1. QCD Phase Transitions & One of Their Astronomical Signals Yuxin Liu （刘玉鑫） Department of Physics, Peking University, China The CSQCDII, Peking University, Beijing, China, May 20-24, 2009 Outline I. Introduction II. QCD Phase Transitions in DSE Approach III. The Astronomical Signal IV. Summary In collaboration with: Dr. Lei C. Dr. Zhang Z., Dr. Wang B., Dr. Gu J.F., Fu W.J., Chen H., Shao G.Y., ······, & Dr. Roberts C.D., Dr Bhagwat M.S., Dr. T. Klaehn,.

2. I. Introduction Schematic QCD Phase Diagram Items Affecting the PTs: Medium Effects ： Temperature, Density (Chem. Potent.) Finite size Intrinsic Effects ： Current mass, Run. Coupl. Strength, Color-Flavor Structure, Related Phase Transitions: Confinement(Hadron.) –– Decconfinement Chiral Symm. Breaking CS Restoration –– CS Restoration Flavor Symmetry –– Flavor Symm. Breaking Chiral Symmetric Quark deconfined  SB SB, Quark confined sQGP  How do the aspects influence the phase transitions ?  Why there exists partial restoration of dynamical  S in low density matter ?  How does matter emerge from vacuum ?

3. Theoretical Methods Theoretical Methods ： Lattice QCD Finite-T QFT, Renormal. Group, Landau T.,  Dynamical Approaches （ models ） : QHD, (p)NJL, QMC, QMF, QCD Sum Roles, Instanton models, Dyson-Schwinger Equations (DSEs),  General Requirements for the approaches: not only involving the chiral symmetry & its breaking, but also manifesting the confinement and deconfinement. AdS/CFT

4. Slavnov-Taylor Identity Dyson-Schwinger Equations axial gauges BBZ covariant gauges QCDQCD DSE Approach of QCD C. D. Roberts, et al, PPNP 33 (1994), 477; 45-S1, 1 (2000); EPJ-ST 140(2007), 53; R. Alkofer, et. al, Phys. Rep. 353, 281 (2001); C.S. Fischer, JPG 32(2006), R253; .

5.  Practical Way at Present Stage  Quark equation at zero chemical potential where is the effective gluon propagator, can be conventionally decomposed as  Quark equation in medium  with No pole at real axis Meeting the requirements!

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

7. Examples of achievements of the DSE of QCD Generation of Dynamical Mass Taken from: The Frontiers of Nuclear Science – A Long Range Plan (DOE, US, Dec. 2007). Origin: MSB, CDR, PCT, et al., Phys. Rev. C 68, 015203 (03) Taken from: Tandy ’ s talk at Morelia-2009

8. II. Our Work on QCD PT in DSE Approach  Effect of the F.-S.-B. () on Meson’s Mass  Effect of the F.-S.-B. (m 0 ) on Meson’s Mass Solving the 4-dimenssional covariant B-S equation with the kernel being fixed by the solution of DS equation and flavor symmetry breaking, we obtain ( L. Chang, Y. X. Liu, C. D. Roberts, et al., Phys. Rev. C 76, 045203 (2007) )

9.  Composition 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))

10. parameters are taken From Phys. Rev. D 65, 094026 (1997), with fitted as  Effect of the Running Coupling Strength on the Chiral Phsae Transition (W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006)) Lattice QCD result PRD 72, 014507 (2005) (BC Vertex: L. Chang, Y.X. Liu, R.D. Roberts, et al., Phys. Rev. C 79, 035209 (2009)) Bare vertex CS phase CSB phase

11. with D = 16 GeV 2,   0.4 GeV  Effect of the Current Quark Mass on the Chiral Phase Transition Solutions of the DSE with Mass function With  =0.4 GeV L. Chang, Y. X. Liu, C. D. Roberts, et al, Phys. Rev. C 75, 015201 (2007) (nucl-th/0605058)

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

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

14. arXiv:0807.3486 (EPJC60, 47(2009) ) gives the 5th solution. Hep-ph/0612061 confirms the existence of the 3rd solution, and give the 4th solution.

15.  Effect of the Chemical Potential on the Chiral Phase Transition Diquark channel: ( W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006) ) Chiral channel: ( L. Chang, H. Chen, B. Wang, W. Yuan,Y.X. Liu, Phys. Lett. B 644, 315 ( L. Chang, H. Chen, B. Wang, W. Yuan, and Y.X. Liu, Phys. Lett. B 644, 315 (2007) ) Chiral Susceptibility of Wigner-Vacuum in DSE Some Refs. of DSE study on CSC 1. D. Nickel, et al., PRD 73, 114028 (2006); 2. D. Nickel, et al., PRD 74, 114015 (2006); 3. F. Marhauser, et al., PRD 75, 054022 (2007); 4. V. Klainhaus, et al., PRD 76, 074024 (2007); 5. D. Nickel, et al., PRD 77, 114010 (2008); 6. D. Nickel, et al., arXiv:0811.2400; …………

16. NJL model  Partial Restoration of Dynamical  S  & Matter Generation H. Chen, W. Yuan, L. Chang, YXL, TK, CDR, Phys. Rev. D 78, 116015 (2008); H. Chen, W. Yuan, YXL, JPG 36 (special issue for SQM2008), 064073 (2009) Bare vertex BC vertex CSB phase BC vertex CS phase Alkofer ’ s Solution-2cc “ Alkofer ’ s Solution ” - BCFit1 BC vertex

