Thermal behavior of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mtext mathvariant="normal">−</mml:mtext><mml:mi>π</mml:mi></mml:math>scattering lengths in the Nambu–Jona-Lasinio model

Loewe, M.; Ruiz, Alex; Rojas, J. C.

doi:10.1103/physrevd.78.096007

Cited by 9 publications

(5 citation statements)

References 19 publications

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“…From the three figures, it is clear that at a finite magnetic field, while a 0 0 decreases as a function of temperature, a 2 0 displays the opposite trend. It is interesting to remark that already the presence of a small magnetic field is sufficient to invert the temperature dependence at a zero magnetic field [33,35]. This effect can be explained by the symmetry of the scattering length parameters, where a 0 0 arises from the trace of the tensor, which is a scalar, whereas the isospin 2 channel corresponds to the most symmetric realization.…”

Section: Results and Conclusionmentioning

confidence: 99%

Thermomagnetic corrections to π−π scattering lengths in the linear sigma model

2019

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In this article, we extend our previous study of the π-π scattering lengths under the presence of an external magnetic field, including finite temperature effects. The novelty of this work is precisely the introduction of temperature into the discussion and its interplay with the magnetic field. As in the previous article, we base our analysis in the linear sigma model, and our calculations are exact within this context. Although the effects are comparatively small, it is interesting to remark that the magnetic field and temperature display opposite effects over the scattering lengths.

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Section: Results and Conclusionmentioning

confidence: 99%

Thermomagnetic corrections to π−π scattering lengths in the linear sigma model

2019

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“…Following [23], we will use two sets of parameters. Set I is given by qq = −(200 MeV) 3 , m = 10.5 MeV, G = 50 GeV −1 and Λ = 627 MeV. Set II is given by qq = −(220 MeV) 3 , m = 7.7…”

Section: Poles Of the Effective Quark Propagator With A Gaussian Regu...mentioning

confidence: 99%

“…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.…”

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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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“…Another attempt in this direction is the Nambu-Jona-Lasinio (NJL) model [12,13]. Although it was originally proposed as a model of interacting nucleons, the NJL model is now interpreted as model of interacting quarks and is vastly used to study thermal properties of QCD [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Unstable quasiparticles as a source of thermodynamic instabilities in the thermal nonlocal Nambu—Jona-Lasinio model

Márquez

2014

Phys. Rev. D

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It has already been shown that in thermal nonlocal Nambu-Jona-Lasinio models some unphysical behavior, such as a negative pressure, may arise. In this article, it is shown how this behavior can be related to the pressence of highly unstable poles of the propagator of the model, for both the Gaussian and Lorentzian regulators cases. Computations are carried out within the real time formalism, which allows to isolate the contributions from different poles and identify the source of these instabilities. It has also been shown in recent articles how these instabilities are softened by the inclusion of the Polyakov loop when a Gaussian regulator is considered. This article shows how the softening of instabilities can be understood by studying the effect of the Polyakov loop on the poles of the propagator for the Gaussian regulator.

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Thermal behavior ofπ−πscattering lengths in the Nambu–Jona-Lasinio model

Cited by 9 publications

References 19 publications

Thermomagnetic corrections to π−π scattering lengths in the linear sigma model

Thermomagnetic corrections to π−π scattering lengths in the linear sigma model

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

Unstable quasiparticles as a source of thermodynamic instabilities in the thermal nonlocal Nambu—Jona-Lasinio model

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