Pion and kaon condensations in three-flavor random matrix theory

Arai, Ryoichi; Yoshinaga, N.

doi:10.1103/physrevd.78.094014

“…Although lattice simulations are hindered when dealing with finite chemical potential, due to the "sign" problem, this can in principle be handled with the situation of finite isospin chemical potential [13,14]. Furthermore, the phase structure has also been investigated in many low-energy effective models, such as ladder QCD [15], the random matrix method [16,17], the quark-meson model [18,19] and the Nambu-Jona-Lasinio (NJL) model [20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation *

Wu

¹

,

Ping

²

,

Zong

³

2021

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The self-consistent mean field approximation of the two-flavor NJL model, with a free parameter to reflect the competition between the "direct" channel and the "exchange" channel, is employed to study the QCD phase structure at finite isospin chemical potential , finite baryon chemical potential and finite temperature T, and especially to study the location of the QCD critical point. Our results show that in order to match the corresponding lattice results of isospin density and energy density, the contributions of the "exchange" channel need to be considered in the framework of the NJL model, and a weighting factor should be taken. It is also found that for fixed isospin chemical potentials, the lower temperature of the phase transition is obtained with increasing in the plane, and the largest difference of the phase transition temperature with different 's appears at . At the temperature of the QCD critical end point (CEP) decreases with increasing , while the critical baryon chemical potential increases. At high isospin chemical potential ( MeV), the temperature of the QCD tricritical point (TCP) increases with increasing , and in the low temperature regions the system will transition from the pion superfluidity phase to the normal phase as increases. At low density, the critical temperature of the QCD phase transition with different 's rapidly increases with at the beginning, and then increases smoothly around MeV. In the high baryon density region, the increase of the isospin chemical potential will raise the critical baryon chemical potential of the phase transition.

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“…Nevertheless, at finite baryon density lattice simulations are hindered by the sign problem [17] and there is no problem for lattice simulations at finite isospin density in principle [18]. Beside that, there are lots of low-energy effective models, such as chiral perturbation theory [14,19], random matrix method [20,21] and Nambu-Jona-Lasinio (NJL) model [22][23][24][25], to be used as tools to investigate the phase structures in isospin matter, in which NJL model described the chiral dynamics of QCD well [26].…”

Section: Introductionmentioning

confidence: 99%

Contributions of the vector-channel at finite isospin chemical potential with the self-consistent mean field approximation

Wu

¹

,

Shi

²

,

Ping

³

et al. 2020

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The self-consistent mean field approximation of two-flavor NJL model, which introduces a free parameter α (α reflects the weight of different interaction channels), is employed to investigate the contributions of the vector-channel at finite isospin chemical potential µI and zero baryon chemical potential µB and zero temperature T . The calculations show that the consideration of the vectorchannel contributions leads to lower value of pion condensate in superfluid phase, compared with the standard Lagrangian of NJL model (α = 0). In superfluid phase, we also obtain lower isospin number density, and the discrepancy is getting larger with the increase of isospin potential. Compared with the recent results from Lattice QCD, the isospin density and energy density we obtained with α = 0.5 agree with the data of lattice well. In the phase diagram in the T − µI plane for µB = 0, we can see that the difference of the critical temperatures of phase transition between the results with α = 0 and α = 0.5 is up to 3% − 5% for a fixed isospin potential. All of these indicate that the vector channels play an important role in isospin medium.

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“…Although lattice simulation are hindered by the "sign" problem when dealing with finite chemical potential, it can in principle deal with the problem of finite isospin chemical potential [13,14]. Furthermore, there are a lot of low-energy effective models, such as the chiral perturbation theory [10,15], random matrix method [16,17], quark-meson model [18,19] and Nambu-Jona-Lasinio (NJL) model [20][21][22][23], to be used as tools to investigate the phase structures in isospin and baryon matter, in which the NJL model describes the chiral dynamics of QCD well [24].…”

Section: Introductionmentioning

confidence: 99%

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

Wu,

Ping,

Zong

2020

Preprint

0

View full text Add to dashboard Cite

The self-consistent mean field approximation of two-flavor NJL model with introducing a free parameter α to reflect the competition between "direct" channel and the "exchange" channel, is employed to study QCD phase structure at finite isospin chemical potential µI , finite baryon chemical potential µB and finite temperature T , especially the location of the QCD critical point. It is found that, for fixed isospin chemical potentials the lower temperature of phase transition is obtained with α increasing in the T − µI plane, and the largest difference of the phase transition temperature with different α's appears at µI ∼ 1.5mπ. At µI = 0 the temperature of the QCD critical end point (CEP) decreases with α increasing, while the critical baryon chemical potential increases. At high isospin chemical potential (µI = 500 MeV), the temperature of the QCD tricritical point (TCP) increases with α increasing, and in the regions of low temperature the system will transit from pion superfluidity phase to the normal phase as µB increases. At low temperatures, the critical temperature of QCD phase transition with different α's rapidly increases with µI at the beginning, and then increases smoothly around µI > 300 MeV. In high baryon density region, the increase of the isospin chemical potential will raise the critical baryon chemical potential of phase transition.

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Pion and kaon condensations in three-flavor random matrix theory

Cited by 6 publications

References 24 publications

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation *

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation *

Contributions of the vector-channel at finite isospin chemical potential with the self-consistent mean field approximation

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

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