A generalized Yang-Mills model, which contains, besides the vector part Vμ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of N...A generalized Yang-Mills model, which contains, besides the vector part Vμ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.展开更多
In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated...In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.展开更多
The Si-O bond breaking event in the a-quartz at the first triplet （T1） excitation state is studied by using ab initio molecular dynamics （AIMD） and nudged elastic band calculations. A meta-stable non-bridging oxyg...The Si-O bond breaking event in the a-quartz at the first triplet （T1） excitation state is studied by using ab initio molecular dynamics （AIMD） and nudged elastic band calculations. A meta-stable non-bridging oxygen hole center and E1 center （NBOHC-E） is observed in the AIMD which consists of a broken Si-O bond with a Si-O distance of 2.54A. By disallowing the re-bonding of the Si and 0 atoms, another defect configuration （lll- Si/V-Si） is obtained and validated to be stable at both ground and excitation states. The NBOHC-E is found to present on the minimal energy pathway of the initial to IlI-Si/V-Si transition, showing that the generating of the NBOHC-E is an important step of the excitation induced structure defect. The energy barriers to produce the NBQHC-E＇ and Ⅲ-Si/V-Si defects are calculated to be 1.19 and 1.28eV, respectively. The electronic structures of the two defects are calculated by the self-consistent GW calculations and the results show a clear electron transition from the bonding orbital to the non-bonding orbital.展开更多
Since the massless quantum electrodynamics in 2＋1 dimensions （QEDa） with nonzero gauge boson mass ζ can be used to explain some important traits of high-Tc superconductivity in planar cuprates, it is worthwhile to...Since the massless quantum electrodynamics in 2＋1 dimensions （QEDa） with nonzero gauge boson mass ζ can be used to explain some important traits of high-Tc superconductivity in planar cuprates, it is worthwhile to apply this model to analyze the nature of chiral phase transition at the critical value ζ. Based on the feature of chiral susceptibility, we show that the system at ζ exhibits a second-order phase transition which accords with the nature of appearance of the high-To superconductivity, and the estimated critical exponents around ζ are illustrated.展开更多
The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background,in which the longitudinal wave dissipation determines some important performances of the slender struc...The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background,in which the longitudinal wave dissipation determines some important performances of the slender structure.To reproduce the longitudinal wave dissipation effects on an elastic rod with a variable cross-section,a structure-preserving approach is developed based on the dynamic symmetry breaking theory.For the dynamic model controlling the longitudinal wave propagating in the elastic rod with the variable cross-section,the approximate multi-symplectic form is deduced based on the multi-symplectic method,and the expression of the local energy dissipation for the longitudinal wave propagating in the rod is presented,referring to the dynamic symmetry breaking theory.A structure-preserving method focusing on the residual of the multi-symplectic structure and the local energy dissipation of the dynamic model is constructed by using the midpoint difference discrete method.The longitudinal wave propagating in an elastic rod fixed at one end is simulated,and the local/total energy dissipations of the longitudinal wave are investigated by the constructed structure-preserving scheme in two typical cases in detail.展开更多
In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the ...In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the critical gauge boson mass for various numbers of the fermion flavors. A comparision with the previous results is presented.展开更多
A method for obtaining the small current quark mass dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach the small current quark mass effects on...A method for obtaining the small current quark mass dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach the small current quark mass effects on dressed-quark propagator have been studied. A comparison with previous results is given.展开更多
In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., t...In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., the current quark mass. By studying the linear response of the dressed quark propagator to the presence of a nonzero quark mass, we derive a model-independent formula for the scalar susceptibility, which contains the dressed quark propagator G（p） and the dressed scalar vertex F（p, 0）. The numerical values of the scalar susceptibility Xs are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach by employing two typical forms of model gluon propagator.展开更多
