By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu J...By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu Jona Lasinio （NJL） model and obtain the Gs-Hs phase diagram, where Gs and Hs are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure （qq） phase when Gs/Hs 〉 2/3, and as Gs/Hs decreases to 2/3 〉 Gs/Hs ≥ 0 one will first have a coexistence phase of the condensates （qq） and （qq） and then a pure （qq） phase. In non-zero bare quark mass case, the critical value of Gs/Hs at which the pure （qq） phase will transfer to the coexistence phase of the condensates （qq） and （qq） will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting sma/lest ratio Gs/Hs after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.展开更多
A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe t...A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe twoflavor normal quark matter. Depending on whether mo/A, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus mo is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value ofmo/A from QCD phenomenology, the phase transition must be of the first order.展开更多
We review the Nambu and Jona-Lasinio model (NJL), proposed long time ago, in the sixties, as a fermion interaction theory with chiral symmetry. The theory is not renormalizable and presents a symmetry breaking due to ...We review the Nambu and Jona-Lasinio model (NJL), proposed long time ago, in the sixties, as a fermion interaction theory with chiral symmetry. The theory is not renormalizable and presents a symmetry breaking due to quantum effects which depends on the strength of the coupling constant. We may associate a phase transition with this symmetry breaking, leading from fermion states to a fermion condensate which can be described effectively by a scalar field. Our purpose in this paper is to exploit the interesting properties of NJL in a different context other than particle physics by studying its cosmological dynamics. We are interested in finding whether possibly the NJL model could be used to describe the still unknown dark energy and/or dark matter, from up to 95% of the energy content of the universe at present time.展开更多
An extended Nambu-Jona-Lasinio(eNJL) model with nucleons as the degrees of freedom is used to investigate properties of nuclear matter and neutron stars(NSs),including the binding energy and symmetry energy of the nuc...An extended Nambu-Jona-Lasinio(eNJL) model with nucleons as the degrees of freedom is used to investigate properties of nuclear matter and neutron stars(NSs),including the binding energy and symmetry energy of the nuclear matter, the core-crust transition density, and mass-radius relation of NSs. The fourth-order symmetry energy at saturation density is also investigated. When the bulk properties of nuclear matter at saturation density are used to determine the model parameters, the double solutions of parameters are obtained for a given nuclear incompressibility. It is shown that the isovector-vector interaction has a significant influence on the nuclear matter and NS properties, and the sign of isovector-vector coupling constant is critical in the determination of the trend of the symmetry energy and equation of state. The effects of the other model parameters and symmetry energy slope at saturation density are discussed.展开更多
We adopt the Nambu–Jona-Lasinio(NJL) model to study the crust-core transition properties in neutron stars(NSs). For a given momentum cutoff and symmetry energy of saturation density in the NJL model, decreasing the s...We adopt the Nambu–Jona-Lasinio(NJL) model to study the crust-core transition properties in neutron stars(NSs). For a given momentum cutoff and symmetry energy of saturation density in the NJL model, decreasing the slope of the symmetry energy gives rise to an increase in the crust-core transition density and transition pressure.Given the slope of the symmetry energy at saturation density, the transition density and corresponding transition pressure increase with increasing symmetry energy. The increasing trend between the fraction of the crustal moment of inertia and the slope of symmetry energy at saturation density indicates that a relatively large momentum cutoff of the NJL model is preferred. For a momentum cutoff of 500 Me V, the fraction of the crustal moment of inertia clearly increases with the slope of symmetry energy at saturation density. Thus, at the required fraction(7%) of the crustal moment of inertia, the NJL model with momentum cutoff of 500 Me V and a large slope of the symmetry energy of saturation density can give the upper limit of the mass of the Vela pulsar to be above 1.40 M.展开更多
We report on our results about spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field,E,and magnetic field,B.A Nambu–Jona–Lasinio model is used to c...We report on our results about spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field,E,and magnetic field,B.A Nambu–Jona–Lasinio model is used to compute the dependence of the chiral condensate at finite temperature,E and B.We study the effect of this background on inverse catalysis of chiral symmetry breaking for E and B of the same order of magnitude.We also consider the effect of equilibration of chiral density,n_5,produced by axial anomaly on the critical temperature.The equilibration of n_5 allows for the introduction of the chiral chemical potential,u_5,which is computed selfconsistently as a function of temperature and field strength.We find that even if the chiral medium is produced by the fields the thermodynamics,with particular reference to the inverse catalysis induced by the external fields,it is not very affected by n_5 at least if the average u_5,at equilibrium is not too large.展开更多
