Thermodynamics of the Polyakov-Nambu-Jona-Lasinio model with nonzero baryon and isospin chemical potentials

Mukherjee, Swagato; Mustafa, Munshi G.; Ray, Rajarshi

doi:10.1103/physrevd.75.094015

Cited by 143 publications

(124 citation statements)

References 93 publications

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“…It has often been shown to reproduce many general features of lattice results at µ B = 0 [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, Email address: steinheimer@th.physik.uni-frankfurt.de (J. Steinheimer) 4, 18,19,20,21,22,23,24,25,26,27,28]. In our comparison we will use a very basic parametrization of the two-flavor PNJL model and extend it to incorporate a repulsive vector interaction.…”

Section: The Pnjl Modelmentioning

confidence: 99%

The problem of repulsive quark interactions – Lattice versus mean field models

Steinheimer

Schramm

2011

Physics Letters B

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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 description of lattice data around T c is obtained for a case of coexistence of hadronic and quark degrees of freedom .Many recent experimental programs in heavy ion physics, e.g. at the relativistic heavy ion collider and the planned FAIR facility, are aimed at a better understanding of bulk properties of QCD matter. In particular the experimental confirmation of the deconfinement and chiral phase transitions as well as the search for the critical end point (CeP) are of great interest to the community. Lattice results at µ B = 0 suggest that both phase transitions exhibit a smooth crossover. Suffering from the so called sign problem at finite baryo chemical potential, lattice studies have so far not been able to constitute a consistent picture of the phase diagram and the existence of the CeP [1,2]. While a Taylor expansion of lattice results at µ b = 0 predict the existence of a critical end point these results may strongly depend on the order to which the Taylor coefficients can be evaluated [3]. Lattice calculations at imaginary chemical potential on the other hand show no indication for a CeP, though these calculations are done on on a coarse lattice with a fermion action that is known to have large discretization errors. Other studies trying to locate the CeP often rely on the applicability of various effective models where CeP's existence and location seems very sensitive on the vector coupling strength at and below T c [4]. The PNJL modelThe PNJL model was introduced in [5,6] as an effective chiral quasi-quark model that incorporates a mean field like coupling to a color background field. It has often been shown to reproduce many general features of lattice results at µ B = 0 [7,

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Section: The Pnjl Modelmentioning

confidence: 99%

The problem of repulsive quark interactions – Lattice versus mean field models

Steinheimer

Schramm

2011

Physics Letters B

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“…One well-known difficulty is given by the so-called sign problem, which arises when dealing with finite real chemical potentials. Thus, it is worth to develop alternative approaches, such as the study of effective models that show consistency with lattice QCD results and can be extrapolated into regions not accessible by lattice techniques.One of these effective theories, proposed quite recently, is the so-called Polyakov-Nambu-JonaLasinio (PNJL) model [5][6][7][8][9][10][11], an extension of the well-known NJL model [12] in which quarks are coupled to the Polyakov loop (PL), providing a common framework to study both the chiral and deconfinement transitions. As a further improvement over the (local) PNJL model, extensions that include covariant non-local quark interactions have also been considered [13][14][15].…”

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Deconfinement and chiral restoration in non-local PNJL models at zero and imaginary chemical potential

2012

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We study the deconfinement and chiral restoration transitions in the context of non-local PNJL models, considering the impact of the presence of dynamical quarks on the scale parameter appearing in the Polyakov potential. We show that the corresponding critical temperatures are naturally entangled for both zero and imaginary chemical potential, in good agreement with lattice QCD results. We also analyze the Roberge Weiss transition, which is found to be first order at the associated endpoint.PACS numbers: 12.39. Ki, 11.30.Rd, 12.38.Mh The detailed understanding of the behavior of strongly interacting matter at finite temperature and baryon density represents an issue of great interest in particle physics [1]. From the theoretical point of view, this problem can be addressed through lattice QCD calculations [2-4], which have been significantly improved in the last years. However, this ab initio approach is not yet able to provide a full understanding of the QCD phase diagram. One well-known difficulty is given by the so-called sign problem, which arises when dealing with finite real chemical potentials. Thus, it is worth to develop alternative approaches, such as the study of effective models that show consistency with lattice QCD results and can be extrapolated into regions not accessible by lattice techniques.One of these effective theories, proposed quite recently, is the so-called Polyakov-Nambu-JonaLasinio (PNJL) model [5][6][7][8][9][10][11], an extension of the well-known NJL model [12] in which quarks are coupled to the Polyakov loop (PL), providing a common framework to study both the chiral and deconfinement transitions. As a further improvement over the (local) PNJL model, extensions that include covariant non-local quark interactions have also been considered [13][14][15]. The non-local character of the interactions arises naturally in the context of several successful approaches to low-energy quark dynamics, and leads to a momentum dependence in the quark propagator that can be made consistent [16] with lattice results. It has been shown [17][18][19][20] that non-local models

