Chiral phase transition within effective models with constituent quarks

Scavenius, O.; Mócsy, Ágnes; Mishustin, I. N.; Rischke, Dirk H.

doi:10.1103/physrevc.64.045202

Cited by 359 publications

(501 citation statements)

References 21 publications

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“…A common approximation in the QM model is to neglect the quantum and thermal fluctuations of the mesons, which is equivalent to the large-N c limit. One hopes that the contributions from the quarks include the most important effects [4,54]. In this paper, we will apply this approximation and defer the use of more sophisticated methods to a subsequent paper [66].…”

Section: Thermodynamics and Numerical Resultsmentioning

confidence: 99%

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Chiral transition in a magnetic field and at finite baryon density

Andersen

Khan

2012

Phys. Rev. D

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We consider the quark-meson model with two quark flavors in a constant external magnetic field B at finite temperature T and finite baryon chemical potential µB. We calculate the full renormalized effective potential to one-loop order in perturbation theory. We study the system in the largeNc limit, where we treat the bosonic modes at tree level. It is shown that the system exhibits dynamical chiral symmetry breaking, i. e. that an arbitrarily weak magnetic field breaks chiral symmetry dynamically, in agreement with earlier calculations using the NJL model. We study the influence on the phase transition of the fermionic vacuum fluctuations. For strong magnetic fields, |qB| ∼ 5m 2 π and in the chiral limit, the transition is first order in the entire µB − T plane if vacuum fluctuations are not included and second order if they are included. At the physical point, the transition is a crossover for µB = 0 with and without vacuum fluctuations.

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Section: Thermodynamics and Numerical Resultsmentioning

confidence: 99%

“…Since we have quark degrees of freedom, we can couple the model to a baryon chemical potential µ B and study finite-density effects. The QM model has been used to study various aspects of the chiral transition at µ B = 0 [3][4][5][6][7] and µ B = 0 [8][9][10]. Schwinger-Dyson equations were used in [12].…”

Section: Introductionmentioning

confidence: 99%

Chiral transition in a magnetic field and at finite baryon density

Andersen

Khan

2012

Phys. Rev. D

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“…The main difference between the two models is thus that the NJL model has no kinetic terms and no quartic terms for the meson fields. In mean-field approximation the meson fields are treated as classical and replaced by their expectation values, neglecting both thermal and quantum fluctuations [76,77]. As in the NJL model, we assume these mean fields to be time independent but, in order to allow for inhomogeneous phases, we retain their dependence on the spatial coordinate x.…”

Section: Mean-field Thermodynamic Potentialmentioning

confidence: 99%

Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

234

258

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The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal's pion condensation, but recently received new momentum through studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg-Landau analyses as well as in specific calculations, both within effective models and in Dyson-Schwinger or large-N c approaches to QCD. Questions about the most favored shape of the modulations and its dimension, and about the effects of nonzero isospin chemical potential, strange quarks, color superconductivity, and external magnetic fields on these inhomogeneous phases will be addressed as well.

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“…The mechanism of chiral symmetry breaking and the study of the dynamics of phase conversion after a temperaturedriven chiral transition can be done conveniently within lowenergy effective models [1][2][3][4][5][6][7][8][9]. In particular, to study the mechanisms of bubble nucleation and spinodal decomposition in a hot expanding plasma [10], it is common to adopt the linear σ-model coupled to quarks [11].…”

Section: Abstract: Chiral Symmetry Breakingmentioning

confidence: 99%

“…This kind of effective potential is commonly used as the coarse-grained thermodynamic potential in a phenomenological description of the chiral transition for an expanding quarkgluon plasma [3][4][5][6].…”

Section: Now We Expandmentioning

confidence: 99%

Nucleation in the chiral transition with an inhomogeneous background

Taketani¹,

Fraga²

2007

Braz. J. Phys.

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We consider an approximation procedure to evaluate the finite-temperature one-loop fermionic density in the presence of a chiral background field which systematically incorporates effects from inhomogeneities in the chiral field through a derivative expansion. Modifications in the effective potential and their consequences for the bubble nucleation process are discussed. Keywords: Chiral symmetry breakingThe mechanism of chiral symmetry breaking and the study of the dynamics of phase conversion after a temperaturedriven chiral transition can be done conveniently within lowenergy effective models [1][2][3][4][5][6][7][8][9]. In particular, to study the mechanisms of bubble nucleation and spinodal decomposition in a hot expanding plasma [10], it is common to adopt the linear σ-model coupled to quarks [11]. The gas of quarks provides a thermal bath in which the long-wavelength modes of the chiral field evolve, and the latter plays the role of an order parameter in a Landau-Ginzburg approach to the description of the chiral phase transition. The standard procedure is then integrating over the fermionic degrees of freedom, using a classical approximation for the chiral field, to obtain a formal expression for the thermodynamic potential from which one can obtain all the physical quantities of interest.To compute correlation functions and thermodynamic quantities, one has to evaluate the fermionic determinant that results from the functional integration over the quark fields within some approximation scheme. Usually one performs a standard one-loop calculation assuming a homogeneous and static background field [12]. Nevertheless, for a system that is in the process of phase conversion after a chiral transition, one expects inhomogeneities in the chiral field configuration due to fluctuations to play a major role in driving the system to the true ground state. In fact, for high-energy heavy ion collisions, hydrodynamical studies have shown that significant density inhomogeneities may develop dynamically when the chiral transition to the broken symmetry phase takes place [6], and inhomogeneities generated during the late stages of the nonequilibrium evolution of the order parameter might leave imprints on the final spatial distributions and even on the integrated, inclusive abundances [13].In this paper we briefly describe an approximation procedure to evaluate the finite-temperature fermionic density in the presence of a chiral background field, which systematically incorporates effects from inhomogeneities in the bosonic field through a gradient expansion. (For details, see Ref. [14].) The method is valid for the case in which the chiral field varies smoothly, and allows one to extract information from its long-wavelength behavior, incorporating corrections order by order in the derivatives of the field. For simplicity, we ignore corrections coming from bosonic fluctuations in what follows. Those would result in a bosonic determinant correction to the effective potential [15]. To focus on the effect of an inhomogeneou...

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Chiral phase transition within effective models with constituent quarks

Cited by 359 publications

References 21 publications

Chiral transition in a magnetic field and at finite baryon density

Chiral transition in a magnetic field and at finite baryon density

Inhomogeneous chiral condensates

Nucleation in the chiral transition with an inhomogeneous background

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