Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU（2） NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons,...Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU（2） NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 〈 0 and μI 〉0 in the phase diagram, and different values for the charged pion mass（or decay constant） and neutral pion mass（or decay constant） at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.展开更多
We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential...We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential and temperature, respectively. The QNS is found to have the highest and sharpest peak at the CEP. It is also found that, when the chemical potential μ is in the range of 60MeV≤ μ ≤ 110MeV, the QNS near the transition temperature is larger than the free field result, which indicates that the space-like damping mode dominates the degree of freedom of motion near the CEP.展开更多
Dynamical chiral symmetry breaking(DCSB) in thermal QED3 with fermion velocity is studied in the framework of Dyson–Schwinger equations. By adopting instantaneous approximation and neglecting the transverse component...Dynamical chiral symmetry breaking(DCSB) in thermal QED3 with fermion velocity is studied in the framework of Dyson–Schwinger equations. By adopting instantaneous approximation and neglecting the transverse component of gauge boson propagator at finite temperature, we numerically solve the fermion self-energy equation in the rainbow approximation. It is found that both DCSB and fermion chiral condensate are suppressed by fermion velocity.Moreover, the critical temperature decreases as fermion velocity increases.展开更多
We study chiral symmetry restoration by analyzing thermal properties of QCD's(pseudo-)Goldstone bo-sons,especially the pion.The meson properties are obtained from the spectral densities of mesonic imaginary-time c...We study chiral symmetry restoration by analyzing thermal properties of QCD's(pseudo-)Goldstone bo-sons,especially the pion.The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions.To obtain the correlation functions,we solve the Dyson-Schwinger equations and the inhomo-geneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation.In chiral limit,the pion and its partner sigma degenerate at the critical temperature T_(c).At T≥T_(c),it was found that the pion rapidly dissociates,which signals deconfinement phase transition.Beyond the chiral limit,the pion dissociation temperature can be used to define the pseudo-critical temperature of the chiral phase crossover,which is consistent with that ob-tained by the maximum point of chiral susceptibility.A parallel analysis for kaon and pseudoscalar ss suggests that heavymesons maysurviveabove T_(c).展开更多
We propose a novel self-consistent mean field approximation method by means of a Fierz transformation,taking the Nambu-Jona-Lasinio model as an example.This new self-consistent mean field approximation introduces a ne...We propose a novel self-consistent mean field approximation method by means of a Fierz transformation,taking the Nambu-Jona-Lasinio model as an example.This new self-consistent mean field approximation introduces a new free parameter a to be determined experimentally.When a assumes the value of 0.5,the approximation reduces to the mean field calculation commonly used in the past.Subsequently,we study the influence of the undetermined parameter a on the phase diagram of the two-flavor strong interaction matter.The value of a plays a crucial role in the strong interaction phase diagram,as it not only changes the position of the phase transition point of strong interaction matter,but also affects the order of the phase transition.For example,when a is greater than the critical valueαc = 0.71,then the strong interaction matter phase diagram no longer has a critical end point.In addition,in the case of zero temperature and finite density,we found that when a>1.044,the pseudo-critical chemical potential corresponds to ～4-5 times the saturation density of the nuclear matter,which agrees with the expected results from the picture of the hadrons degree of freedom.The resulting equations of state of strong interaction matter at low temperatures and high densities will have an important impact on studies concerning the mass radius relationship of neutron stars and the merging process of binary neutron stars.展开更多
Conserved charge fluctuations can be used to probe the phase structure of strongly interacting nuclear matter in relativistic heavy-ion collisions. To obtain the characteristic signatures of the conserved charge fluct...Conserved charge fluctuations can be used to probe the phase structure of strongly interacting nuclear matter in relativistic heavy-ion collisions. To obtain the characteristic signatures of the conserved charge fluctuations for the quantum chromodynamics(QCD) phase transition, we study the susceptibilities of dense quark matter up to eighth order in detail, using an effective QCD-based model. We studied two cases, one with the QCD critical end point(CEP) and one without owing to an additional vector interaction term. The higher order susceptibilities display rich structures near the CEP and show sign changes as well as large fluctuations. These can provide us information about the presence and location of the CEP. Furthermore, we find that the case without the CEP also shows a similar sign change pattern, but with a relatively smaller magnitude compared with the case with the CEP. Finally, we conclude that higher order susceptibilities of conserved charge can be used to probe the QCD phase structures in heavyion collisions.展开更多
