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24 pages, 641 KiB

Open AccessArticle

Charged Pion Condensation in Dense Quark Matter: Nambu–Jona-Lasinio Model Study

by Tamaz Khunjua, Konstantin Klimenko and Roman Zhokhov

Symmetry 2019, 11(6), 778; https://doi.org/10.3390/sym11060778 - 11 Jun 2019

Cited by 17 | Viewed by 2647

In this short review we tried to give an outline of investigations of charged pion condensation (PC) in dense baryonic (quark) matter in the framework of effective Nambu–Jona-Lasinio (NJL)-type models. The possibility of charged PC phase in dense quark matter with isospin asymmetry [...] Read more.

In this short review we tried to give an outline of investigations of charged pion condensation (PC) in dense baryonic (quark) matter in the framework of effective Nambu–Jona-Lasinio (NJL)-type models. The possibility of charged PC phase in dense quark matter with isospin asymmetry is investigated. First, it is demonstrated that this phase can be realized in the framework of massless NJL model. However, the existence of this phase is enormously fragile to the values of current quark mass and we show that charged PC phase is forbidden in electrically neutral dense quark matter with

β

-equilibrium when current quark masses are close to their physical value of 5.5 MeV. Nevertheless, then it is shown that in real physical systems there could be conditions promoting the appearance of charged PC phenomenon in dense quark matter; specifically, it was shown that if one takes into consideration the fact that system can have finite size, then a dense charged PC phase can be realized there. It was also demonstrated that the possibility of inhomogeneous pion condensate might allow this phase to appear. In addition, more recently it was revealed that there is another interesting factor that can induce a charged PC phase in dense quark matter even without isospin imbalance. It is a chiral imbalance of the system (non-zero difference between densities of left- and right-handed quarks). These results can be interesting in heavy ion collision experiments, where it is expected to get high baryon densities. It is of interest also in the context of neutron stars, where quark matter might be realized in the core and very high baryon and isospin densities are attained. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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32 pages, 471 KiB

Open AccessFeature PaperArticle

Mean-Field Expansion, Regularization Issue, and Multi-Quark Functions in Nambu–Jona-Lasinio Model

by Aydan A. Garibli, Rauf G. Jafarov and Vladimir E. Rochev

Symmetry 2019, 11(5), 668; https://doi.org/10.3390/sym11050668 - 14 May 2019

Cited by 11 | Viewed by 2142

Abstract

In this paper, the results of the investigation of multi-quark equations in the Nambu–Jona-Lasinio (NJL) model in the mean-field expansion are presented. The multi-quark functions have been considered up to the third order of expansion. One of the purposes of our computations is [...] Read more.

In this paper, the results of the investigation of multi-quark equations in the Nambu–Jona-Lasinio (NJL) model in the mean-field expansion are presented. The multi-quark functions have been considered up to the third order of expansion. One of the purposes of our computations is the study of corrections of higher orders to parameters of the model. The important problem of the application of the NJL model is regularization. We compare the NJL model with 4-dimensional cutoff regularization and the dimensionally analytical regularization. We also discuss so-called “predictive regularization” in the NJL model, and a modification of this regularization, which is free of the Landau pole, is proposed. To calculate the high-order corrections, we use the Legendre transform method in the framework of bilocal-source formalism, which allows one effectively to take into consideration the symmetry constraints. A generalization of the mean-field expansion for other types of multi-quark sources is also discussed. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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22 pages, 349 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Imaginary Chemical Potential, NJL-Type Model and Confinement–Deconfinement Transition

by Kouji Kashiwa

Symmetry 2019, 11(4), 562; https://doi.org/10.3390/sym11040562 - 18 Apr 2019

Cited by 13 | Viewed by 2819

Abstract

In this review, we present of an overview of several interesting properties of QCD at finite imaginary chemical potential and those applications to exploring the QCD phase diagram. The most important properties of QCD at a finite imaginary chemical potential are the Roberge–Weiss [...] Read more.

