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
The analysis based on the renormalized effective potential indicates that, similar to in the 4D two-flavor Nambu-Jona-Lasinio （NJL） model, in a 2D two-flavor Gross-Neveu model, the interplay between the quark-antiqu...The analysis based on the renormalized effective potential indicates that, similar to in the 4D two-flavor Nambu-Jona-Lasinio （NJL） model, in a 2D two-flavor Gross-Neveu model, the interplay between the quark-antiquark and the diquark ,condensates in vacuum also depends on Gs/Hs, the ratio of the coupling constants in scalar quarkantiquark and scalar diquark channel. Only the pure quark-antiquark condensates exist if Gs/Hs 〉 2/3, which is just the ratio of the color numbers of the quarks participating in the diquark and quark-antiquark condensates. The two condensates will coexist if 0 〈 Gs/Hs 〈 2/3. However, different from the 4D NJL model, the pure diquark condensates arise only at Gs/Hs = 0 and are not in a possibly finite region of Gs/Hs below 2/3.展开更多
We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in L...We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A（p^2） in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics （QCD）, we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.展开更多
By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equati...By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by A（p^2）ψ - B（p^2）, we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A（p^2） = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.展开更多
The color number Nc-dependence of the interplay between quark-antiquark condensates （q^-q） and diquark condensates （qq） in vacuum in two-flavor four-fermion interaction models is researched. The results show that ...The color number Nc-dependence of the interplay between quark-antiquark condensates （q^-q） and diquark condensates （qq） in vacuum in two-flavor four-fermion interaction models is researched. The results show that the Gs-Hs （the coupling constant of scalar （q^-q）2-scalar （qq）2 channel） phase diagrams will be qualitatively consistent with the case of Nc = 3 as Nc varies in 4D Nambu-Jona-Lasinio model and 219 Gross Neveu （GN） model, However, in 3D GN model, the behavior of the Gs-Hp （the coupling constant of pseudoscalar （qq）^2 channel） phase diagram will obviously depend on No. The known characteristic that a 3D GN model does not have the coexistence phase of the condensates （q^-q） and （qq） is proven to appear only in the case of Nc ≤ 4. In all the models, the regions occupied by the phases containing the diquark condensates （qq） in corresponding phase diagrams will gradually decrease as Nc grows up and finally go to zero if Nc → ∞, i.e. in this limit only the pure （q^-q） phase could exist.展开更多
The effective potential analysis indicates that, in a 3D two-flavor Gross-Neveu model in vacuum, depending on whether Gs/Hp is less or bigger than the critical value 2/3, where G s and H p are respectively the couplin...The effective potential analysis indicates that, in a 3D two-flavor Gross-Neveu model in vacuum, depending on whether Gs/Hp is less or bigger than the critical value 2/3, where G s and H p are respectively the coupling constants of scalar quark-antiquark channel and pseudoscalar diquark channel, the system will have the ground state with pure diquark condensates or with pure quark-antiquark condensates, but never with coexistence of the two forms of condensates. The similarities and differences in the interplay between the quark-antiquark and the diquark condensates in vacuum in the 2D, 3D and 4D two-flavor four-fermion interaction models are summarized.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The analysis based on the renormalized effective potential indicates that, similar to in the 4D two-flavor Nambu-Jona-Lasinio （NJL） model, in a 2D two-flavor Gross-Neveu model, the interplay between the quark-antiquark and the diquark ,condensates in vacuum also depends on Gs/Hs, the ratio of the coupling constants in scalar quarkantiquark and scalar diquark channel. Only the pure quark-antiquark condensates exist if Gs/Hs 〉 2/3, which is just the ratio of the color numbers of the quarks participating in the diquark and quark-antiquark condensates. The two condensates will coexist if 0 〈 Gs/Hs 〈 2/3. However, different from the 4D NJL model, the pure diquark condensates arise only at Gs/Hs = 0 and are not in a possibly finite region of Gs/Hs below 2/3.
文摘We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A（p^2） in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics （QCD）, we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.
文摘By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by A（p^2）ψ - B（p^2）, we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A（p^2） = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.
基金supported by the National Natural Science Foundation of China under Grant No. 10475113
文摘The color number Nc-dependence of the interplay between quark-antiquark condensates （q^-q） and diquark condensates （qq） in vacuum in two-flavor four-fermion interaction models is researched. The results show that the Gs-Hs （the coupling constant of scalar （q^-q）2-scalar （qq）2 channel） phase diagrams will be qualitatively consistent with the case of Nc = 3 as Nc varies in 4D Nambu-Jona-Lasinio model and 219 Gross Neveu （GN） model, However, in 3D GN model, the behavior of the Gs-Hp （the coupling constant of pseudoscalar （qq）^2 channel） phase diagram will obviously depend on No. The known characteristic that a 3D GN model does not have the coexistence phase of the condensates （q^-q） and （qq） is proven to appear only in the case of Nc ≤ 4. In all the models, the regions occupied by the phases containing the diquark condensates （qq） in corresponding phase diagrams will gradually decrease as Nc grows up and finally go to zero if Nc → ∞, i.e. in this limit only the pure （q^-q） phase could exist.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475113
文摘The effective potential analysis indicates that, in a 3D two-flavor Gross-Neveu model in vacuum, depending on whether Gs/Hp is less or bigger than the critical value 2/3, where G s and H p are respectively the coupling constants of scalar quark-antiquark channel and pseudoscalar diquark channel, the system will have the ground state with pure diquark condensates or with pure quark-antiquark condensates, but never with coexistence of the two forms of condensates. The similarities and differences in the interplay between the quark-antiquark and the diquark condensates in vacuum in the 2D, 3D and 4D two-flavor four-fermion interaction models are summarized.
