1. Hadron to Quark Phase Transition in the Global Color Symmetry Model of QCD Yu-xin Liu Department of Physics, Peking University Collaborators: Guo H., Gao D.F., Chang L. Wang B., Song H.C., Chao J.Y. et al., at PKU; Wang F., Zong H.S., et al., at NJU; Lue X.F. at SCU; Zhao E.G. at ITP; Chao W.Q. at IHEP.

2. Outline I. Introduction II. The Framework III. Numerical Results IV. Remarks

3. I. Introduction  Two Puzzles in Current Physics (in T.D. Lee’s words) :  Chiral Symmetry and its Spontaneous Breaking  Color Confinement  Characteristics Identifying Quark Deconfinement and Chiral Symmetry Restoration: Hadron Properties Vacuum Structure Lattice QCD, pQCD (Factorization, Re-summation), Confinement Mechanism: Flux Tube, Center Vertex, ··· Intuitive view? NJL model, QMC, QMF, Truncated DSE, Instanton, GCM, ···

4. How the Chiral Symmetry is Restored ? Quark condensates are usually taken as characteristics of Vacuum Structure Order Parameters.  Theoretical approaches: Composite-operator, Sum rules, QMC, Walecka model, Dirac-Brueckner, S-D Equation, Instanton dilute liquid model, … Different results have been obtained!! Chi. Sym. C S B

5. (Comp.-Op., PRD41,1610(’90) )( QSR, NP A642, 171 (’98) ) ( D-S Eq. PR C55, 1577(’97) ) (DS Eq. PR C57, 2821(’98) ) (IDLM, NP A642, 83(’98) ) (Walecka, PR C55, 521 (‘97))

6. Hadron Properties are essential in describing finite nuclei and strong interaction matter  Effective mass EMC effect, nuclear structure & reaction  Nucleon swell EMC effect  Bag constant Quark confinement  Theoretical Approaches: Bag Models, QMC, QMF bag constant, bag energy, radius Phenomenologically! QCD foundation ??? the GCM appears

7. II. The Framework of the GCM 1. The Main Point of Global Color Symmetry Model R.T. Cahill, C.D. Roberts, Phys. Rev. D 32 (1985) 2419

10. Lue, Liu, Zhao, Zong, Phys. Rev. C 58 (1998) 1195 Prog. Part. Nucl. Phys. 39 (1997) 117; Phys. Rev. D49 (1994) 125; Phys. Rev. C53 (1996) 2410; ······. Effective degrees of freedom becomes quark and chiral mesons

11. 2. GCM in Strongly Interacting Matter

17. 3. The Scalar Quark Condensates

18. 4. The mass and decay constant of pion

19. 5. Relation Between the Chemical Potential and the Density

20. GCM, Global Color Symmetry Model: an effective field theory model of QCD Truncated DSE NJL, ChPT QCD GCM Hadronisation Observables BM, QMC, QHD Lattice Hadron Correlation With the GCM, one can explore the QCD foundation of bag models, the chiral symmetry breaking and restoration, the quark confinement and deconfinment,.

21. III. Numerical Results New approach to determine the vacuum configuration of the GCM B = m in instanton model Property of pion and sigma meson Lue, Liu, Zhao, Zong, Phys. Rev. C 58 (1998) 1195

22. Relation between  and 

23. Nucleon bag constant B(0)=(172 MeV) 4 Y. X. Liu, et al, Nucl. Phys. A 695 (2001) 353, A 725 (2003) 127

24. Nucleon radius and mass R(0)=0.7 fmm(0)=939 MeV Y. X. Liu, et al, Nucl. Phys. A 695 (2001) 353; A725 (2003) 127.

25. Quark condensates In nuclear matter Y. X. Liu, et al, Phys. Rev. C68 (2003), 035204.

26.  With a full gluon propagator  -  relation nucleon properties Y. X. Liu, et al, Nucl. Phys. A 750 (2005), 324.

27. quark condensate

28. Quark Gluon mixed Condensate Zhao Zhang, Wei-qin Chao, Phys. Lett. B 610 (2005), 235

29. The effective potential at and quark confinement results from the self-adjustment among/between quarks

30. The effective potential at finite and quark deconfinement and chiral symmetry restoration may take place

31. The mass and decay constant of pion

32. Susceptibilities: Zong H. S. et al., Phys. Lett. B 557 (2003) 33 Zong H. S. et al., Phys. Lett. B 576 (2003) 289 Zong H. S. et al., Phys. Rev. D 67 (2003) 074004 Zhang Z., Chao W.Q., Phys. Lett. B 612 (2005) 207 Axial vector vertex Zong H. S. et al., Phys. Rev. C 66 (2002) 015201 New Approach to Evaluate the Quark Propagator at Finite Chemical Potential Zong, Chang, Hou, Sun, Liu, Phys. Rev. C 71 (2005) 015205

33. IV. Remarks   The density dependence of the bag constant, the  mass and radius of nucleons and the pion mass and  decay constant are studied in an effective field  theory model of QCD ， namely the GCM   The scalar local and nonlocal quark condensates  are also investigated.  Calculated result 1: with the increase of the density before a critical value is reached, the B N and M N decrease, the M  almost maintains constant, the R N, the f  and the condensates increase.

34.  Calculated result 1: with the increase of the density before a critical value is reached, the B N and M N decrease, the M  almost maintains constant, the R N,,, the f  and the condensates increase.  Calculated result 2: at the critical density, the B N and M N vanish gradually, the M , f  and the, etc, disappear suddenly, the R N becomes infinite.  Quark deconfinement and the chiral symmetry restoration phase transitions happen at the critical density.  Chiral symmetry restoration process: broken more strongly gradually, at least, at the same scale, then restored suddenly.

35. Thanks !!!