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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. Outline I. Introduction Ⅱ . The Approach Ⅲ . P.Ts. in Intrinsic Space & in Medium Ⅳ . Possible Observables V . Summary. Yuxin Li u

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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 Outline I. Introduction Ⅱ. The Approach Ⅲ. P.Ts. in Intrinsic Space & in Medium Ⅳ. Possible Observables V. Summary Yuxin Liu Department of Physics, Peking University, China The 3rd ATHIC，IOPP, CCNU, Wuhan, Oct. 18--20, 2010

  2. I. Introduction  The Evolution Process of the Universe Quarks and gluons get confined  Hadrons Non-confined quarks and gluons and leptons (F.S.) (F.S.B.) Nuclear synthesis  nuclei

  3. Items Influencing the Phase Transitions: Medium：Temperature T , Density  ( or  ) Size Intrinsic：Current mass, Coupling Strength, Color-flavor structure, ••• •••  The Phase Transitions and Schematic PD Phase Transitions involved： Deconfinement–confinement DCS– DCSB Flavor Sym.– FSB Chiral Symmetric Quark deconfined sQGP SB, Quark confined

  4.  Theoretical Approaches：Two kinds-Continuum & Discrete (lattice)  Lattice QCD： Running coupling behavior， Vacuum Structure， Temperature effect， “Small chemical potential”；    Continuum： (1)Phenomenological models NJL、QMC、QMF、 (2)Field Theoretical Chiral perturbation, Renormalization Group, QCD sum rules, Instanton(liquid) model, DS equations , AdS/CFT, HD(T)LpQCD ,    The approach should manifest simultaneously: (1)DCSB & its Restoration, (2)Confinement & Deconfinement .

  5.  A comment on the DSE approach in 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;  .

  6. Ⅱ. The Dyson-Schwinger Equation Approach 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;  .

  7. Quark equation in medium • with  Practical Algorithm at Present Stage Quark equation at zero chemical potential where is the effective gluon propagator, can be conventionally decomposed as Meeting the requirements!

  8.  Models of Vertex (1) Bare Vertex (Rainbow-Ladder Approx.) (2) Ball-Chiu Vertex (3) Curtis-Pennington Vertex

  9. 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

  10. Ⅲ. The Phase Transitions in I.-S. & in Medium • 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)

  11. Bare vertex CS phase CSB phase  Effect of the Running Coupling Strength on the Chiral Phase 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, Y.X. Liu, R.D. Roberts, et al., Phys. Rev. C 79, 035209 (2009))

  12.  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

  13. Hep-ph/0612061 confirms the existence of the 3rd solution, and give the 4th solution . Euro. Phys. J. C 60, 47 (2009) gives the 5th solution .

  14.  Part of the QCD Phase Diagram in terms of the Current Mass and Coupling Strength  The one with multi-node solutions is more complicated and more interesting.

  15.  Special Topic (1) of the P.T. in Medium：Critical EndPoint (CEP) The Position of CEP is a highly debated problem!  (p)NJL model & others give quite large E/TE (> 3.0) Sasaki, et al., PRD 77, 034024 (2008); Costa, et al., PRD 77, 096001 (2008); Fu, et al., PRD 77, 014006 (2008); Ciminale, et al., PRD 77, 054023 (2008); Fukushima, PRD 77, 114028 (2008); Kashiwa, et al., PLB 662, 26 (2008); Abuki, et al., PRD 78, 034034 (2008); Schaefer, et al., PRD 79, 014018 (2009); Costa, et al., PRD 81, 016007 (2010);  Hatta, et al., PRD 67, 014028 (2003); Cavacs, et al., PRD 77, 065016(2008);  • What can sophisticated DSE calculation produce ? • Why different models give distinct results ? Lattice QCD gives smaller E/TE ( 0.4 ~ 1.1) Fodor, et al., JHEP 4, 050 (2004); Gavai, et al., PRD 71, 114014 (2005); Gupta, arXiv:~0909.4630[nucl-ex]; Li, et al., NPA 830, 633c (2009);   RHIC Exp. Estimate hints quite small E/TE ( ~ 0.33) R.A. Lacey, et al., nucl-ex/0708.3512;   Simple DSE Calculations with Different Effective Gluon Propagators Generate Different Results (0.0, 1.3) Blaschke, et al, PLB 425, 232 (1998); He, et al., PRD 79, 036001 (2009); 

  16.  Special topic (2) of the P.T. in Medium： Coexistence region (Quarkyonic ? )  Lattice QCD Calculations de Forcrand, et al., NPB-PS 153, 62 (2006);  gives coexistence region. quarkyonic Generaal (large-Nc) Analysis McLerran, et al., NPA 796, 83 (‘07); NPA 808, 117 (‘08); NPA 824, 86 (‘09),  claims that there exists a quarkyonic phase.  Inconsistent with Coleman-Witten Theorem !!  Can sophisticated continuous field approach of QCD give the coexistence (quarkyonic) phase ?  What can we know more for the coexistence phase?