Based on the global color symmetry mode/ （GCM）, a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator c...Based on the global color symmetry mode/ （GCM）, a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator containing the quark loop effects in the Nambu-Goldstone and Wigner phases are quite different. In solving the quark self-energy functions in the two different phases and subsequent study of bag constant one shouM use the above dressed gluon propagator as input. The above approach for obtaining the current quark mass effects on the dressed gluon propagator is quite general and can also be used to calculate the chemical potential dependence of the dressed gluon propagator.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 solved the Dyson–Schwinger(DS)equations for a two-flavor system with symmetry to study its flavor mixing effects.Initially,we employed the point interaction model and bare vertex approximation to reveal the struct...We solved the Dyson–Schwinger(DS)equations for a two-flavor system with symmetry to study its flavor mixing effects.Initially,we employed the point interaction model and bare vertex approximation to reveal the structure of the solutions.Using the point interaction model,the DS equations can be solved analytically,and we found that these solutions can be classified into three groups,each forming an ellipse.These solutions exhibit SO(2)symmetry,while the original SU(2)symmetry at the Lagrangian level is dynamically broken to SO(2),corresponding to the emergence of flavor mixing effects.However,this flavor mixing effect does not manifest in the final physical state.By utilizing the system's SO(2)symmetry,we can diagonalize the propagators of the DS equations,eliminating the flavor mixing effect but causing the originally degenerate masses at the Lagrangian level to split.These mass eigenstates have identical quantum numbers but different masses.If we can correspond these to quark particles of different generations,we can explain why the three generations of quarks have different masses and obtain the corresponding quark mass spectrum.Finally,we provide the corresponding numerical results using a more realistic interaction model.展开更多
Starting from the generalized Yang-Mills model which contains, besides the vector part Vμ, also a scalar part S and a pseudoscalar part P. It is shown, in terms of the Nambu-Jona-Lasinio （NJL） mechanism, that CP vi...Starting from the generalized Yang-Mills model which contains, besides the vector part Vμ, also a scalar part S and a pseudoscalar part P. It is shown, in terms of the Nambu-Jona-Lasinio （NJL） mechanism, that CP violation can be realized dynamically. The combination of the generalized Yang-Mills model and the NJL mechanism provides a new way to explain CP violation.展开更多
By using the generalized Yang-Mills model, CP violation behavior at finite temperature is investigated, and it is shown that dynamical CP violation of the generalized Yang-Mills model at zero temperature can be restor...By using the generalized Yang-Mills model, CP violation behavior at finite temperature is investigated, and it is shown that dynamical CP violation of the generalized Yang-Mills model at zero temperature can be restored at finite temperature.展开更多
We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing the following aspects: confinement and dynamical chiral symmetry breaking; the hadron spe...We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing the following aspects: confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small-to large-Q2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.展开更多
The coupling dynamic problems,such as the vehicle-bridge interaction problem,are difficult to be analyzed.In this paper,the generalized multi-symplectic approach is employed to investigate the coupling dynamic behavio...The coupling dynamic problems,such as the vehicle-bridge interaction problem,are difficult to be analyzed.In this paper,the generalized multi-symplectic approach is employed to investigate the coupling dynamic behaviors in the vehicle-bridge interaction system.A simply-supported damping beam model carrying a moving mass is considered and the generalized multi-symplectic form with the dynamical symmetry breaking factors is deduced firstly.And then,Preissmann’s scheme is employed to discretize the generalized multi-symplectic form,and the discrete structure-preserving condition for the numerical scheme is presented.According to the discrete structure-preserving condition,the permitted moving speed of the mass with different damping factors and different time step lengths is obtained to ensure the structure-preserving properties of the numerical scheme.Finally,the effects of the damping factor of the beam and the moving speed of the mass on the vibration of the beam are investigated by Preissmann’s scheme.The main contribution of this work is to provide a structure-preserving analysis approach for the vehicle-bridge interaction problem.展开更多
Two basic motivations for an upgraded JLab facility are the needs： to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking （DCSB）; and to understand nucleon structure and...Two basic motivations for an upgraded JLab facility are the needs： to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking （DCSB）; and to understand nucleon structure and spectroscopy in terms of QCD＇s elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson- Schwinger equation perspective on this effort with numerous illustrations, amongst them： an interpretation of string^breaking; a symmetry-preserving truncation for mesons; the nucleon＇s strangeness σ-term; and the neutron＇s charge distribution.展开更多
