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Phase Transitions of Strong Interaction System in Dyson-Schwinger Equation Approach

Phase Transitions of Strong Interaction System in Dyson-Schwinger Equation Approach. Yu-xin Liu （刘玉鑫） Department of Physics, Peking University, China. Outline I. Introduction II. The Approach

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Phase Transitions of Strong Interaction System in Dyson-Schwinger Equation Approach

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  1. Phase Transitions of Strong Interaction System in Dyson-Schwinger Equation Approach Yu-xin Liu（刘玉鑫） Department of Physics, Peking University, China Outline I. Introduction II. The Approach III. Some Numerical Results of Our Group IV. Summary & Outlook 第13届全国中高能核物理大会，中国科技大学，合肥，2009年11月5-7日

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

  3. 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),  AdS/CFT General Requirements for the approaches: not only involving the chiral symmetry & its breaking , but also manifesting the confinement and deconfinement .

  4. II. The DSE Approach of QCD Dyson-Schwinger Equations Slavnov-Taylor Identity axial gauges BBZ covariant gauges 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. Quark equation in medium • with  Practical Way at Present Stage Quark equation at zero chemical potential where is the effective gluon propagator, can be conventionally decomposed as Meeting the requirements!

  6. Cuchieri, et al, PRL, 2008  Effective Gluon Propagators (1) MN Model (2)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.  Models of Vertex (1) Bare Vertex (Rainbow-Ladder Approx.) (2) Ball-Chiu Vertex (3) Curtis-Pennington Vertex

  8. For Hadron Structure (1) Bethe-Salpeter Equation approach (2) Soliton Model (non-local fields)

  9. Examples of achievements of the DSE of QCD Generation of Dynamical Mass Taken from: Tandy’s talk at Morelia-2009 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)

  10. More recent result for the mass splitting between ρ& a1 mesons

  11. III. Some Numerical Results of Our Group • Chiral Susceptibility (S & SB phases simultaneously): Signature of the Chiral Phsae Transition Point Interaction  S Phase Y. Zhao, L. Chang, W. Yuan, Y.X. Liu, Eur. Phys. J. C 56, 483 (2008)

  12. Bare vertex CS phase CSB phase Effect of the Running Coupling Strength on the Chiral Phsae Transition (W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006)) parameters are taken From Phys. Rev. D 65, 094026 (1997), with fitted as Lattice QCD result PRD 72, 014507 (2005) (BC Vertex: L. Chang, YXL, RDR, Zong, et al., Phys. Rev. C 79, 035209 (‘09))

  13. Effect of the Current Quark Mass on the Chiral Phase Transition 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

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

  15. Phase Diagram in terms of the Current Mass and the Running Coupling Strength BC vertex gives qualitatively same results.

  16. Hep-ph/0612061 confirms the existence of the 3rd solution, and give the 4th solution . Euro. Phys. J. C 60, 47 (2009) gives the 4th solution .

  17. Effect of the Chemical Potential on the Chiral Phase Transition 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) ) 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; ………… Chiral Susceptibility of Wigner-Vacuum in DSE

  18. Alkofer’s Solution-2cc NJL Model Solution with BC vertex Alkofer’s Solution-BCFit1 BC vertex CSB phase Bare vertex  Partial Restoration of Dynamical S • & Matter Generation BC vertex BC vertex BC vertex CS phase 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)

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

  20. Density Dependence of some Properties of Nucleon in DSE Soliton Model - relationnucleon properties (Y. X. Liu, et al., Nucl. Phys. A 695, 353 (2001); NPA 725, 127 (2003); NPA 750, 324 (2005) )

  21.  Chemical Potential Dependence of N L. Chang,Y. X. Liu, H. Guo, Phys. Rev. D 72, 094023 (2005) Newly result (H. Chen, YXL, et al., to be published) : In BC vertex: N = (60~80) MeV。

  22. Temperature Dependence of the Propagators of Gluon and Ghost Lattice QCD Results (A. Maas, et al., EPJC 37, 335 (2004); A. Cucchieri, et al., PRD 75, 076003 (2007) ): with Previous DSE solutions in torus momentum space do not give the same results (C.S. Fischer, et al., Ann. Phys. 321, 1918 (2006); ··· ) .

  23. Our Newly Results in continuum momentum space Solving coupled equations of gluon and ghost:  (H. Chen, R. Alkofer, Y.X. Liu, to be published)

  24. Phase Diagram of Strong Interaction Matter Result in bare vertex Result in Ball-Chiu vertex   (GeV) S.X. Qin, L. Chang, Y.X. Liu, to be published.

  25. Phase Diagram of the（2+1）Flavor System 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

  26. An Astronomical Signal Identifying the QCD Phase Transition Neutron Star: RMF, Quark Star: Bag Model Frequency of g-mode oscillation W.J. Fu, H.Q. Wei, and Y.X. Liu, arXiv: 0810.1084, Phys. Rev. Lett. 101， 181102 (2008)

  27. Taking into account the SB effect

  28. 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 oscillation 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.

  29.  QCD Phase Transitions:With the DSE approach of QCD, we show that IV. Summary & Discussion：  above a critical coupling strength and below a critical current mass, DCSB appears; Thanks !!!  above a criticalμ, S can be restored partially. A mechanism is proposed !  The finite-T effect on the pure gauge fields are given.  Phase diagram of strong interaction matter (T-μ) ?!  We develop the Polyakov-NJL model for (2+1) flavor system and study the phase transitions.  Driving the Polyakov-loop from DSE ?!  We propose an astronomical signal manifesting the quark deconfinement phase transition in dense matter.  Being checked in sophisticated DSE approach !

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

  31. 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.

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

  33. 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.

  34. 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 ). • For a newly born SQS, we implement the MIT bag model for its equation of state. We choose , and a bag constant .

  35. 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 MSun , 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 MSQS = 1.4Msun , ω changes to 100.2, 91.4, 73.0 Hz, respectively.  As MSQS = 1.68Msun , ω changes to 108.8, 100.9, 84.5 Hz, respectively.

  36. 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.

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