17.  P-NJL Model of （ 2+1 ） Flavor Quark System and the related Phase Transitions ( W.J. Fu, Z. Zhao, Y.X. Liu, Phys. Rev. D 77, 014006 (2008) (2+1 flavor) )

18. Phase Diagram of the （ 2+1 ） Flavor System in P-NJL Model  -  relation nucleon properties Simple case: 2-flavor, Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 064910 (2007) ) Simple case: 2-flavor, Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 064910 (2007) ) (W.J. Fu, Z. Zhao, Y.X. Liu, Phys. Rev. D 77, 014006 (2008) (2+1 flavor)

19. Collective Quantization: Nucl. Phys. A790, 593 (2007).  Properties of Nucleon in DSE Soliton Model B. Wang, H. Chen, L. Chang, & Y. X. Liu, Phys. Rev. C 76, 025201 (2007) Model of the effective gluon propagator

20.  Density Dependence of some Properties of Nucleon in DSE Soliton Model  -  relation nucleon properties (L. Chang, Y. X. Liu, H. Guo, Nucl. Phys. A 750, 324 (2005))

21.  Temperature dependence of some properties of  and  -mesons in PNJL model ( Wei-jie Fu, and Yu-xin Liu, Phys. Rev. D 79, 074011 (2009) ) Goldberger-Treiman Relation: GM-O-Renner Relation: with

22.  Effects of Quarks and CSC on the M-R Relation of Compact Stars Many signals have been proposed: e.g., r-mode instability, Larger dissipation rate, Cooled more rapidly, Spin rate more close to Kepler Limit, ······. J.F. Gu, H. Guo, X.G. Li, Y.X. Liu, et al., Phys. Rev. C 73, 055803 (2006); Eur. Phys. J. A 30, 455 (2006); . III. The Astronomical Signal of QCD PT

23.  Distinguishing Newly Born Strange Quark Stars from Neutron Stars W.J. Fu, H.Q. Wei, and Y.X. Liu, arXiv: 0810.1084,1084 Phys. Rev. Lett. 101 ， 181102 (2008) Neutron Star: RMF, Quark Star: Bag Model Frequency of g-mode oscillation

24. Taking into account the  SB effect

25. Ott et al. have found that these g-mode pulsation of supernova cores are very efficient as sources of g-waves (PRL 96, 201102 (2006) ) DS Cheng, R. Ouyed, T. Fischer, ····· The g-mode pulsation frequency can be a signal to distinguish the newly born strange quark stars from neutron stars, i.e, an astronomical signal of QCD phase transition.

26. IV. Summary ：  QCD Phase Transitions With the DSE approach of QCD, we show that  the vacuum of the system with finite isospin chemical potential contains not only pion condensation but also mixed quark-gluon condensate;  above a critical coupling strength and bellow a critical current mass, DCSB appears;  meson mass splitting induced by the flavor symmetry breaking is not significant;  above a criticalμ, PR-  S occurs & matter appears.  We develop the Polyakov-NJL model for (2+1) flavor system and study the phase transitions.  We p ropose a signal of distinguishing the newly born Strange stars from neutron stars, i.e, an astronomical signature of QCD PT.

27. Thanks !!! Thanks !!!

28. 背景简介 ( F.Weber, J.Phys.G 25, R195 (1999) ) Composition of Compact Stars

29. Calculations of the g-mode oscillation Oscillations of a nonrotating, unmagnetized and fluid star can be described by a vector field, and the Eulerian (or “local”) perturbations of the pressure, density, and the gravitational potential,,, and. Employing the Newtonian gravity, the nonradial oscillation equations read We adopt the Cowling approximation, i.e. neglecting the perturbations of the gravitational potential.

30. Factorizing the displacement vector as, one has the oscillation equations as where is the eigenfrequency of a oscillation mode; is the local gravitational acceleration.

31. The eigen-mode can be determined by the oscillation Eqns when complemented by proper boundary conditions at the center and the surface of the star The Lagrangian density for the RMF is given as Five parameters are fixed by fitting the properties of the symmetric nuclear matter at saturation density.

32. For a newly born SQS, we implement the MIT bag model for its equation of state. We choose, and a bag constant. The equilibrium sound speed can be fixed for an equilibrium configuration, with baryon density, entropy per baryon, and the lepton fraction being functions of the radius. ( taken from Dessart et al. ApJ,645,534,2006 ).

33. We calculate the properties of the g-mode oscillations of newly born NSs at the time t=100, 200 and 300ms after the core bounce, the mass inside the radius of 20km is 0.8, 0.95, and 1.05 M Sun, respectively. We assume that the variation behaviors of and for newly born SQSs are the same as for NSs.  As ω changes to 100.7, 105.9, 96.1 Hz, respectively.  When M SQS = 1.4M sun, ω changes to 100.2, 91.4, 73.0 Hz, respectively.  As M SQS = 1.68M sun, ω changes to 108.8, 100.9, 84.5 Hz, respectively.

34. The reason for the large difference in the g-mode oscillation eigenfrequencies between newly born NSs and SQSs, is due to The components of a SQS are all extremely relativistic and its EOS can be approximately parameterized as are highly suppressed.

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