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QCD Phase Transition in Dyson-Schwinger Equation Approach

QCD Phase Transition in Dyson-Schwinger Equation Approach. Yuxin Liu Department of Physics, Peking University Beijing 100871, China. Outline I. Introduction II. Brief View of DSE Approach

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QCD Phase Transition in Dyson-Schwinger Equation Approach

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  1. QCD Phase Transition in Dyson-Schwinger Equation Approach Yuxin Liu Department of Physics, Peking University Beijing 100871, China Outline I. Introduction II. Brief View of DSE Approach III. Some of Our Work IV. Summary SQM2008，Beijing，China，October 6-10, 2008

  2. I. Introduction The History of the Universe

  3. Aspects influencing QCD P.-T. Medium：Temperature, Density ( or ) Finite size Intrinsic：Current mass, Coupling Str., C-F structure, ••• ••• It relates Confinement – Deconf. S Breaking – Restoration Flavor symmetry breaking Schematic QCD Phase Diagram Chiral Symmetric Quark deconfined sQGP SB, Quark confined

  4. Theoretical Approaches： Lattice QCD Finite Temperature Field Theory, RG, LT with dynamical theory (model): QHD, (p)NJL, QMC, QMF, QSR, INST, DSE, GCM,··· AdS/CFT Key Points: Representing the two main features of QCD: Chiral Symmetry & its Breaking Confinement

  5. II. Brief Description of DSEs in QCD  Dyson-Schwinger Equations  General Point of View D-S equation is a set of coupled integral eqs. among quark, gluon, ghost and vertex functions, where the n-point function depends on the (n+1)-and higher point functions. C. D. Roberts, et al, Prog. Part. Nucl. Phys. 33 (1994), 477; 45-S1, 1 (2000); EPJ-ST 140(2007,53; R. Alkofer, et. al, Phys. Rept. 353, 281 (2001);  .

  6. Quark equation in medium • with  Rain-Bow Approximation Quark equation at zero chemical potential where is the effective gluon propagator, can be conventionally decomposed as

  7.  Effective Gluon Propagators (1) MN Model (2) (3) (2)Model (3) More Realistic model (4) An Analytical Expression of the Realistic Model: Maris-Tandy Model (5) Point Interaction: (P) NJL Model

  8. Phys. Rev. C 68, 015203 (2003) Example of the success of the DSE: Generation of Dynamical Mass

  9. III. Some of Our Recent WorkEffect of Current Quark Mass on Meson Mass ( L. Chang, Y. X. Liu, C. D. Roberts, et al., Phys. Rev. C 76, 045203 (2007) ) Solving the B-S equation with the kernel being fixed by the solution of DS equation and flavor symmetry breaking, we obtain

  10. (W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006)) Effect of the running coupling strength on the chiral phase transition parameters are taken From Phys. Rev. D 65, 094026 (1997), with fitted as Lattice QCD result PRD 72, 014507 (2005)

  11. Effect of Current Mass on PT L. Chang, Y. X. Liu, C. D. Roberts, et al, Phys. Rev. C 75, 015201 (2007) (nucl-th/0605058) Solutions of the DSE with Mass function With =0.4 GeV with D = 16 GeV2,   0.4 GeV

  12. Phase Diagram in terms of the Current Mass and the Running Coupling Strength

  13. Distinguishing the Dynamical Breaking from the Explicit Breaking ( L. Chang, Y. X. Liu, C. D. Roberts, et al, Phys. Rev. C 75, 015201 (2007) )

  14. Effect of the chemical potential dependence of the gluon propagator on PT Chiral channel: ( L. Chang, H. Chen, B. Wang, W. Yuan,and Y.X. Liu, Phys. Lett. B 644, 315 (2007) ) Diquark channel: ( W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006) )

  15. Components of the vacuum of the system with finite isospin chemical potential Case 1.， , ， ； Case 2. , , ， ； Case 3.， ， , ； Case 4.， , ，No Solution. (Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 035201 (2007))

  16. Chiral Susceptibility & PT in NJL Model Y. Zhao, L. Chang, W. Yuan, Y.X. Liu, Eur. Phys. J. C 56, 483 (2008)

  17. Phase Diagram of Quark Matter in P-NJL Model (W.J. Fu, Z. Zhao, Y.X. Liu, Phys. Rev. D 77, 014006 (2008) (2+1 flavor) Simple case: 2-flavor, Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 064910 (2007) ) - relationnucleon properties

  18. Order of the QCD Phase Transitions ( W.J. Fu, Z. Zhao, Y.X. Liu, Phys. Rev. D 77, 014006 (2008) (2+1 flavor) )

  19. Nucleon as a Soliton in DSE B. Wang, H. Chen, L. Chang, & Y. X. Liu, Phys. Rev. C 76, 025201 (2007) Collective Quantization: Nucl. Phys. A790, 593 (2007).

  20. Variation of Nucleon Properties with Respect to the Density of the Matter (L. Chang, Y. X. Liu, H. Guo, Nucl. Phys. A 750, 324 (2005)) - relationnucleon properties

  21. Phase with SB & Confinement is stable hadron matter appears  Phase transition from vacuum to matter H. Chen, W. Yuan, L. Chang, YXL, TK, CDR, arXiv:0807.2755

  22. Distinguishing Newly Born SQS From NS NS: RMF, SQS: Bag Model W.J. Fu, H.Q. Wei, and Y.X. Liu, arXiv: 0810.1084, to appear in Phys. Rev. Lett.

  23. IV. Summary  We discussed the QCD Phase Transitions ;  running coupling strong enough,  current mass lower than a critical value,Dynamical chiral symmetry breaking Matter can be generated from vacuum through the chiral phase transitionFundamental & Quite Perspective ! Great efforts are still required !

  24. Thanks !!!

  25. Three different solutions exist in chiral limit M+ shifts upward too.

  26. Chang, Liu, et al., Phys. Rev C 75, 015201 (2007) M+ shifts upward too.

  27. Chang, Liu, et al., Phys. Rev C 75, 015201 (2007)

  28. Chang, Liu, et al., Phys. Rev C 75, 015201 (2007)

  29. Shape of Nucleus Sphere Deforemation quadrupole octupole hexadecupole  Modes of Nuclear Collective Motion vibration & GR axial rotation ( prolate, oblate) -soft rotation triaxial rotation ••• ••• ••• •••

  30. E. S. Paul et al.，Phys. Rev. Lett. 98，012501 (2007)

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