Based on the Dyson-Schwinger Equations （DSEs）, the two-quark vacuum condensate, the four-quark vacuum condensate, and the quark gluon mixed vacuum condensate in the non-perturbative QCD vacuum state are investigated...Based on the Dyson-Schwinger Equations （DSEs）, the two-quark vacuum condensate, the four-quark vacuum condensate, and the quark gluon mixed vacuum condensate in the non-perturbative QCD vacuum state are investigated by solving the DSEs with rainbow truncation at zero- and finite- temperature, respectively. These condensates are important input parameters in QCD sum rule with zero and finite temperature, and in studying hadron physics, as well as predicting the quark mean squared momentum rn02- also called quark virtuality in the QCD vacuum state. The present calculated results show that these physical quantities are almost independent of the temperature below the critical point temperature Tc=131 MeV, and above Tc the chiral symmetry is restored. For comparison we calculate the temperature dependence of the ＂in-hadron condensate＂ for pion. At the same time, we also calculate the ratio of the quark gluon mixed vacuum condensate to the two-quark vacuum condensate by using these condensates, and the unknown quark mean squared momentum in the QCD vacuum state has been obtained. The results show that the ratio m2/0（T） is almost fiat in the temperature region from 0 to To, although there are drastic changes of the quark vacuum condensate and the quark gluon mixed vacuum condensate at the region. Our predicted ratio comes out to be m2/0（T）=2.41 GeV2 at the Chiral limit, which is consistent with other theory model predictions, and strongly indicates the significance that the quark gluon mixed vacuum condensate has played in the virtuality calculations.展开更多
文摘A generalized Yang-Mills model, which contains, besides the vector part Vμ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
文摘In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10744048 and 11202032the Defense Industrial Technology Development Program of China under Grant No B1520132013
文摘The Si-O bond breaking event in the a-quartz at the first triplet （T1） excitation state is studied by using ab initio molecular dynamics （AIMD） and nudged elastic band calculations. A meta-stable non-bridging oxygen hole center and E1 center （NBOHC-E） is observed in the AIMD which consists of a broken Si-O bond with a Si-O distance of 2.54A. By disallowing the re-bonding of the Si and 0 atoms, another defect configuration （lll- Si/V-Si） is obtained and validated to be stable at both ground and excitation states. The NBOHC-E is found to present on the minimal energy pathway of the initial to IlI-Si/V-Si transition, showing that the generating of the NBOHC-E is an important step of the excitation induced structure defect. The energy barriers to produce the NBQHC-E＇ and Ⅲ-Si/V-Si defects are calculated to be 1.19 and 1.28eV, respectively. The electronic structures of the two defects are calculated by the self-consistent GW calculations and the results show a clear electron transition from the bonding orbital to the non-bonding orbital.
基金Supported by the Natural Science Foundation of Jiangsu Province under Grant No BK20130387the Fundamental Research Funds for the Central Universities under Grant No 2242014R30011
文摘Since the massless quantum electrodynamics in 2＋1 dimensions （QEDa） with nonzero gauge boson mass ζ can be used to explain some important traits of high-Tc superconductivity in planar cuprates, it is worthwhile to apply this model to analyze the nature of chiral phase transition at the critical value ζ. Based on the feature of chiral susceptibility, we show that the system at ζ exhibits a second-order phase transition which accords with the nature of appearance of the high-To superconductivity, and the estimated critical exponents around ζ are illustrated.
基金Projected supported by the National Natural Science Foundation of China(Nos.11872303,12172281,11972284)the Fund for Distinguished Young Scholars of Shaanxi Province of China(No.2019JC-29)+2 种基金the Foundation Strengthening Programme Technical Area Fund(No.2021-JCJQ-JJ-0565)the Fund of the Youth Innovation Team of Shaanxi Universitiesthe Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment(No.GZ19103)。
文摘The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background,in which the longitudinal wave dissipation determines some important performances of the slender structure.To reproduce the longitudinal wave dissipation effects on an elastic rod with a variable cross-section,a structure-preserving approach is developed based on the dynamic symmetry breaking theory.For the dynamic model controlling the longitudinal wave propagating in the elastic rod with the variable cross-section,the approximate multi-symplectic form is deduced based on the multi-symplectic method,and the expression of the local energy dissipation for the longitudinal wave propagating in the rod is presented,referring to the dynamic symmetry breaking theory.A structure-preserving method focusing on the residual of the multi-symplectic structure and the local energy dissipation of the dynamic model is constructed by using the midpoint difference discrete method.The longitudinal wave propagating in an elastic rod fixed at one end is simulated,and the local/total energy dissipations of the longitudinal wave are investigated by the constructed structure-preserving scheme in two typical cases in detail.
