早期宇宙强相互作用物质的演化 北京大学 物理系 中国科技大学， 2015年4月3日 提 纲 I. 演化过程与物理图像 Ⅱ. 理论描述 刘玉鑫 北京大学 物理系 提 纲 I. 演化过程与物理图像 Ⅱ. 理论描述 Ⅲ. 实验观测 Ⅳ. 小结 中国科技大学， 2015年4月3日

I. 演化过程与物理图像 核 合 成 原 子 复 合 时 期 原 子 星 系 形 成 现 在 宇 宙 不束缚的夸克、 胶子及电子等 为何禁闭? 如何禁闭? Mu,d >= 100mu,d , 如何产生？ 强作用非微扰效应 ！? 核力？关联模式? 集体运动模式及其相变? 手征对称性硬破缺, Higgs机 制, Higgs 机制的微观基础?! 核 合 成 原 子 复 合 时 期 原 子 mq > 0 ， 呈6味3代 . 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 高度对称, mq = 0 . “全新”形态物质： QGP? sQGP? 强子结构？ “已知”明亮物质：原子、分子 (强子)物质

？ ？ ？ 对基本问题归结为相变，研究正如火如荼 Schematic QCD Phase Diagram 涉及相变： 禁闭（强子化） – 退禁闭 手征对称性破缺 – 恢复 味对称 – 味对称性破缺 ？ Chiral Symmetric Quark deconfined ？ 影响QCD相变的因素: 介质效应：温度, 密度 (或化学势) 有限尺度 内禀因素：流质量, 跑动耦合强度, 色味结构, ••• sQGP ？ SB, Quark confined 研究方法： 实验：RHIC、Ast-Obs. 理论：离散场论、连续场论 计算：实现理论、模拟

目前关注的核心问题(1): 相变级次与相变机制 Y. Aoki, et al., Nature 443, 675 (2006) : Lattice QCD: T Crossover, Evolve smoothly. F. Wilczek, Nature 443, 637 (2006)； Nature Phys. 3, 375 (2007); 包含有限流夸克质量效应的强相互作用物质的相结构和相变级次及机制是相关研究的核心问题之一! 密度效应 ?!

目前关注的核心问题(2): 手征相变与禁闭相变的关系 目前关注的核心问题(2): 手征相变与禁闭相变的关系  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 (PRL 45, 100 (‘80)): Confinement coincides with DCSB !!  Is any hierarchy between the two kind PTs ?

目前关注的核心问题(3): 临界终点的存在性及其位置和观测信号 目前关注的核心问题(3): 临界终点的存在性及其位置和观测信号  (p)NJL model & others give quite large Eq/TE (> 3.0) Sasaki, et al., PRD 77, 034024 (2008); 82, 076003 (2010); 82, 116004 (1010); 0). Costa, et al., PRD 77, 096001 (‘08); EPL 86, 31001 (‘09); PRD 81, 016007(‘10); 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); Hatta, et al., PRD 67, 014028 (2003); Cavacs, et al., PRD 77, 065016(2008); Bratovic, et al., PLB 719, 131(‘13); Bhattacharyya, et al., PRD 87,054009(‘13); Jiang, et al., PRD 88, 016008 (2013); Ke, et al., PRD 89, 074041 (2014);   Lattice QCD gives smaller Eq/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., PRD 84, 071503 (2011); Gupta，et al., Science 332, 1525 (2011); PRD 90, 034001 (2014);   DSE Calculations with different techniques generate different results for the Eq/TE (0.0, 1.1 ~ 1.3, 1.4 ~ 1.6, ) Blaschke, et al, PLB 425, 232 (1998); He, et al., PRD 79, 036001 (2009); Qin, et al., PRL 106, 172301 (2011); Fischer, et al., PLB 702, 438 (‘11); PLB 718, 1036 (‘13); PRD 90, 034022 (‘14)  各大装置都将之列为最重要的研究目标，国际上有每年一次的专题研讨会，足见对该问题的重视程度。 R.A. Lacey, et al., nucl-ex/0708.3512; 但到现在仍未正式发表。

目前关注的核心问题(4): 手征相变赝临界温度之上物质的性质 目前关注的核心问题(4): 手征相变赝临界温度之上物质的性质 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: 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’s the nature of the matter in npQCD?

Ⅱ. 理论描述 Ⅱ-1. 概述：两类：连续场论、离散场论 (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 be non-perturbative and manifest simultaneously: (1) DCSB & its Restoration , (2) Confinement & Deconfinement .

