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早期宇宙强相互作用物质演化 的非微扰 QCD 研究

早期宇宙强相互作用物质演化 的非微扰 QCD 研究. 刘玉鑫 （ Yuxin Li u ） 北京大学物理学院理论物理研究所 Depart ment of Physics, Peking University, China yxliu@pku.edu.cn. Outline I. Introduction Ⅱ . The Approach Ⅲ . The Evolution in Phase Transition View Ⅳ . Possible Observables V . Summary.

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早期宇宙强相互作用物质演化 的非微扰 QCD 研究

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  1. 早期宇宙强相互作用物质演化的非微扰QCD研究 刘玉鑫 （Yuxin Liu） 北京大学物理学院理论物理研究所 Department of Physics, Peking University, China yxliu@pku.edu.cn Outline I. Introduction Ⅱ. The Approach Ⅲ. The Evolution in Phase Transition View Ⅳ. Possible Observables V. Summary 第十四届全国核结构大会，湖州师院，2012年4月12日

  2.  Content of the Long Rang Plan of Nuclear Sciencein USA I. Introduction

  3. 如何禁闭? 为何禁闭? 明亮物质~5%. > 95% ? ? 暗物质？ 暗能量？ 早期宇宙物质的组分及演化涉及的基本问题 Mu,d>= 100mu,d ,如何产生？ 强作用非微扰效应！? 手征对称性硬破缺,Higgs机制, Higgs 粒子？测量LHC信号？ 核 合 成 原 子 核 复 合 时 期 原 子 高度对称, mq = 0 . 夸克、 胶子 囚禁 强子 星 系 形 成 现 在 宇 宙 不束缚的夸克、 胶子及电子等 mq> 0 ，呈6味3代 . 全“新”形态物质： QPG? sQGP? “已知”明亮物质：原子、分子 (强子)物质

  4. Items Influencing the Phase Transitions: Medium：Temperature T, Density(CheP.) Size Intrinsic：Current mass, Coupling Strength, Color-Flavor Stru. Fundamental Process: Phase Transitions Phase Transitions involved： Deconfinement–confinement DCS– DCSB Flavor Sym.– FSB Schematic QCD Phase Diagram Chiral Symmetric Quark deconfined sQGP SB, Quark confined Approaches: Expt.：RHIC、Ast-Obs. Theor.：Disc FT、ContFT, Compt.：Theor., Simulation

  5. Experimental Aspects： （1）Relativistic Heavy Ion Collisions Thin Pancakes Lorentz g=100 Nuclei pass thru each other < 1 fm/c Huge Stretch Transverse Expansion High Temperature (?!) The Last Epoch: Final Freezeout-- Large Volume We measure the “final” state, we are most interested in the “intermediate” state, we need to understand the “initial” state… （2） Compact Star Observations

  6.  Theoretical Approaches：Two kinds-Continuum & Discrete (lattice)  Lattice QCD： Running coupling behavior， Vacuum Structure， Temperature effect， “Small chemical potential”；    Continuum： (1)Phenomenological models (p)NJL、(p)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 .

  7. 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;  .

  8. 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

  9.  Models of the Vertex (1) Bare Vertex (Rainbow-Ladder Approx.) (2) Ball-Chiu Vertex 满足W-T恒等式, 对纵向分量给出标准. (3) Curtis-Pennington Vertex 满足相乘性重整化。 (4) BC+ACM Vertex(Chang, Liu, Roberts, PRL 106, 072001 (‘11) )

  10. Cuchieri, et al, PRD, 2008  Effective Gluon Propagators (1) MN Model (2) Point Interaction: (P) NJL Model (3) (3)Model (2) A.C. Aguilar, et al., JHEP 1007-002 (4) Realistic model <i> Maris-Tandy Model <ii> Infrared Constant Model Taking in the coefficient of the above expres. Qin, Chang, Liu, et al., PRC 84, 042202(R), (‘11); 85, 035202, (‘12).

  11. Dynamical chiral symmetry breaking (SB) generates the mass of Fermion < qq >0 ~ - (240 MeV)3  Dynamical Mass SB In DSE approach DSE approach meets the requirements!