文摘In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the critical gauge boson mass for various numbers of the fermion flavors. A comparision with the previous results is presented.
文摘A method for obtaining the small current quark mass dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach the small current quark mass effects on dressed-quark propagator have been studied. A comparison with previous results is given.
基金The project supported in part by National Natural Science Foundation of China under Grant No.10575050the Research Fund for the Doctoral Program of Higher Education under Grant No.20060284020
文摘In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., the current quark mass. By studying the linear response of the dressed quark propagator to the presence of a nonzero quark mass, we derive a model-independent formula for the scalar susceptibility, which contains the dressed quark propagator G（p） and the dressed scalar vertex F（p, 0）. The numerical values of the scalar susceptibility Xs are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach by employing two typical forms of model gluon propagator.
基金The project supported in part by National Natural Science Foundation of China under Grant Nos. 10575050 and 10135030 and the Research Fund for the Doctoral Program of Higher Education under Grant No. 20030284009.
文摘Based on the global color symmetry mode/ （GCM）, a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator containing the quark loop effects in the Nambu-Goldstone and Wigner phases are quite different. In solving the quark self-energy functions in the two different phases and subsequent study of bag constant one shouM use the above dressed gluon propagator as input. The above approach for obtaining the current quark mass effects on the dressed gluon propagator is quite general and can also be used to calculate the chemical potential dependence of the dressed gluon propagator.
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 Contract Nos.11435001 and 11775041the National Science Foundation of China under Grants No.12175007 and No.12247107。
文摘We solved the Dyson–Schwinger(DS)equations for a two-flavor system with symmetry to study its flavor mixing effects.Initially,we employed the point interaction model and bare vertex approximation to reveal the structure of the solutions.Using the point interaction model,the DS equations can be solved analytically,and we found that these solutions can be classified into three groups,each forming an ellipse.These solutions exhibit SO(2)symmetry,while the original SU(2)symmetry at the Lagrangian level is dynamically broken to SO(2),corresponding to the emergence of flavor mixing effects.However,this flavor mixing effect does not manifest in the final physical state.By utilizing the system's SO(2)symmetry,we can diagonalize the propagators of the DS equations,eliminating the flavor mixing effect but causing the originally degenerate masses at the Lagrangian level to split.These mass eigenstates have identical quantum numbers but different masses.If we can correspond these to quark particles of different generations,we can explain why the three generations of quarks have different masses and obtain the corresponding quark mass spectrum.Finally,we provide the corresponding numerical results using a more realistic interaction model.
文摘Starting from the generalized Yang-Mills model which contains, besides the vector part Vμ, also a scalar part S and a pseudoscalar part P. It is shown, in terms of the Nambu-Jona-Lasinio （NJL） mechanism, that CP violation can be realized dynamically. The combination of the generalized Yang-Mills model and the NJL mechanism provides a new way to explain CP violation.
文摘By using the generalized Yang-Mills model, CP violation behavior at finite temperature is investigated, and it is shown that dynamical CP violation of the generalized Yang-Mills model at zero temperature can be restored at finite temperature.
基金Supported by the Project of Knowledge Innovation Program of the Chinese Academy of Sciences under Grant No. KJCX2.YW.W10Sistema Nacional de Investigadores+8 种基金CONACyT grant 46614-Fthe University of Adelaide and the Australian Research Council through Grant No. FL0992247Coordinación de la Investigación Científica (UMSNH) under Grant 4.10the U. S. Department of Energy, Office of Nuclear Physics, Grant No. DE-AC02-06CH11357Fundao de Amparo Pesquisa do Estado de So Paulo, Grant Nos. 2009/51296-1 and 2010/05772-3the National Natural Science Foundation of China under Grant Nos. 10425521, 10675002, 10705002, 10935001 and 11075052the Major State Basic Research Development Program, under Grant No. G2007CB815000Forschungszentrum Jülich GmbHthe U. S.National Science Foundation under Grant No. PHY-0903991, in conjunction with a CONACyT Mexico-USA Collaboration Grant
文摘We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing the following aspects: confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small-to large-Q2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.