  17.  Special Topic (3) of the P.T. in Medium： QM at T above but near Tc • HTL Cal.(Pisarski, PRL 63, 1129(‘89); Blaizot, PTP S168, 330(’07)), Lattice QCD (Karsch, et al., NPA 830, 223 (‘09); PRD 80, 056001 (’09)) & NJL Cal. (Wambach, et al., PRD 81, 094022(2010))show: there exists thermal & Plasmino excitations in hot QM. • Other Quenched Lattice QCD Simulations • (Hamada, et al., Phys. Rev. D 81, 094506 (2010)) claims:NO • qualitative difference between the quark propagators in the deconfined and confined phases near the Tc. • RHIC experiments (Gyulassy, et al., NPA 750, 30 (2005); Shuryak, • PPNP 62, 48 (2009); Song, et al., JPG 36, 064033 (2009); ) indicate: • the matter is in sQGP state.  What is the nature of the matter in DSE?

  18. Phase Diagram of Strong Interaction Matter in Present DSE Approach of QCD PD in bare vertex PD in Ball-Chiu vertex S.X. Qin, L. Chang, Y.X. Liu, C.D. Roberts, to be published.

  19. Model Parameter Dependence of the CEP Small  short range in momentum space long range in coordinate space MN model infinite range in r-space NJL model “zero” range in r-space Stronger & Longer range Int.Smaller E/TE

  20. Property of the matter above but near the Tc Solving quark’s DSE  Quark’s Propagator Maximum Entropy Method (Asakawa, et al., PPNP 46,459 (2001); Nickel, Ann. Phys. 322, 1949 (2007)) • Spectral • Function S.X. Qin, L. Chang, Y.X. Liu, C.D. Roberts, to be published.

  21. Disperse Relation and Momentum Dependence of the Residues of the Quasi-particles’ poles at T=3.0Tc and T = 1.1Tc T = 1.1Tc T = 3.0Tc S.X. Qin, L. Chang, Y.X. Liu, C.D. Roberts, to be published.

  22. Property of the matter above but near the Tc At high momentum, the N.T. mode plays the main role & behaves like free particle. At high temperature (e.g., T = 3.0Tc), there exists Normal thermal mode & Plasmino mode excitations.  At the temperature near but above the Tc (e.g., T = 1.1Tc), there exists a zero mode, besides the N.T. mode and the P. mode.  The zero mode exists at low momentum (<7.0Tc), and is long-range correlation ( ~ 1 >FP) .  The quark at the T where S is restored involves still rich phases. And the matter is sQGP.

  23. General idea， Phenom. Calc., Sophist.Calc., quark may get deconfined(QCD PT) at high T and/or  Ⅳ. Possible Observables “QCD” Phase Transitions may Happen QCD Phase Transitions Signals for QCD Phase Transitions: In Lab. Expt. Jet Q., v2, Viscosity, CC Fluct. & Correl., Hadron Prop.,··· In Astron. Observ. M-R Rel., R.S., Rad., Inst. R. Oscil., Freq. G. Oscil., ···

  24. Density & Temperature Dependence of some Properties of Nucleon in DSE Soliton Model (Y. X. Liu, et al., NP A 695, 353 (2001); NPA 725, 127 (2003); NPA 750, 324 (2005) ) ( Y. Mo, S.X. Qin, and Y.X. Liu, Phys. Rev. C 82, 025206 (2010) )

  25. Temperature dependence of some properties of  & -mesons in the model with contact interaction ( Wei-jie Fu, and Yu-xin Liu, Phys. Rev. D 79, 074011 (2009) )  Fluctuation & Correlation of Conserved Charges ( W.J. Fu, Y.X. Liu, & Y.L. Wu, Phys. Rev. D 79, 014028 (2010) )

  26.  Frequency of Gravitational-mode Pulsation in Newly Born Quark Star & Neutron Star Neutron Star: RMF, Quark Star: Bag Model Frequency of g-mode pulsation W.J. Fu, H.Q. Wei, and Y.X. Liu, arXiv: 0810.1084, Phys. Rev. Lett. 101， 181102 (2008)

  27. Taking into account the DCSB 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 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.

  29. V. Summary & Remarks  Coexistence Phase； CEP (E/TEcomparable with Lattice D & EE) Effects of the C.-Strength & Current Mass  Discussed some aspects of QCD phase transitions in the DS equation approach of QCD  Far from Well Established !  Observables ?!  Mechanism ?! Process ?!       Thanks !!

  30.  Color Superconductivity ( CSC）

  31.  Analytic Continuation from Euclidean Space to Minkowskian Space • = 0, ei=1, • ==> E.S. • = , ei=1, • ==> M.S. ( W. Yuan, S.X. Qin, H. Chen, & YXL, PRD 81, 114022 (2010) )

  32. Dynamical chiral symmetry breaking (DCSB) generates the mass of Fermion < qq >0 ~ - (240 MeV)3  Dynamical Mass SB Maris & Roberts

  33.  Hadron Structure

  34. Some Numerical Results

  35. Effect of the F.-S.-B. (m0) on Meson’s Mass Solving the 4-dimenssional covariant B-S equation with the kernel being fixed by the solution of DS equationand flavor symmetry breaking, we obtain ( L. Chang, Y. X. Liu, C. D. Roberts, et al., Phys. Rev. C 76, 045203 (2007) )

  36. DSE Soliton Description of Nucleon B. Wang, H. Chen, L. Chang, & Y. X. Liu, Phys. Rev. C 76, 025201 (2007) Collective Quantization: Nucl. Phys. A790, 593 (2007).

  37. Compositions and Phase Structure of Compact Stars and their Identification Composition & Structure of NS are Still Under Study ! Radio Pulses = “Neutron” Stars

  38. Possible Composition of Compact Stars 背景简介 ( F.Weber, PPNP 54, 193 (2005) )

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