In this review, we present of an overview of several interesting properties of QCD at finite imaginary chemical potential and those applications to exploring the QCD phase diagram. The most important properties of QCD at a finite imaginary chemical potential are the Roberge–Weiss periodicity and the transition. We summarize how these properties play a crucial role in understanding QCD properties at finite temperature and density. This review covers several topics in the investigation of the QCD phase diagram based on the imaginary chemical potential. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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31 pages, 1579 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Phase Diagram, Scalar-Pseudoscalar Meson Behavior and Restoration of Symmetries in (2 + 1) Polyakov-Nambu-Jona-Lasinio Model

by Pedro Costa and Renan Pereira

Symmetry 2019, 11(4), 507; https://doi.org/10.3390/sym11040507 - 08 Apr 2019

Cited by 10 | Viewed by 2765

Abstract

We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2 + 1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the (

T, μ_{B})

-plane, with its isentropic trajectories, paying [...] Read more.

We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2 + 1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the (

T, μ_{B})

-plane, with its isentropic trajectories, paying special attention to the chiral critical end point (CEP). Chiral and deconfinement transitions are examined. The modifications of mesonic observables in the medium are explored as a tool to analyze the effective restoration of chiral symmetry for different regions of the phase diagram. It is shown that the meson masses, namely that of the kaons, change abruptly near the CEP, which can be relevant for its experimental search. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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14 pages, 2572 KiB

Open AccessArticle

Solving the Gap Equation of the NJL Model through Iterations: Unexpected Chaos

by Angelo Martínez and Alfredo Raya

Symmetry 2019, 11(4), 492; https://doi.org/10.3390/sym11040492 - 04 Apr 2019

Cited by 3 | Viewed by 2798

Abstract

We explore the behavior of the iterative procedure to obtain the solution to the gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily large values of the coupling constant and in the presence of a magnetic field and a thermal bath. We find [...] Read more.

We explore the behavior of the iterative procedure to obtain the solution to the gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily large values of the coupling constant and in the presence of a magnetic field and a thermal bath. We find that the iterative procedure shows a different behavior depending on the regularization scheme used. It is stable and very accurate when a hard cut-off is employed. Nevertheless, for the Paul-Villars and proper time regularization schemes, there exists a value of the coupling constant (different in each case) from where the procedure becomes chaotic and does not converge any longer. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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20 pages, 661 KiB

Open AccessArticle

Four-Fermion Interaction Model on ℳ^D−1 ⊗ S¹

by Tomohiro Inagaki, Yamato Matsuo and Hiromu Shimoji

Symmetry 2019, 11(4), 451; https://doi.org/10.3390/sym11040451 - 01 Apr 2019

Cited by 6 | Viewed by 2215

Abstract

Four-fermion interaction models are often used as simplified models of interacting fermion fields with the chiral symmetry. The chiral symmetry is dynamically broken for a larger four-fermion coupling. It is expected that the broken symmetry is restored under extreme conditions. In this paper, [...] Read more.

Four-fermion interaction models are often used as simplified models of interacting fermion fields with the chiral symmetry. The chiral symmetry is dynamically broken for a larger four-fermion coupling. It is expected that the broken symmetry is restored under extreme conditions. In this paper, the finite size effect on the chiral symmetry breaking is investigated in the four-fermion interaction model. We consider the model on a flat spacetime with a compactified spatial coordinate,

M^{D - 1} \otimes S^{1}

and obtain explicit expressions of the effective potential for arbitrary spacetime dimensions in the leading order of the

1 / N

expansion. Evaluating the effective potential, we show the critical lines which divide the symmetric and the broken phase and the sign-flip condition for the Casimir force. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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18 pages, 443 KiB