Ⅱ-2. The Dyson-Schwinger Eq. 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); LYX, Roberts, et al., CTP 58 (2012), 79;  .

？ ？  Algorithms of Solving the DSEs of QCD Solving the coupled quark, ghost and gluon (parts of the diagrams) equations, e.g., (2) Solving the truncated quark equation with the symmetries being preserved. ？ ？

 Expression of the quark gap equation  Truncation：Preserving Symm.  Quark Eq.  Decomposition of the Lorentz Structure  Quark Eq. in Vacuum : 

 Quark Eq. in Medium S S Matsubara Formalism Temperature T :  Matsubara Frequency Density  ：  Chemical Potential S S Decomposition of the Lorentz Structure S S

 Models of the eff. gluon propagator Commonly Used: Maris-Tandy Model (PRC 56, 3369) Cuchieri, et al, PRD, 2008 (3) Recently Proposed: Infrared Constant Model ( Qin, Chang, Liu, Roberts, Wilson, PRC 84, 042202(R), (2011). ) A.C. Aguilar, et al., JHEP 1007-002 Taking in the coefficient of the above expression Derivation and analysis in PRD 87, 085039 (2013) show that the one in 4-D should be infrared constant.

 Models of quark-gluon interaction vertex (1) Bare Ansatz (Rainbow-Ladder Approx.) (2) Ball-Chiu Ansatz Satisfying W-T Identity, L-C. restricted (3) Curtis-Pennington Ansatz Satisfying Prod. Ren. (4) BC+ACM (Chang, Liu, etc, PRL 106, 072001, Qin, etc, PLB 722)

DSE approach meets the requirements! DSE approach meets the requirement to describe the evolution process of early universe SIM  SB Dynamical Mass < qq >0 ~ - (240 MeV)3 In DSE approach DSE approach meets the requirements!

 A comment on the DSE approach of QCD Dyson-Schwinger Equations 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); LYX, et al., CTP 58, 79 (2012);  .

Ⅱ-2. QCD Phase Transitions via the DSE  Quantity to identify the phase transition  Traditionally Criterion in Dynamics: Equating Effective TPs With fully Nonperturbative approach, one could not have the ETPs. New Criterion must be established!

 New Criterion: Chiral Susceptibility For 2nd order PT & Crossover, s diverge at same states. For 1st order PT, the s diverge at different states.  the  criterion can not only give the phase boundary, but also determine the position of the CEP. Phase diagram in bare vertex Phase diagram in BC vertex S.X. Qin, L. Chang, H. Chen, Y.X. Liu, C.D. Roberts, PRL 106, 172301(‘11)

 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) Bare vertex CS phase CSB phase (BC Vertex: L. Chang, Y.X. Liu, R.D. Roberts, et al., Phys. Rev. C 79, 035209 (2009))

 Intuitive picture of Mass Generation K.L. Wang, L. Chang, Y.X. Liu, C.D. Roberts, et al., Phys. Rev. D 86, 114001 (2012); 

 DCSB still exists beyond chiral limit L. Chang, Y. X. Liu, C. D. Roberts, et al, arXiv: nucl-th/0605058; R. Williams, C.S. Fischer, M.R. Pennington, arXiv: hep-ph/0612061. Solutions of the DSE with With  = 0.4 GeV with D = 16 GeV2,   0.4 GeV

 Effective Thermal Potential gets deformed In chiral limit Beyond chiral limit K.L. Wang, L. Chang, Y.X. Liu, C.D. Roberts, et al., Phys. Rev. D 86, 114001 (2012)

 Analyzing the spectral density function in the DSE can demonstrate the confinement-deconfinement PT well H. Chen, YXL, et al., Phys. Rev. D 78, 116015 (2008) S.X. Qin, D. Rischke, Phys. Rev. D 88, 056007 (2013)

Phase diagram is given, CEP is proposed Phase diagram in bare vertex Phase diagram in BC vertex S.X. Qin, L. Chang, H. Chen, Y.X. Liu, & C.D. Roberts, Phys. Rev. Lett. 106, 172301 (2011)

 Diff. of CEP comes from diff. Conf. 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)

 Property of the matter above but near the Tc Solving quark’s DSE  Quark’s Propagator In M-Space, only Yuan, Liu, etc, PRD 81, 114022 (2010). Usually in E-Space, Analytical continuation is required. 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)

 The zero mode exists at low momentum (<7.0Tc), Disperse Relation and Momentum Dependence of the Residues of the Quasi-particles’ poles T = 3.0Tc T = 1.1Tc Normal T. Mode 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, et al., Phys. Rev. D 84, 014017(2011); F. Gao, S.X. Qin, Y.X. Liu, et al., Phys. Rev. D 89, 076009 (2014).