It is shown on general ground that there exist two qualitatively distinct solutions of the Dyson-Schwinger equation for the quark propagator in the case of non-zero current quark mass. One solution corresponds to the ...It is shown on general ground that there exist two qualitatively distinct solutions of the Dyson-Schwinger equation for the quark propagator in the case of non-zero current quark mass. One solution corresponds to the “Nambu- Goldstone” phase and the other one corresponds to the “Wigner” phase in the chiral limit.展开更多
Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic bounda...Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudotransition temperature T;of the crossover, showing a significant decrease in T;as L decreases below 3 fm.展开更多
In this study,we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio(NJL)model and compare it with the two-flavor NJL model.The self-consistent mean field approximation introduces ...In this study,we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio(NJL)model and compare it with the two-flavor NJL model.The self-consistent mean field approximation introduces a new parameter,α,that cannot be fixed in advance by the mean field approach itself.Due to the lack of experimental data,the parameter,α,is undetermined.Hence,it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation.αaffects numerous properties of the chiral phase transitions,such as the position of the phase transition point and the order of phase transition.Additionally,increasingαwill decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero.Finally,we observed thatαaffects the equation of state(EOS)of the quark matter,and the sound velocity can be calculated to determine the stiffness of the EOS,which provides a good basis for studying the neutron star mass-radius relationship.展开更多
The effective Lagrangian of a finite volume system should, in principle, depend on the system size. In the framework of the Nambu-Jona-Lasinio(NJL) model, by considering the influence of quark feedback on the effectiv...The effective Lagrangian of a finite volume system should, in principle, depend on the system size. In the framework of the Nambu-Jona-Lasinio(NJL) model, by considering the influence of quark feedback on the effective coupling, we obtain a modified NJL model so that its Lagrangian depends on the volume. Based on the modified NJL model, we study the influence of finite volume on the chiral phase transition at finite temperature, and find that the pseudo-critical temperature of crossover is much lower than that obtained in the normal NJL model. This clearly shows that the volume dependent effective Lagrangian plays an important role in the chiral phase transitions at finite temperature.展开更多
We discuss the sign and energy dependence of second to tenth order susceptibilities of the baryon number,charge number, and strangeness for the analysis of critical conditions in heavy ion collisions in the LHC and RH...We discuss the sign and energy dependence of second to tenth order susceptibilities of the baryon number,charge number, and strangeness for the analysis of critical conditions in heavy ion collisions in the LHC and RHIC by applying a modified Nambu-Jona-Lasinio model. This model is fitted to the quark condensate of the lattice QCD result at finite temperature and zero baryon chemical potential. The presence of a critical point made these susceptibilities deviate considerably from a Hadron-Resonance-Gas model that shows no criticality. The sign, magnitude, and energy dependence of these higher order fluctuations hint towards the existence and location of a critical point that could be discovered in future heavy ion collision experiments.展开更多
We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformat...We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potentiM Vg and an additive Coriolis-induced geometric potential in the co-rotationM curvilinear coordinates. This novel effective potential, which is included in the surface Schr6dinger equation and is coupled with the mean curvature of S, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.展开更多
基金Supported by National Natural Science Foundation of China(11175088,11475085,11535005,11690030)the Fundamental Research Funds for the Central Universities(020414380074)
文摘Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU（2） NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 〈 0 and μI 〉0 in the phase diagram, and different values for the charged pion mass（or decay constant） and neutral pion mass（or decay constant） at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11105122,11275097 and 11475085the Foundation of Graduate School of Nanjing University under Grant No 2014CL02
文摘We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential and temperature, respectively. The QNS is found to have the highest and sharpest peak at the CEP. It is also found that, when the chemical potential μ is in the range of 60MeV≤ μ ≤ 110MeV, the QNS near the transition temperature is larger than the free field result, which indicates that the space-like damping mode dominates the degree of freedom of motion near the CEP.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11535005the Natural Science Foundation of Jiangsu Province under Grant No.BK20130387
文摘Dynamical chiral symmetry breaking(DCSB) in thermal QED3 with fermion velocity is studied in the framework of Dyson–Schwinger equations. By adopting instantaneous approximation and neglecting the transverse component of gauge boson propagator at finite temperature, we numerically solve the fermion self-energy equation in the rainbow approximation. It is found that both DCSB and fermion chiral condensate are suppressed by fermion velocity.Moreover, the critical temperature decreases as fermion velocity increases.
