter in the Nonlocal PNJL Model
Universidade Federal do ABC（圣保罗联邦大学ABC分校）；Comisión Nacional de Energía Atómica（国家原子能委员会）；CONICET（国家科学研究委员会）；Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA)（天文与空间物理研究所）
Various thermodynamic quantities and the phase diagram of strongly interacting hot and dense magnetized quark matter are obtained with the $ 2 $-flavour Nambu-Jona-Lasinio model with Polyakov loop considering finite values of the anomalous magnetic moment (AMM) of the quarks. Susceptibilities associated with constituent quark mass and traced Polyakov loop are used to evaluate chiral and deconfinement transition temperatures. It is found that, inclusion of the AMM of the quarks in presence of the background magnetic field results in a substantial decrease in the chiral as well as deconfinement …
QCD thermodynamics is studied using a model which combines Polyakov loop dynamics with spontaneous chiral symmetry breaking and its restoration (the PNJL model). The input is fixed entirely by pure-gauge lattice QCD results and by pion properties in vacuum. Successful comparisons with results from thermal lattice QCD are achieved, including extrapolations to finite quark chemical potential. The phase diagram and selected susceptibilities for two quark flavors are investigated with inclusion of diquark degrees of freedom.
The pressure of hot QCD has recently been determined to the last perturbatively computable order g^6 ln(g) by Kajantie et al. using three-dimensional effective theories. A similar method is applied here to the pressure in the presence of small but non-vanishing quark chemical potentials, and the result is used to derive the quark number susceptibilities in the limit mu = 0. The diagonal quark number susceptibility of QCD with n_f flavours of massless quarks is evaluated to order g^6ln(g) and compared with recent lattice simulations. It is observed that the results qualitatively resemble the la…
We evaluate the second and fourth order quark number susceptibilities in hot QCD using two variations of resummed perturbation theory. On one hand, we carry out a one-loop calculation within hard-thermal-loop perturbation theory, and on the other hand perform a resummation of the four-loop finite density equation of state derived using a dimensionally reduced effective theory. Our results are subsequently compared with recent high precision lattice data, and their agreement thoroughly analyzed.
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
Building on the experience of [1], we develop a formalism to construct operators for higher derivatives of the pressure in hot QCD with respect to the quark chemical potential $μ$. We provide formulae for the operators up to the sixth derivative, and obtain continuum-extrapolated results from lattice EQCD at zero and finite $μ$ and at six different pairs of temperature T and number of massless quark flavors $n_f$. Our data is benchmarked against full-QCD lattice and perturbative results, allowing to judge the quality of the perturbative series expansion in EQCD and the dimensional reduction pr…
Effects of a uniform (electro-) magnetic background field are investigated in the two-flavor nonlocal Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. Temperature-dependences of the chiral order-parameter and the Polyakov-loop are investigated under the magnetic field. In the nonlocal PNJL model with four-dimensional momentum dependent distribution function, pseudo-critical temperatures of the chiral and deconfinement transitions are coincident each other even if the magnetic field is strong. It means that we can check the reliability of the distribution function under the strong magne…
We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of …
Renormalization of meson susceptibilities and RG-invariant symmetry ratios in QCD
National Taiwan Normal University（台湾师范大学）；Academia Sinica（中央研究院）；National Taiwan University（台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
We investigate the phase structure of SU(3) gauge theory in four and five dimensions with one compact dimension by using perturbative one-loop and PNJL-model-based effective potentials, with emphasis on spontaneous gauge symmetry breaking. When adjoint matter with the periodic boundary condition is introduced, we have rich phase structure in the quark-mass and compact-size space with gauge-symmetry-broken phases, called the $SU(2)\times U(1)$ split and the $U(1)\times U(1)$ re-confined phases. Our result is qualitatively consistent with the recent lattice calculations. When fundamental quarks …
