THE EFFECT OF FINITE TEMPERATURE ON THE NUCLEON PROPERTIES IN THE EXTENDED LINEAR SIGMA MODEL

2012 ◽  
Vol 21 (06) ◽  
pp. 1250061 ◽  
Author(s):  
M. ABU-SHADY
Keyword(s):  
Finite Temperature ◽  
Sigma Model ◽  
Magnetic Moments ◽  
Mean Field ◽  
Field Approximation ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
Coupling Constant ◽  
Field Equations ◽  
Pion Nucleon

The extended quark sigma model, which includes higher-order mesonic interactions is applied at finite temperature. The field equations are solved using the mean-field approximation. Nucleon properties such as the nucleon mass, the magnetic moments of the proton and neutron, and the pion-nucleon coupling constant are examined as functions of temperature. The obtained results indicate that the deconfinement phase transition conditions are satisfied in the present work at higher values of temperature. A comparison with other models is presented.

EFFECT OF LOGARITHMIC MESONIC POTENTIAL ON NUCLEON PROPERTIES

2009 ◽  
Vol 24 (20) ◽  
pp. 1617-1629 ◽  
Author(s):  
M. ABU-SHADY
Keyword(s):  
Sigma Model ◽  
Mean Field ◽  
Field Approximation ◽  
Logarithmic Potential ◽  
Measured Data ◽  
Original Model ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
Field Equations

A linear sigma model with logarithmic mesonic potential is proposed for computing nucleon properties. The logarithmic potential is based on some aspects of QCD. The field equations have been solved in mean-field approximation. Obtained results for nucleon properties are good in comparison with the original model and agree with measured data.

THE DEPENDENCE OF THE NUCLEON MASS ON THE PION MASS IN THE EXTENDED QUARK SIGMA MODEL

2010 ◽  
Vol 19 (10) ◽  
pp. 2051-2062 ◽  
Author(s):  
M. ABU-SHADY
Keyword(s):  
Sigma Model ◽  
Pion Mass ◽  
Mean Field ◽  
Field Approximation ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
Nucleon Mass ◽  
Field Equations ◽  
Analytic Expressions ◽  
The Mean

The dependence of the nucleon mass on the pion mass is studied in the framework of the extended quark sigma model. We apply the modified quark sigma model to analyze the pion–nucleon sigma term. Analytic expressions are derived using the Feynman–Hellman theorem. The field equations are solved in the mean-field approximation. The results are compared with the CP-PACS group and the cloudy bag model. The results indicate that the extended linear sigma model provides good agreement compared to other models in the mean-field approximation.

QUARK AND SIGMA MASS DEPENDENCE OF NUCLEON PROPERTIES FROM LINEAR SIGMA MODEL

2011 ◽  
Vol 20 (06) ◽  
pp. 1509-1517 ◽  
Author(s):  
T. S. T. ALI
Keyword(s):  
Axial Vector ◽  
Mean Field ◽  
Field Approximation ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
Model Parameters ◽  
Coupling Constant ◽  
Field Equations ◽  
Vector Coupling ◽  
The Mean

The sensitivity of static nucleon properties (magnetic moment, axial-vector coupling constant gA, pion–nucleon coupling constant gπNN and sigma commutator term σπN) to the quark and sigma masses have been investigated in the mean-field approximation. We have solved the field equations in the mean-field approximation with different sets of model parameters. Good results have been obtained in comparison with the other models and experimental data.

EXTENDED LINEAR SIGMA MODEL IN HIGHER ORDER MESONIC INTERACTIONS

2006 ◽  
Vol 15 (01) ◽  
pp. 143-152 ◽  
Author(s):  
M. RASHDAN ◽  
M. ABU-SHADY ◽  
T. S. T. ALI
Keyword(s):  
Sigma Model ◽  
Mean Field ◽  
Field Approximation ◽  
Higher Order ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
Field Equations ◽  
The Mean ◽  
Better Than ◽  
Good Agreement

The Gell-Mann and Levy model, as well as the Birse and Banerjee model, describe quark interactions via the exchange of σ- and π-mesons. We extend these models to include higher order mesonic interactions. The field equations were solved in the mean-field approximation and good agreement with the data for nucleon properties was obtained. Our agreement is better than that obtained by the original model of Birse and Banerjee and by other models. This indicates the importance of including higher order meson correlations.

CHIRAL LOGARITHMIC QUARK MODEL OF N AND Δ WITH AN A-TERM IN THE MEAN-FIELD APPROXIMATION

2011 ◽  
Vol 26 (02) ◽  
pp. 235-249 ◽  
Author(s):  
M. ABU-SHADY
Keyword(s):  
Quark Model ◽  
Sigma Model ◽  
Magnetic Moments ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Spontaneous Breaking ◽  
Baryon State ◽  
Field Equations ◽  
The Mean

The A-term is included in the logarithmic quark sigma model, which is based on chiral symmetry and its spontaneous breaking. We investigate the consequences of this term and its relevance to baryon properties. The field equations have been solved in the mean-field approximation for the hedgehog baryon state. We found that including the A-term in the logarithmic quark model leads to lower energies of the nucleon and delta masses and reduces the values of the sigma commutator σπN(0), proton μp(N), and neutron μn(N) of the magnetic moments. This indicates that the inclusion of the A-term improves the calculated nucleon properties in comparison with previous work and other models.

scholarly journals Locating the critical end point using the linear sigma model coupled to quarks.