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“…Perturbative QCD cannot describe confinement and, although lattice QCD is able to reproduce successfully hadron properties, like masses and coupling constants [4], it has problems when dealing with finite baryon chemical potential (the sign problem). However, there are effective models which include explicitly confinement, as, for example, different versions of the bag model [5][6][7][8], Dyson-Schwinger models [9-13], or the Polyakov loop effective action coupled to DysonSchwinger or NJL models [14][15][16][17].The nonlocal NJL model (nNJL) is another attempt in this direction [18][19][20][21]. When the gluon degrees of freedom are integrated out in the QCD action, a nonlocal quark action emerges and confinement should be hidden there.…”

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confidence: 99%

Thermal nonlocal Nambu–Jona-Lasinio model in the real time formalism

Loewe

Morales²,

Villavicencio³

2011

Phys. Rev. D

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The real time formalism at finite temperature and chemical potential for the nonlocal NambuJona-Lasinio model is developed in the presence of a Gaussian covariant regulator. We construct the most general thermal propagator, by means of the spectral function. As a result, the model involves the propagation of massive quasiparticles. The appearance of complex poles is interpreted as a confinement signal, and, in this case, we have unstable quasiparticles with a finite decay width. An expression for the propagator along the critical line, where complex poles start to appear, is also obtained. A generalization to other covariant regulators is proposed. The Nambu-Jona-Lasinio model (NJL) has been vastly considered for studying nonperturbative aspects of QCD. Nowadays, it is mainly used to explore finite temperature and density effects in the frame of the mean-field approximation [1][2][3]. One of the big challenges in QCD is to understand the confinement mechanism and the dynamics behind confinement. Perturbative QCD cannot describe confinement and, although lattice QCD is able to reproduce successfully hadron properties, like masses and coupling constants [4], it has problems when dealing with finite baryon chemical potential (the sign problem). However, there are effective models which include explicitly confinement, as, for example, different versions of the bag model [5][6][7][8], Dyson-Schwinger models [9-13], or the Polyakov loop effective action coupled to DysonSchwinger or NJL models [14][15][16][17].The nonlocal NJL model (nNJL) is another attempt in this direction [18][19][20][21]. When the gluon degrees of freedom are integrated out in the QCD action, a nonlocal quark action emerges and confinement should be hidden there. The idea of the nNJL approach is to incorporate nonlocal vertices through the presence of appropriate regulators.Since the NJL model is nonrenormalizable, a momentum cutoff is needed in order to handle the UV divergences. The applicability of the model is, therefore, restricted to energy scales below the cutoff. Nonlocal extensions of the NJL model are designed to regularize the model in such a way that UV divergences are controlled, internal symmetries are preserved, and quark confinement is incorporated. The nNJL model has been extended to a finite temperature and density scenario [22][23][24][25][26][27][28][29][30][31][32] through the usual Matsubara formalism [33,34]. Here, nevertheless, the exact summation of Matsubara frequencies turns out to be cumbersome, due to the complicated shape of the regulators. In most cases, it is necessary to cut the series at some order.The idea of this work is to develop the finite temperature real time formalism for the nNJL model. In this way, we are able to calculate temperature corrections, providing a physical picture in terms of quasiparticles. On the one hand, those states with real masses can propagate freely in the deconfined phase. On the other hand, the existence of complex poles of the propagator in the confined phase produces a strong dam...

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Thermodynamics of the Polyakov-Nambu-Jona-Lasinio model with nonzero baryon and isospin chemical potentials

Cited by 143 publications

References 93 publications

The problem of repulsive quark interactions – Lattice versus mean field models

The problem of repulsive quark interactions – Lattice versus mean field models

Deconfinement and chiral restoration in non-local PNJL models at zero and imaginary chemical potential

Thermal nonlocal Nambu–Jona-Lasinio model in the real time formalism

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