基金Supported in part by the National Natural Science Foundation of China(12075117,11775112,11535005,11690030,11905104,11805024,11947406)Jiangsu Provincial Natural Science Foundation of China(BK20180323)。
文摘We study chiral symmetry restoration by analyzing thermal properties of QCD's(pseudo-)Goldstone bo-sons,especially the pion.The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions.To obtain the correlation functions,we solve the Dyson-Schwinger equations and the inhomo-geneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation.In chiral limit,the pion and its partner sigma degenerate at the critical temperature T_(c).At T≥T_(c),it was found that the pion rapidly dissociates,which signals deconfinement phase transition.Beyond the chiral limit,the pion dissociation temperature can be used to define the pseudo-critical temperature of the chiral phase crossover,which is consistent with that ob-tained by the maximum point of chiral susceptibility.A parallel analysis for kaon and pseudoscalar ss suggests that heavymesons maysurviveabove T_(c).
基金Supported in part by the National Natural Science Foundation of China(11690030,11475085,11535005)National Major state Basic Research and Development of China(2016YFE0129300)
文摘We propose a novel self-consistent mean field approximation method by means of a Fierz transformation,taking the Nambu-Jona-Lasinio model as an example.This new self-consistent mean field approximation introduces a new free parameter a to be determined experimentally.When a assumes the value of 0.5,the approximation reduces to the mean field calculation commonly used in the past.Subsequently,we study the influence of the undetermined parameter a on the phase diagram of the two-flavor strong interaction matter.The value of a plays a crucial role in the strong interaction phase diagram,as it not only changes the position of the phase transition point of strong interaction matter,but also affects the order of the phase transition.For example,when a is greater than the critical valueαc = 0.71,then the strong interaction matter phase diagram no longer has a critical end point.In addition,in the case of zero temperature and finite density,we found that when a>1.044,the pseudo-critical chemical potential corresponds to ～4-5 times the saturation density of the nuclear matter,which agrees with the expected results from the picture of the hadrons degree of freedom.The resulting equations of state of strong interaction matter at low temperatures and high densities will have an important impact on studies concerning the mass radius relationship of neutron stars and the merging process of binary neutron stars.
基金Supported in part by the National Natural Science Foundation of China(11475085,11535005,11690030,11575069,11221504)the MoST of China 973-Project(2015CB856901)
文摘Conserved charge fluctuations can be used to probe the phase structure of strongly interacting nuclear matter in relativistic heavy-ion collisions. To obtain the characteristic signatures of the conserved charge fluctuations for the quantum chromodynamics(QCD) phase transition, we study the susceptibilities of dense quark matter up to eighth order in detail, using an effective QCD-based model. We studied two cases, one with the QCD critical end point(CEP) and one without owing to an additional vector interaction term. The higher order susceptibilities display rich structures near the CEP and show sign changes as well as large fluctuations. These can provide us information about the presence and location of the CEP. Furthermore, we find that the case without the CEP also shows a similar sign change pattern, but with a relatively smaller magnitude compared with the case with the CEP. Finally, we conclude that higher order susceptibilities of conserved charge can be used to probe the QCD phase structures in heavyion collisions.