2018 ◽  
Vol 172 ◽  
pp. 02003
Author(s):  
Alejandro Ayala ◽  
J. A. Flores ◽  
L. A. Hernández ◽  
S. Hernández-Ortiz
Keyword(s):  
Sigma Model ◽  
Chemical Potential ◽  
Potential Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Baryon Density ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
End Point ◽  
The Mean

We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.

scholarly journals SU(3) Polyakov linear-sigma model with finite isospin asymmetry: QCD phase diagram

2019 ◽  
Vol 34 (31) ◽  
pp. 1950199 ◽  
Author(s):  
Abdel Nasser Tawfik ◽  
Abdel Magied Diab ◽  
M. T. Ghoneim ◽  
H. Anwer
Keyword(s):  
Phase Structure ◽  
Sigma Model ◽  
Chemical Potential ◽  
Mean Field ◽  
Field Approximation ◽  
Linear Sigma Model ◽  
Dense Medium ◽  
Mean Field Approximation ◽  
Isospin Asymmetry ◽  
Qcd Phase Diagram

The SU(3) Polyakov linear-sigma model (PLSM) in mean-field approximation is utilized in analyzing the chiral condensates [Formula: see text], [Formula: see text], [Formula: see text] and the deconfinement order parameters [Formula: see text], [Formula: see text], at finite isospin asymmetry. The bulk thermodynamics including pressure density, interaction measure, susceptibility and second-order correlations with baryon, strange and electric charge quantum numbers are studied in thermal and dense medium. The PLSM results are confronted to the available lattice quantum chromodynamics (QCD) calculations. The excellent agreement obtained strengthens the reliability of fixing the PLSM parameters and therefore supports further predictions even beyond the scope of the lattice QCD numerical applicability. From the QCD phase structure at finite isospin chemical potential [Formula: see text], we find that the pseudocritical temperatures decrease with the increase in [Formula: see text]. We conclude that the QCD phase structure in [Formula: see text] plane seems to extend the one in [Formula: see text] plane.

NUCLEON PROPERTIES FROM MODIFIED SIGMA MODEL

2007 ◽  
Vol 22 (14n15) ◽  
pp. 2673-2681 ◽  
Author(s):  
M. RASHDAN ◽  
M. ABU-SHADY ◽  
T. S. T. ALI
Keyword(s):  
Sigma Model ◽  
Mean Field ◽  
Field Approximation ◽  
Higher Order ◽  
Original Model ◽  
Mean Field Approximation ◽  
Field Equations ◽  
The Mean ◽  
Better Than ◽  
Good Agreement

Birse and Banerjee model is extended to include higher-order mesonic interactions. The field equations have been solved in the mean-field approximation and a good agreement with the data for the nucleon properties has been obtained. The agreement is better than that obtained by the original model of Birse and Banerjee which indicates the important of the inclusion of higher-order meson correlations.

Self-consistent approximations for field theories at finite temperature

1993 ◽  
Vol 71 (5-6) ◽  
pp. 285-294
Author(s):  
M. H. Thoma
Keyword(s):  
Finite Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Two Dimensions ◽  
Mean Field Approximation ◽  
Coupling Constant ◽  
Starting Point ◽  
Consistent Approximations ◽  
The Mean ◽  
Mean Field Approximations

Various mean field approximations at finite temperature are used for calculating ground state energies and propagators of the [Formula: see text] theory in two dimensions and quantum chromodynamics (QCD). In the case of the [Formula: see text] theory a symmetry restoration is observed above a critical coupling constant if a temperature independent renormalization is used. In the case of QCD the mean field approximation is insufficient but can be regarded as a starting point for more complicated approximations, which are discussed qualitatively.

scholarly journals SU(3) Polyakov linear-sigma model: Conductivity and viscous properties of QCD matter in thermal medium

2016 ◽  
Vol 31 (34) ◽  
pp. 1650175 ◽  
Author(s):  
Abdel Nasser Tawfik ◽  
Abdel Magied Diab ◽  
M. T. Hussein
Keyword(s):  
Lattice Qcd ◽  
Mean Field ◽  
Field Approximation ◽  
Linear Sigma Model ◽  
Dense Medium ◽  
Mean Field Approximation ◽  
Chiral Phase ◽  
Strange Quarks ◽  
Transition Formula ◽  
Thermal Medium

In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-[Formula: see text] model (PLSM) is analyzed for chiral phase transition, [Formula: see text] and [Formula: see text] and for deconfinement order-parameters, [Formula: see text] and [Formula: see text] of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates [Formula: see text]. All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modeling of the relaxation time is utilized in estimating the conductivity properties of the QCD matter in thermal medium, namely electric [Formula: see text] and heat [Formula: see text] conductivities. We found that the PLSM results on the electric conductivity and on the specific heat agree well with the available lattice QCD calculations. Also, we have calculated bulk and shear viscosities normalized to the thermal entropy, [Formula: see text] and [Formula: see text], respectively, and compared them with recent lattice QCD. Predictions for [Formula: see text] and [Formula: see text] are introduced. We conclude that our results on various transport properties show some essential ingredients, that these properties likely come up with, in studying QCD matter in thermal and dense medium.

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