Quark Sigma Model Research Articles

Magnetic Catalysis in the Higher-Order Quark Sigma Model

The effect of the higher-order mesonic interactions is investigated on the chiral symmetry breaking in the presence of an external magnetic field. The effective of higher-order mesonic potential is employed and is numerically solved in the mean-field approximation. The chiral symmetry breaking increases with increasing magnetic field. Two sets of free parameterization are investigated on the magnetic catalysis. A comparison is discussed with the original sigma model and other studies. The obtained results are included that the higher-order mesonic interactions play an important role in the magnetic catalysis.

The effect of finite temperature and chemical potential on nucleon properties in the logarithmic quark sigma model

The logarithmic quark sigma model is applied to study the nucleon properties at finite temperature and chemical potential. The field equations have been solved numerically in the mean-field approximation by using the extended iteration method at finite temperature and baryon chemical potential. Baryon properties are investigated, such as the hedgehog mass, the magnetic moments of the proton and neutron, and the pion-nucleon coupling constant. We find that the hedgehog mass and the magnetic moments of the proton and neutron increase with increasing temperature and chemical potential, while the pion-nucleon coupling constant decreases. A comparison with the original sigma model and QCD sum rules is presented. We conclude that the logarithmic quark sigma model successfully describes baryon properties of a hot and dense medium.

The Chiral Quark-Sigma Model with Modified Logarithmic Potential for Nucleon Properties

A modified logarithmic mesonic potential which based on some aspects of quantum chromodynamics (QCD) theory is investigated. The modified logarithmic mesonic potential is far from the singularity point which comes at vanishing of pion and sigma-meson contributions ( σ2 +π2 = 0 ) . The field equations have been solved in the mean-field approximation using the iteration method. The obtained results of nucleon properties are improved in comparison with the original quark-sigma model and other models. In particular, the nucleon and delta masses, the pion-nucleon coupling constant, and the sigma term are in good agreement with experimental data. In addition, A comparison with the recent quark models such as the extended Skyrme model and the perturbative quark model is discussed. We conclude that the modified logarithmic quark model successfully predicts nucleon properties and avoid difficulty that found in the previous works.

Chiral logarithmic sigma model at finite temperature and baryonic chemical potential

A logarithmic potential is suggested to study the chiral phase transition, the critical temperature, and the meson masses at finite temperature and baryonic chemical potential. The logarithmic potential is based on some aspects of quantum chromodynamics (QCD) theory. The model has been solved in the mean-field approximation. We found that the behavior of meson masses takes a similar behavior as in the original sigma model and the Nambu–Jona-Lasinio model. The critical temperature is reduced in comparison with the original sigma model and it is in good agreement with recent lattice QCD results. The chiral phase transition is crossover in the case of chiral explicit breaking symmetry. The Goldstone boson theorem is studied, in which the meson mass is massive and pion mass is massless at lower temperatures. Our conclusions indicate to the present model successfully predicts the phase transition as well as in the original quark sigma model and the Nambu–Jona–Lasinio model. A new advantage of the present model, the critical temperature is in good agreement with lattice QCD results at zero chemical potential. A condition of spontaneous breaking symmetry is necessary to satisfy the Goldstone theorem in the chiral limit.

Nucleon Properties at Finite Temperature in the Extended Quark-Sigma Model

Hadron properties are studied at hot medium using the quark sigma model. The quark sigma model is extended to include eighth-order of mesonic interactions based on some aspects of quantum chromodynamic (QCD) theory. The extended effective potential tends to the original effective potential when the coupling between the higher order mesonic interactions equal to zero. The field equations have been solved in the mean-field approximation by using the extended iteration method. We found that the nucleon mass increases with increasing temperature and the magnetic moments of proton and neutron increase with increasing temperature. A comparison is presented with recent previous works and other models. We conclude that higher-order mesonic interactions play an important role in changing the behavior of nucleon properties at finite temperature. In addition, the deconfinement phase transition is satisfied in the present model.

The extended quark sigma model at finite temperature and baryonic chemical potential