Ⅲ. 实验观测研究方法： (1) 相对论性重离子碰撞（RHIC）等 (u23u) (2) 对致密星性质等的观测 Observations 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… 正运行的装置：美国的RHIC, CERN的ALICE-LHC 正(拟)建造的装置：FAIR(德), NICA(俄), HIAF(中) (2) 对致密星性质等的观测 Observations

 Possible Observables “QCD” Phase Transitions may Happen General idea， Phenom. Calc., Sophist. Calc., quark may get deconfined(QCD PT) at high T and/or  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-M. Oscil., ···

Some properties of mesons in DSE-BSE Present work ( L. Chang, & C.D. Roberts, Phys. Rev. C 85, 052201(R) (2012) ) ( S.X. Qin, L. Chang, Y.X. Liu, C.D. Roberts, et al., Phys. Rev. C 84, 042202(R) (2011) )

Chiral Symmetry Breaking generates the Anomalous Magnetic Moment of Quark Consequently, nucleon has anomalous magnetic moment. L. Chang, Y.X. Liu, & C.D. Roberts, PRL 106, 072001 (‘11)

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) )

T-dependence of the screening masses of some hadrons in contact interaction model Degenerate Chiral symmetry restored. , when , the color gets deconfined. Hadron properties provide signals for not only the chiral phase transt. but also the confinement-deconfnmt. phase transition. ( Wei-jie Fu, and Yu-xin Liu, Phys. Rev. D 79, 074011 (2009) ; Kun-lun Wang, Yu-xin Liu, et al., Phys. Rev. D 87, 074038 (2013)

● 守恒荷的涨落与关联 粒子数 守恒荷的二阶、四阶、六阶涨落 其中 广义磁化率 并有两守恒荷间的关联

 Quark Number Density Fluctuations vs T via full DSE X.Y. Xin, S.X. Qin, YXL, PRD 90, 076006 (2014)

 Quark Number Density Fluctuations vs μ via full DSE X.Y. Xin, S.X. Qin, YXL, PRD 90, 076006 (2014)

 Critical Behavior & the Phase Diagram Fei Gao, Yu-xin Liu, et al., to be published

 Only the star matter including deconfined quarks can give stars 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;

 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)

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

Thanks !! Ⅳ. Summary & Remarks Evol. of EU SIM is described in view of QCD PTs QCD phase transitions are investigated via DSE  Dynamical Mass is generated by DCSB;  Phase Diagram is given;  Critical exponents & the CEP are Proposed;  sQGP above but near the Tc is discussed. Some possible observables are discussed .  Sig. topic for Fund.-Prob. under developing ! Thanks !!

 Criterion for Confinement ♠ Positivity Violation of the Spectral Function S.X. Qin, and D.H. Rischke, Phys. Rev. D 88, 056007 (2013) Maximum Entropy Method ( Asakawa, et al., PPNP 46,459 (2001); Nickel, Ann. Phys. 322, 1949 (2007) ) Result in DSE

Ⅳ. Hadrons via DSE  Approach 1: Soliton bag model Pressure difference provides the bag constant. Approach 2: BSE + DSE  Mesons BSE with DSE solutions being the input  Baryons Fadeev Equation or Diquark model (BSE+BSE) L. Chang, et al., PRL 103, 081601 (2009)。

 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 equation and flavor symmetry breaking, we obtain ( L. Chang, Y. X. Liu, C. D. Roberts, et al., Phys. Rev. C 76, 045203 (2007) )

Electromagnetic Property & PDF of hadrons Proton electromagnetic forma factor P. Maris & PCT, PRC 61, 045202 (‘00) L. Chang et al., AIP CP 1354, 110 (‘11) PDF in pion PDF in kaon R.J. Holt & C.D. Roberts, RMP 82, 2991(2010); T. Nguyan, CDR, et al., PRC 83, 062201 (R) (2011)

T-dependence of some properties of  & -mesons and - S-L 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) )

Taking into account the DCSB effect

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) )

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

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