  12. 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))

  13.  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. One Solution (ECSB) Three Solutions (ECSB + DCSB)

  14.  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;  .

  15. III. The Evolution in Phase Transition View Special Topic (1) : 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 & Liu, 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’s the criterion of PT when not knowing the ETP? • 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); Gupta & Xu, et al., Science 332, 1525 (2011);   RHIC Exp. Estimate hints quite small E/TE (  1) 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): Coexistence region (Quarkyonic ? )  Lattice QCD Calculation de Forcrand, et al., Nucl. Phys. B Proc. Suppl. 153, 62 (2006);  quarkyonic and General (large-Nc) Analysis McLerran, et al., NPA 796, 83 (‘07); NPA 808, 117 (‘08); NPA 824, 86 (‘09),  claim 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. Chiral susceptibility can be the criterion! Phase diagram is given, CEP is fixed. Phase diagram in bare vertex Phase diagram in BC vertex S.X. Qin, L. Chang, H. Chen, Y.X. Liu, et al, PRL 106, 172301(‘11)

  18.  Dif. of CEP come from dif. Confin. Length Small σ long range in coordinate space MN model  infinite range in r-space NJL model “zero” range in r-space Longer range Int. Smaller E/TE S.X. Qin, L. Chang, H. Chen, Y.X. Liu, et al, PRL 106, 172301(‘11)

  19.  Special Topic (3): Quark Matter 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 (Wambach, et al., PRD 81, 094022(2010)) & Simple DSE Cal. (Fischer et al., EPJC 70, 1037 (2010) ) show: there exists thermal & Plasmino excitations in hot QM. • Other Lattice QCD Simulations • (Hamada, et al., Phys. Rev. D 81, 094506 (2010)) claims: • Noqualitative 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’s the nature of the matter in npQCD?

  20. Property of the matter above but near the Tc In M-Space, only Yuan, Liu, etc, PRD 81, 114022 (2010). Usually in E-Space, Analytical continuation is required. 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 Qin, Chang, Liu, et al., PRD 84, 014017(2011)

  21. Disperse Relation and Momentum Dependence of the Residues of the Quasi-particles’ poles T = 1.1Tc Normal T. Mode T = 3.0Tc Zero Mode Plasmino M.  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. S.X. Qin, L. Chang, Y.X. Liu, C.D. Roberts, PRD 84, 014017(‘11)

  22. 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. 5. D. Nickel, et al., PRD 77, 114010 (2008); ………… Chiral Susceptibility of Wigner-Vacuum in DSE

  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., Rad. Sp., 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. T-dependence of some properties of &-mesons and  -  S-L. in the model with contact interaction ( Wei-jie Fu, and Yu-xin Liu, Phys. Rev. D 79, 074011 (2009) )

  26. Fluctuation & Correlation of Conserved ChargesRecent Lattice QCD results agree with ours excellently! W.J. Fu, Y.X. Liu, & Y.L. Wu, PRD 79, 014028 (2010)。 HotQCD Collaboration, 1203.0784

  27.  Gravitational Mode Pulsation Frequency can be an Excellent Astronomical Signal 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)

  28. Taking into account the SB effect

  29. 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, ····· g-mode pulsation frequency can be a signal identifying the QCD phase transitions in high density matter ( compact star matter).

  30.  Only the star matter including deconfined quarks can give the one with M  2.0Msun  Hadron-star’s mass can not be larger than 1.8Msun G.Y. Shao, Y. X. Liu, Phys. Rev. D 82, 055801 (2010).  Quark-star’s mass can be larger than 2.0Msun （Nature 467, 1081 (2010) reported） H.S. Zong, et al., PRD 82, 065017 (2010); MPL 25, 47 (2010); PRD 83, 025012 (2011); PRD 85, 045009 (2012); etc;

  31. V. Summary & Remarks  Dynamical Mass is Generated by DCSB;  Phase Diagram is given;  CEP is fixed & Coexisting Phase is discussed; Some observables are proposed. • Discussed some aspects of the Early Universe • Matter Evolution in view of the QCD phase • transitions in the DS equation approach of QCD  Far from Well Established !  Observables ?!  Mechanism ?! Process ?!    Thanks !!

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