Open AccessArticle

Effects of Hadron-Quark Phase Transitions in Hybrid Stars within the NJL Model

by Ignacio Francisco Ranea-Sandoval, Milva Gabriela Orsaria, Germán Malfatti, Daniela Curin, Mauro Mariani, Gustavo Aníbal Contrera and Octavio Miguel Guilera

Symmetry 2019, 11(3), 425; https://doi.org/10.3390/sym11030425 - 22 Mar 2019

Cited by 11 | Viewed by 2495

Abstract

We study local and non-local Polyakov Nambu-Jona-Lasinio models and analyze their respective phase transition diagram. We construct hybrid stars using the zero temperature limit of the local and non-local versions of Nambu-Jona-Lasinio model for quark matter and the modern GM1(L) parametrization of the [...] Read more.

We study local and non-local Polyakov Nambu-Jona-Lasinio models and analyze their respective phase transition diagram. We construct hybrid stars using the zero temperature limit of the local and non-local versions of Nambu-Jona-Lasinio model for quark matter and the modern GM1(L) parametrization of the non-linear relativistic mean field model for hadronic matter. We compare our models with data from PSR J1614-2230 and PSR J0343+0432 and also from GW170817 and its electromagnetic counterpart GRB170817A and AT2017gfo. We study observational signatures of the appearance of a mixed phase as a result of modeling a phase transition that mimics the Gibbs formalism and compare the results with the sharp first-order phase transition obtained using the Maxwell construction. We also study in detail the g-mode associated with discontinuities in the equation of state, and calculate non-radial oscillation modes using relativistic Cowling approximation. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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20 pages, 732 KiB

Open AccessArticle

Nonextensive Quasiparticle Description of QCD Matter

by Jacek Rożynek and Grzegorz Wilk

Symmetry 2019, 11(3), 401; https://doi.org/10.3390/sym11030401 - 19 Mar 2019

Cited by 7 | Viewed by 1970

Abstract

The dynamics of QCD matter is often described using effective mean field (MF) models based on Boltzmann–Gibbs (BG) extensive statistics. However, such matter is normally produced in small packets and in violent collisions where the usual conditions justifying the use of BG statistics [...] Read more.

The dynamics of QCD matter is often described using effective mean field (MF) models based on Boltzmann–Gibbs (BG) extensive statistics. However, such matter is normally produced in small packets and in violent collisions where the usual conditions justifying the use of BG statistics are not fulfilled and the systems produced are not extensive. This can be accounted for either by enriching the original dynamics or by replacing the BG statistics by its nonextensive counterpart described by a nonextensivity parameter

q \neq 1

(for

q \to 1

, one returns to the extensive situation). In this work, we investigate the interplay between the effects of dynamics and nonextensivity. Since the complexity of the nonextensive MF models prevents their simple visualization, we instead use some simple quasi-particle description of QCD matter in which the interaction is modeled phenomenologically by some effective fugacities, z. Embedding such a model in a nonextensive environment allows for a well-defined separation of the dynamics (represented by z) and the nonextensivity (represented by q) and a better understanding of their relationship. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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Review

Jump to: Research

29 pages, 1151 KiB

Open AccessFeature PaperReview

Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems

by Ryosuke Yoshii and Muneto Nitta

Symmetry 2019, 11(5), 636; https://doi.org/10.3390/sym11050636 - 06 May 2019

Cited by 8 | Viewed by 2565

Abstract

We review various connections between condensed matter systems with the Nambu–Jona-Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Recent findings of a duality between the Nambu–Jona-Lasinio model [...] Read more.

We review various connections between condensed matter systems with the Nambu–Jona-Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Recent findings of a duality between the Nambu–Jona-Lasinio model and nonlinear sigma models enables us to investigate various properties underlying both theories. In this review, we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu–Jona-Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in nonlinear sigma models owing to the duality. The recent progress on interacting systems in finite systems is also reviewed. Full article

(This article belongs to the Special Issue Nambu-Jona-Lasinio model and its applications)

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