An extended quark sigma model which includes higher-order mesonic interactions is studied at the ˇnite baryonic chemical potential uB and temperature T. Theeld equations have been solved in the mean-ˇeld approximation by using the modied iteration method atnite baryonic chemical potential uB and temperature T. The Goldstone theorem is satised below a critical temperature in the chiral limit for uB =0 . As expected from general universality, the chiral phase transition is second-order. By including the higher-order mesonic interactions, the critical temperature is reduced compared to that found in recent works and is in good agreement with lattice QCD results. The nucleon mass is examined in the (uB ,T ) plane, showing a strong dependence on uB and T. Wend that an increase in both the baryonic chemical potential uB and the temperature T leads to an increase in the values of the nucleon mass. This is evidence for the quarkAgluon deconnement phase transition at higher values of temperature. �·¥¤¸E ¢²¥´ · ¸I¨·¥´´ O ±¢ ·±μ¢ O ¸¨£³ -³μ¤¥ ²O, ¢±²OI OÐ O ¢§ ¨³μ¤¥°¸E¢¨O ³¥§μ´μ¢ ¢O¸- I¨I ¶μ·O¤±μ¢. Œμ¤¥²O · ¸¸³ E·¨¢ ¥E¸O ¸ ±μ´¥I´O³¨ i ·¨μ´´O³ I¨³¨I¥¸±¨³ ¶μE¥´I¨ ²μ³ uB ¨ E¥³¶¥· EE·μ° T. �μ²¥¢O¥ E· ¢´¥´¨O ·¥I OE¸O ¢ ¶·¨i²¨|¥´¨¨ ¸·¥¤´¥£μ ¶μ²O ¸ ¶μ³μÐOO ³μ¤¨- E¨I¨·μ¢ ´´μ£μ ³¥Eμ¤ ¨E¥· I¨° ¤²O ±μ´¥I´OI i ·¨μ´´μ£μ I¨³¨I¥¸±μ£μ ¶μE¥´I¨ ² uB ¨E ¥³¶¥- · EE·O T. '¥μ·¥³ ƒμ²¤¸EμE´ ¢O¶μ²´O¥E¸O ´¨|¥ ±·¨E¨I¥¸±μ° E¥³¶¥· EE·O ¢ ±¨· ²O´μ³ ¶·¥¤¥²¥ ¤²O uB =0 . ‚ ¸μμE¢¥E¸E¢¨¨ ¸ μ|¨¤ ´¨O³¨ μiÐ¥° E´¨¢¥·¸ ²O´μ¸E¨ ±¨· ²O´O° E §μ¢O° ¶¥·¥Iμ¤ ¢O¶μ²´O¥E¸O ¢μ ¢Eμ·μ³ ¶μ·O¤±¥. �·¨ EI¥E¥ ³¥§μ´´OI ¢§ ¨³μ¤¥°¸E¢¨° ¢O¸I¨I ¶μ·O¤±μ¢ ¢¥²¨I¨´ ±·¨E¨I¥¸±μ° E¥³¶¥· EE·O ¸´¨| ¥E¸O ¶μ ¸· ¢´¥´¨O ¸ ¢¥²¨I¨´ ³¨, ¶μ²EI¥´´O³¨ ¢ ´¥¤ ¢´μ μ¶E- i²¨±μ¢ ´´OI · iμE I, ¨ ´ I줨E¸O ¢ Iμ·μI¥³ ¸μ£² ¸¨¨ ¸ ·¥§E²OE E ³¨ ·¥I¥EμI´μ° S•". Œ ¸¸ ´E±²μ´ · ¸¸³ E·¨¢ ¥E¸O ¢ ¶²μ¸±μ¸E¨ (uB ,T ) ¨ ¤¥³μ´¸E·¨·E¥E ¸¨²O´EO § ¢¨¸¨³μ¸EO μE uBT . �μ± § ´μ, IEμ μ¤´μ¢·¥³¥´´μ¥ E¢¥²¨I¥´¨¥ ¶μE¥´I ¨ ² ¨ E¥³¶¥· EE·O ¶·¨¢μ¤¨E ± E¢¥²¨I¥´¨O ³ ¸¸O ´E±²μ´ , IEμ O¢²O¥E¸O ¶·μO¢²¥´¨¥³ ±¢ ·±-£²Oμ´´μ£μ E §μ¢μ£μ ¶¥·¥Iμ¤ ¤¥±μ´E °´³¥´E ¶·¨ ¢O- ¸μ±¨I E¥³¶¥· EE· I.

Lowering Critical Temperature in the Extended Quark Sigma Model at Finite Temperature

A phase transition, a critical temperature, and meson masses are studied in the extended quark sigma model, in which the effective mesonic potential is extended to include eighth-order mesonic interactions. The second derivative of the effective mesonic potential is applied to calculate the effective sigma and pion masses as functions of temperature. We find that the critical temperature assumes a lower value in comparison with that of original quark sigma model. A comparison with recent calculations of lattice QCD is introduced. The behavior of the phase transition remains unchanged when the higher-order mesonic interactions are included. We find that the spontaneous symmetry-breaking condition is necessary to satisfy the Goldstone theorem at low temperatures.

Improved Nucleon Properties in the Extended Quark Sigma Model

The quark sigma model describes the quarks interacting via exchange the pions and sigma meson fields. A new version of mesonic potential is suggested in the frame of some aspects of the quantum chromodynamics (QCD). The field equations have been solved in the mean-field approximation for the hedgehog baryon state. The obtained results are compared with previous works and other models. We conclude that the suggested mesonic potential successfully calculates nucleon properties.

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

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.

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

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.

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

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.

Baryons as solitonic solutions of the chiral sigma model.

Self-consistent solitonic solutions with baryon number one are obtained in the chiral quark sigma model. The translational invariant vacuum is stabilized by a Landau ghost subtraction procedure based on the requirement of the K{umlt a}ll{acute e}n-Lehmann (KL) representation for the meson propagators. The connection of this ghost free model (KL model) to the more popular Nambu-Jona-Lasinio (NJL) model is discussed in detail. {copyright} {ital 1996 The American Physical Society.}