基金Supported in part by the National Natural Science Foundation of China under Grant Nos 10175033, 10135030, and 10575050, and the Research Fund for the Doctoral Program of Higher Education under Grant No 20030284009.
文摘It is shown on general ground that there exist two qualitatively distinct solutions of the Dyson-Schwinger equation for the quark propagator in the case of non-zero current quark mass. One solution corresponds to the “Nambu- Goldstone” phase and the other one corresponds to the “Wigner” phase in the chiral limit.
基金Supported by National Natural Science Foundation of China(11475085,11535005,11690030,51405027)the Fundamental Research Funds for the Central Universities(020414380074)+1 种基金China Postdoctoral Science Foundation(2016M591808)Open Research Foundation of State Key Lab.of Digital Manufacturing Equipment&Technology in Huazhong University of Science&Technology(DMETKF2015015)
文摘Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudotransition temperature T;of the crossover, showing a significant decrease in T;as L decreases below 3 fm.
文摘In this study,we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio(NJL)model and compare it with the two-flavor NJL model.The self-consistent mean field approximation introduces a new parameter,α,that cannot be fixed in advance by the mean field approach itself.Due to the lack of experimental data,the parameter,α,is undetermined.Hence,it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation.αaffects numerous properties of the chiral phase transitions,such as the position of the phase transition point and the order of phase transition.Additionally,increasingαwill decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero.Finally,we observed thatαaffects the equation of state(EOS)of the quark matter,and the sound velocity can be calculated to determine the stiffness of the EOS,which provides a good basis for studying the neutron star mass-radius relationship.
基金Supported by the National Natural Science Foundation of China(11475085,11535005,11690030)the National Major state Basic Research and Development(2016YFE0129300)
文摘The effective Lagrangian of a finite volume system should, in principle, depend on the system size. In the framework of the Nambu-Jona-Lasinio(NJL) model, by considering the influence of quark feedback on the effective coupling, we obtain a modified NJL model so that its Lagrangian depends on the volume. Based on the modified NJL model, we study the influence of finite volume on the chiral phase transition at finite temperature, and find that the pseudo-critical temperature of crossover is much lower than that obtained in the normal NJL model. This clearly shows that the volume dependent effective Lagrangian plays an important role in the chiral phase transitions at finite temperature.
基金Supported in part by the MoST of China 973-Project(2015CB856901)the National Natural Science Foundation of China(11475085,11535005,11690030,11575069,11221504,11890711,11861131009)the Fundamental Research Funds for the Central Universities(020414380074,CCNU19QN054)
文摘We discuss the sign and energy dependence of second to tenth order susceptibilities of the baryon number,charge number, and strangeness for the analysis of critical conditions in heavy ion collisions in the LHC and RHIC by applying a modified Nambu-Jona-Lasinio model. This model is fitted to the quark condensate of the lattice QCD result at finite temperature and zero baryon chemical potential. The presence of a critical point made these susceptibilities deviate considerably from a Hadron-Resonance-Gas model that shows no criticality. The sign, magnitude, and energy dependence of these higher order fluctuations hint towards the existence and location of a critical point that could be discovered in future heavy ion collision experiments.
基金Supported by the National Natural Science Foundation of China under Grants Nos 11047020,11404157,11274166,11275097,11475085 and 11535005the Natural Science Foundation of Shangdong Province under Grants Nos ZR2012AM022 and ZR2011AM019
文摘We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potentiM Vg and an additive Coriolis-induced geometric potential in the co-rotationM curvilinear coordinates. This novel effective potential, which is included in the surface Schr6dinger equation and is coupled with the mean curvature of S, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.
