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
High density phase transitions in a 4-dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of...High density phase transitions in a 4-dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of both the gap equation and the effective potential approach. The phase transitions are proven to be second-order at a high temperature T; however at T = 0 they are first- or second-order, depending on whether A/m(0), the ratio of the momentum cutoff A in the fermion-loop integrals to the dynamicalfermion mass m(0) at zero temperature, is less than 3.387 or not. The former condition cannot be satisfied in some models. The discussions further show complete effectiveness of the critical analysis based on the gap equation for second order phase transitions including determination of the condition of their occurrence.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
In this paper,we study the influences of magnetic fields on the coexistence of diquark and chiral condensates in an extended Nambu-Jona-Lasinio model with QCD axial anomaly,as it relates to color-flavor-locked quark m...In this paper,we study the influences of magnetic fields on the coexistence of diquark and chiral condensates in an extended Nambu-Jona-Lasinio model with QCD axial anomaly,as it relates to color-flavor-locked quark matter.Due to the coupling of rotated-charged quarks to magneticfields,diquark condensates become split,and the coexistence region is thus superseded in favor of a specific diquark Bose-Einstein condensation(BEC),denoted as the BECIphase.For strong magnetic fields,we find that the BECItransition is pushed to larger quark chemical potentials.The effect of magnetic catalysis tends to disrupt the BEC-BCS(Bardeen-Cooper-Schrieffer)crossover predicted in previous works.For intermediate fields,the effect of inverse magnetic catalysis is observed,and the axial-anomaly-induced phase structure is essentially unchanged.展开更多
In terms of the Nambu-Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple localgauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalarfi...In terms of the Nambu-Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple localgauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalarfields is derived by solving the Euler equation for the gauge fields. Based on this relation the SU(3) gauge potential isgiven which can be used to explain the asymptotic freedom and confinement of quarks in a hadron. The confinementbehavior at finite temperatures is also investigated and it is shown that color confinement at zero temperature can bemelted away under high temperatures.展开更多
By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the criti...By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μ<SUB>c</SUB> in 2D and 3D Gross-Neveu (GN) model and these physically explain the first-order feature of the corresponding symmetry restoring phase transitions. For the second-order phase transitions in the 3D GN model when T → 0 and in 4D Nambu–Jona–Lasinio (NJL) model when T = 0, it is proven that the particle density itself will be continuous across μ<SUB>c</SUB> but its derivative over the chemical potential μ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point in the 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.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 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
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
In this paper,the Debye mass of quarks is investigated in the Nambu–Jona-Lasinio model at zero and nonzero chemical potentials.In a uniform plasma,the Debye mass usually behaves as a monotonous increasing function of...In this paper,the Debye mass of quarks is investigated in the Nambu–Jona-Lasinio model at zero and nonzero chemical potentials.In a uniform plasma,the Debye mass usually behaves as a monotonous increasing function of the temperature,the chemical potential and the magnetic field.At the fixed coupling interaction G,we find that the magnetic catalysis(MC)on the occurrence of the chiral restoration could be revealed by the susceptibility of the Debye mass dmD/dT at low chemical potential and by the quantity TdmD/dT in the region of moderate densities.However,the inverse MC is realized under a thermomagnetic coupling constant G(B,T)by the behavior of the Debye mass at both zero and nonzero chemical potentials.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High density phase transitions in a 4-dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of both the gap equation and the effective potential approach. The phase transitions are proven to be second-order at a high temperature T; however at T = 0 they are first- or second-order, depending on whether A/m(0), the ratio of the momentum cutoff A in the fermion-loop integrals to the dynamicalfermion mass m(0) at zero temperature, is less than 3.387 or not. The former condition cannot be satisfied in some models. The discussions further show complete effectiveness of the critical analysis based on the gap equation for second order phase transitions including determination of the condition of their occurrence.
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 the National Natural Science Foundation of China(NSFC)under Contract No.10875058。
文摘In this paper,we study the influences of magnetic fields on the coexistence of diquark and chiral condensates in an extended Nambu-Jona-Lasinio model with QCD axial anomaly,as it relates to color-flavor-locked quark matter.Due to the coupling of rotated-charged quarks to magneticfields,diquark condensates become split,and the coexistence region is thus superseded in favor of a specific diquark Bose-Einstein condensation(BEC),denoted as the BECIphase.For strong magnetic fields,we find that the BECItransition is pushed to larger quark chemical potentials.The effect of magnetic catalysis tends to disrupt the BEC-BCS(Bardeen-Cooper-Schrieffer)crossover predicted in previous works.For intermediate fields,the effect of inverse magnetic catalysis is observed,and the axial-anomaly-induced phase structure is essentially unchanged.
文摘In terms of the Nambu-Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple localgauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalarfields is derived by solving the Euler equation for the gauge fields. Based on this relation the SU(3) gauge potential isgiven which can be used to explain the asymptotic freedom and confinement of quarks in a hadron. The confinementbehavior at finite temperatures is also investigated and it is shown that color confinement at zero temperature can bemelted away under high temperatures.
基金The project supported by National Natural Science Foundation ot China
文摘By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μ<SUB>c</SUB> in 2D and 3D Gross-Neveu (GN) model and these physically explain the first-order feature of the corresponding symmetry restoring phase transitions. For the second-order phase transitions in the 3D GN model when T → 0 and in 4D Nambu–Jona–Lasinio (NJL) model when T = 0, it is proven that the particle density itself will be continuous across μ<SUB>c</SUB> but its derivative over the chemical potential μ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point in the 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.
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 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 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The authors would like to thank support from the National Natural Science Foundation of China under the Grant Nos.11875181,12147215,and 11705163This work was also sponsored by the Fund for Shanxi‘1331 Project’Key Subjects Construction.
文摘In this paper,the Debye mass of quarks is investigated in the Nambu–Jona-Lasinio model at zero and nonzero chemical potentials.In a uniform plasma,the Debye mass usually behaves as a monotonous increasing function of the temperature,the chemical potential and the magnetic field.At the fixed coupling interaction G,we find that the magnetic catalysis(MC)on the occurrence of the chiral restoration could be revealed by the susceptibility of the Debye mass dmD/dT at low chemical potential and by the quantity TdmD/dT in the region of moderate densities.However,the inverse MC is realized under a thermomagnetic coupling constant G(B,T)by the behavior of the Debye mass at both zero and nonzero chemical potentials.
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.