The diquark condensate susceptibility in neutral colour superconductor at moderate baryon density is calculated in the frame of the two-flavour Nambu-Jona-Lasinio model with the mean field approximation. When colour c...The diquark condensate susceptibility in neutral colour superconductor at moderate baryon density is calculated in the frame of the two-flavour Nambu-Jona-Lasinio model with the mean field approximation. When colour chemical potential is introduced to keep charge neutrality, the dlquark condensate susceptibility ＆ negative in the directions without diquark condensate in colour space, which may be regarded as a signal of the instability of the conventional ground state with only diquark condensate in the colour-3 direction.展开更多
We investigate nucleon mass splitting at finite isospin chemical potential in the frame of the two-flavour Nambu-Jona-Lasinio model. It is analytically proven that in the phase with explicit isospin symmetry breaking,...We investigate nucleon mass splitting at finite isospin chemical potential in the frame of the two-flavour Nambu-Jona-Lasinio model. It is analytically proven that in the phase with explicit isospin symmetry breaking, the proton mass decreases and the neutron mass increases linearly in the isospin chemical potential.展开更多
We investigate current-current correlation functions,or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density.The linear response is investigated introducing the co...We investigate current-current correlation functions,or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density.The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach.The response functions can be obtained by expanding the generational functional in powers of the external sources.We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics,namely mean-field theory and a beyond-mean-field theory,taking into account mesonic contributions.Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation.We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation,showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons,respectively.Noting that the mesonic contributions are not taken into account in the random phase approximation,we also derive the response functions parallel to the beyond-mean-field theory.We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions:the Aslamazov-Lakin contribution,the self-energy or density-of-state contribution,and the Maki-Thompson contribution.Unlike the equilibrium case,in evaluating the fluctuation contributions,we need to carefully treat the linear terms in external sources and the induced perturbations.In the chiral symmetry breaking phase,we find an additional chiral order parameter induced contribution,which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities.These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover,where the mesonic degrees of freedom are still important.展开更多
Generalized Yang-Mills theory has a covariant derivative which contains both vector and scalar gauge bosons. Based on this theory, we construct an SU(3) unified model of electromagnetic and weak interactions to simpli...Generalized Yang-Mills theory has a covariant derivative which contains both vector and scalar gauge bosons. Based on this theory, we construct an SU(3) unified model of electromagnetic and weak interactions to simplify the Weinberg-Salam model. By using the Nambu-Jona-Lasinio mechanism, the symmetry breaking can be realized dynamically. The masses of W<sup>±</sup>, Z<sup>0</sup> are obtained and interactions between various particles are the same as that of the Weinberg-Salam model. At the same time, sin<sup>2</sup> θ<sub>w</sub> =1/4 can be given.展开更多
We investigate the quark matter in a strong magnetic field in the framework of SU(2) NJL model with a magnetic-field-dependent coupling. The spin polarization, the entropy per baryon, and the energy are studied by ana...We investigate the quark matter in a strong magnetic field in the framework of SU(2) NJL model with a magnetic-field-dependent coupling. The spin polarization, the entropy per baryon, and the energy are studied by analyzing the competition of the magnetic effect and the thermal effect. The stronger magnetic field can enhance the spin polarization, arrange quarks in a uniform spin orientation, and change the energy per baryon drastically. However,it can hardly affect the entropy per baryon, which is dominated by the temperature. As the temperature increases, more quarks will be excited from the lowest Landau level up to higher Landau levels.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No, 10475113
文摘By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu Jona Lasinio （NJL） model and obtain the Gs-Hs phase diagram, where Gs and Hs are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure （qq） phase when Gs/Hs 〉 2/3, and as Gs/Hs decreases to 2/3 〉 Gs/Hs ≥ 0 one will first have a coexistence phase of the condensates （qq） and （qq） and then a pure （qq） phase. In non-zero bare quark mass case, the critical value of Gs/Hs at which the pure （qq） phase will transfer to the coexistence phase of the condensates （qq） and （qq） will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting sma/lest ratio Gs/Hs after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475113
文摘A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe twoflavor normal quark matter. Depending on whether mo/A, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus mo is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value ofmo/A from QCD phenomenology, the phase transition must be of the first order.