基金supported by the National Natural Science Foundation of China (12172281,11872303 and 11972284)Fund for Distinguished Young Scholars of Shaanxi Province (2019JC-29)+2 种基金Foundation Strengthening Programme Technical Area Fund (2021-JCJQ-JJ-0565)the Fund of the Science and Technology Innovation Team of Shaanxi (2022TD-61)the Fund of the Youth Innovation Team of Shaanxi Universities (21JP079).
文摘The coupling dynamic problems,such as the vehicle-bridge interaction problem,are difficult to be analyzed.In this paper,the generalized multi-symplectic approach is employed to investigate the coupling dynamic behaviors in the vehicle-bridge interaction system.A simply-supported damping beam model carrying a moving mass is considered and the generalized multi-symplectic form with the dynamical symmetry breaking factors is deduced firstly.And then,Preissmann’s scheme is employed to discretize the generalized multi-symplectic form,and the discrete structure-preserving condition for the numerical scheme is presented.According to the discrete structure-preserving condition,the permitted moving speed of the mass with different damping factors and different time step lengths is obtained to ensure the structure-preserving properties of the numerical scheme.Finally,the effects of the damping factor of the beam and the moving speed of the mass on the vibration of the beam are investigated by Preissmann’s scheme.The main contribution of this work is to provide a structure-preserving analysis approach for the vehicle-bridge interaction problem.
基金Supported by National Natural Science Foundation of China (10705002)Department of Energy, Office of Nuclear Physics(DE-FG03-97ER4014, DE-AC02-06CH11357)
文摘Two basic motivations for an upgraded JLab facility are the needs： to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking （DCSB）; and to understand nucleon structure and spectroscopy in terms of QCD＇s elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson- Schwinger equation perspective on this effort with numerous illustrations, amongst them： an interpretation of string^breaking; a symmetry-preserving truncation for mesons; the nucleon＇s strangeness σ-term; and the neutron＇s charge distribution.
基金Supported by National Natural Science Foundation of China(11365002)Guangxi Natural Science Foundation for Young Researchers(2013GXNSFBB053007,2011GXNSFA018140)+2 种基金Guangxi Education Department(2013ZD049)Guangxi Grant for Excellent Researchers(2011-54)Guangxi University of Science and Technology Foundation for Ph Ds(11Z16)
文摘Based on the Dyson-Schwinger Equations （DSEs）, the two-quark vacuum condensate, the four-quark vacuum condensate, and the quark gluon mixed vacuum condensate in the non-perturbative QCD vacuum state are investigated by solving the DSEs with rainbow truncation at zero- and finite- temperature, respectively. These condensates are important input parameters in QCD sum rule with zero and finite temperature, and in studying hadron physics, as well as predicting the quark mean squared momentum rn02- also called quark virtuality in the QCD vacuum state. The present calculated results show that these physical quantities are almost independent of the temperature below the critical point temperature Tc=131 MeV, and above Tc the chiral symmetry is restored. For comparison we calculate the temperature dependence of the ＂in-hadron condensate＂ for pion. At the same time, we also calculate the ratio of the quark gluon mixed vacuum condensate to the two-quark vacuum condensate by using these condensates, and the unknown quark mean squared momentum in the QCD vacuum state has been obtained. The results show that the ratio m2/0（T） is almost fiat in the temperature region from 0 to To, although there are drastic changes of the quark vacuum condensate and the quark gluon mixed vacuum condensate at the region. Our predicted ratio comes out to be m2/0（T）=2.41 GeV2 at the Chiral limit, which is consistent with other theory model predictions, and strongly indicates the significance that the quark gluon mixed vacuum condensate has played in the virtuality calculations.