文摘We review the Nambu and Jona-Lasinio model (NJL), proposed long time ago, in the sixties, as a fermion interaction theory with chiral symmetry. The theory is not renormalizable and presents a symmetry breaking due to quantum effects which depends on the strength of the coupling constant. We may associate a phase transition with this symmetry breaking, leading from fermion states to a fermion condensate which can be described effectively by a scalar field. Our purpose in this paper is to exploit the interesting properties of NJL in a different context other than particle physics by studying its cosmological dynamics. We are interested in finding whether possibly the NJL model could be used to describe the still unknown dark energy and/or dark matter, from up to 95% of the energy content of the universe at present time.
基金Supported by Hunan Provincial Natural Science Foundation of China(2015JJ2005)the Science Research Foundation of Education Department of Hunan Province(15C0029)+1 种基金the National Natural Science Foundation of China(11103001)the construct program of the key discipline in Hunan province
文摘An extended Nambu-Jona-Lasinio(eNJL) model with nucleons as the degrees of freedom is used to investigate properties of nuclear matter and neutron stars(NSs),including the binding energy and symmetry energy of the nuclear matter, the core-crust transition density, and mass-radius relation of NSs. The fourth-order symmetry energy at saturation density is also investigated. When the bulk properties of nuclear matter at saturation density are used to determine the model parameters, the double solutions of parameters are obtained for a given nuclear incompressibility. It is shown that the isovector-vector interaction has a significant influence on the nuclear matter and NS properties, and the sign of isovector-vector coupling constant is critical in the determination of the trend of the symmetry energy and equation of state. The effects of the other model parameters and symmetry energy slope at saturation density are discussed.
基金Supported by National Natural Science Foundation of China(11775049,11275048)the China Jiangsu Provincial Natural Science Foundation(BK20131286)
文摘We adopt the Nambu–Jona-Lasinio(NJL) model to study the crust-core transition properties in neutron stars(NSs). For a given momentum cutoff and symmetry energy of saturation density in the NJL model, decreasing the slope of the symmetry energy gives rise to an increase in the crust-core transition density and transition pressure.Given the slope of the symmetry energy at saturation density, the transition density and corresponding transition pressure increase with increasing symmetry energy. The increasing trend between the fraction of the crustal moment of inertia and the slope of symmetry energy at saturation density indicates that a relatively large momentum cutoff of the NJL model is preferred. For a momentum cutoff of 500 Me V, the fraction of the crustal moment of inertia clearly increases with the slope of symmetry energy at saturation density. Thus, at the required fraction(7%) of the crustal moment of inertia, the NJL model with momentum cutoff of 500 Me V and a large slope of the symmetry energy of saturation density can give the upper limit of the mass of the Vela pulsar to be above 1.40 M.
基金supported by the CAS President’s International Fellowship Initiative(No.2015PM008)the National Natural Science Foundation of China(Nos.11135011 and 11575190)
文摘We report on our results about spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field,E,and magnetic field,B.A Nambu–Jona–Lasinio model is used to compute the dependence of the chiral condensate at finite temperature,E and B.We study the effect of this background on inverse catalysis of chiral symmetry breaking for E and B of the same order of magnitude.We also consider the effect of equilibration of chiral density,n_5,produced by axial anomaly on the critical temperature.The equilibration of n_5 allows for the introduction of the chiral chemical potential,u_5,which is computed selfconsistently as a function of temperature and field strength.We find that even if the chiral medium is produced by the fields the thermodynamics,with particular reference to the inverse catalysis induced by the external fields,it is not very affected by n_5 at least if the average u_5,at equilibrium is not too large.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10428510, 10435080, 10447122 and 10575058, and the Specialized Research Fund for the Doctoral Program of Higher Education （SRFDP） under Grant No 20040003103.
文摘The diquark condensate susceptibility in neutral colour superconductor at moderate baryon density is calculated in the frame of the two-flavour Nambu-Jona-Lasinio model with the mean field approximation. When colour chemical potential is introduced to keep charge neutrality, the dlquark condensate susceptibility ＆ negative in the directions without diquark condensate in colour space, which may be regarded as a signal of the instability of the conventional ground state with only diquark condensate in the colour-3 direction.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10428510 and 10575058. One of the authors （Chang S.） thanks the High Energy Nuclear Physics Group of Tsinghua University for kind hospitality and Lianyi He and Xuewen Hao for helpful discussions.
文摘We investigate nucleon mass splitting at finite isospin chemical potential in the frame of the two-flavour Nambu-Jona-Lasinio model. It is analytically proven that in the phase with explicit isospin symmetry breaking, the proton mass decreases and the neutron mass increases linearly in the isospin chemical potential.
基金Supported by the National Natural Science Foundation of China(11775123,11890712,11747312,11475062)the National Key R&D Program of China(2018YFA0306503)
文摘We investigate current-current correlation functions,or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density.The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach.The response functions can be obtained by expanding the generational functional in powers of the external sources.We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics,namely mean-field theory and a beyond-mean-field theory,taking into account mesonic contributions.Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation.We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation,showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons,respectively.Noting that the mesonic contributions are not taken into account in the random phase approximation,we also derive the response functions parallel to the beyond-mean-field theory.We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions:the Aslamazov-Lakin contribution,the self-energy or density-of-state contribution,and the Maki-Thompson contribution.Unlike the equilibrium case,in evaluating the fluctuation contributions,we need to carefully treat the linear terms in external sources and the induced perturbations.In the chiral symmetry breaking phase,we find an additional chiral order parameter induced contribution,which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities.These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover,where the mesonic degrees of freedom are still important.
文摘Generalized Yang-Mills theory has a covariant derivative which contains both vector and scalar gauge bosons. Based on this theory, we construct an SU(3) unified model of electromagnetic and weak interactions to simplify the Weinberg-Salam model. By using the Nambu-Jona-Lasinio mechanism, the symmetry breaking can be realized dynamically. The masses of W<sup>±</sup>, Z<sup>0</sup> are obtained and interactions between various particles are the same as that of the Weinberg-Salam model. At the same time, sin<sup>2</sup> θ<sub>w</sub> =1/4 can be given.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11475110,11135011,and 11575190
文摘We investigate the quark matter in a strong magnetic field in the framework of SU(2) NJL model with a magnetic-field-dependent coupling. The spin polarization, the entropy per baryon, and the energy are studied by analyzing the competition of the magnetic effect and the thermal effect. The stronger magnetic field can enhance the spin polarization, arrange quarks in a uniform spin orientation, and change the energy per baryon drastically. However,it can hardly affect the entropy per baryon, which is dominated by the temperature. As the temperature increases, more quarks will be excited from the lowest Landau level up to higher Landau levels.
