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QCD Phase Transitions in an Improved PNJL Model

QCD Phase Transitions in an Improved PNJL Model. Outline I. Introduction Ⅱ . The Improved PNJL Model Ⅲ . Numerical Results Ⅳ . Remarks. 刘玉鑫 北京大学 物理系. The 10 th Workshop on QCD Phase Transitions & RHIC Physics, Sichuan University, Chengdu, Aug. 8-10, 2013. 为何禁闭 ? 如何禁闭 ?. 明亮物质 ~ 5% .

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QCD Phase Transitions in an Improved PNJL Model

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  1. QCD Phase Transitions in an Improved PNJL Model Outline I. Introduction Ⅱ. The Improved PNJL Model Ⅲ. Numerical Results Ⅳ. Remarks 刘玉鑫 北京大学 物理系 The 10th Workshop on QCD Phase Transitions & RHIC Physics, Sichuan University, Chengdu, Aug. 8-10, 2013

  2. 为何禁闭? 如何禁闭? 明亮物质~5%. >95% ? ? 暗物质？ 暗能量？ 宇宙的形成、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 粒子的确认！？ 核 合 成 原 子 核 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： QPG? sQGP? 强子结构？ “已知”明亮物质：原子、分子 (强子)物质

  3. 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,••• 对基本问题归结为相变，研究正如火如荼 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 ？ Schematic QCD Phase Diagram Chiral Symmetric Quark deconfined ？ ？ 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

  4.  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 .

  5. Special Topic: Relation Between the DCSB & the Confinement ?  Coleman-Witten Theorem (conjecture): They coincide with each other (PRL 1980)  Lattice QCD Calculation de Forcrand, et al., Nucl. Phys. B Proc. Suppl. 153, 62 (2006);  andGeneral (large-Nc) Analysis McLerran, et al., NPA 796, 83 (‘07); NPA 808, 117 (‘08); NPA 824, 86 (‘09),  quarkyonic claim that there exists a quarkyonic phase. == DCSB does not coincide with confinement !  What practical approaches can give ? • Phase boundaries ? CEPs?

  6. Ⅱ. The Improved PNJL Model NJL Model can describe DCS-DCSB PT well ! Lagrangian (three flavors, traditional ) Effective Thermodynamical Potential

  7. Ⅱ. The Improved PNJL Model PNJL Model can describe conf.-deconf. phl. Intuitive View : ♣ SUc(3) has center Z3 ,  color appears if Z3 broken ! ● ● ♣ Pure gauge effective thermal potential ● PNJL Effective Thermodynamical Potential

  8. Improvement on the PNJL Model PNJL Model ΩPNJL = ΩNJL + U P-loop Originally U P-loop=T4f (T0, T, Φ, Φ*) , One commonly used form of f : f = ̶̶ a(T,T0) +b(T,T0)ln[1 ̶̶ 6Φ*Φ+ 4(Φ*3+Φ3) ̶̶ 3(Φ*Φ)2] with Result in 2+1 flavor DSE (arXiv:1306.6022) hints: T4P SB = T4+T2μ2+μ4

  9. Improvement on the PNJL Model Our Improvement (1) T4 T4+AT2μ2+Bμ4 ~ rescaled-P SB= T4+ 0.288 T2μ2+ 0.0146 μ4 (2) In the functions a(T,T0) and b(T,T0) , with A, B, and η being parameters .

  10. Ⅲ. Numerical Results Preliminary calculations are carried out with A = 0.30 ( ~ 0.288 , the one in rescaled P SB ) , {PNJL parameters} = { commonly used } , and B and η as free parameters . The Improvement gives: T induces crossover, μ drives first order phase transition !

  11. Ⅲ. Numerical Results Detailed data for: T induces crossover, μ drives first order phase transition !

  12. Ⅲ. Numerical Results Phase Diagram (TEc,µEc) = (135MeV, 363MeV) Quarkyonic phase Stable! Quarkyonic phase Stable! (TEc,µEc) = (147MeV, 193MeV) Quarkyonic phase Metastable!

  13. IV. Summary & Remarks  Phase Diagrams of the two PTs are given; The two PTs separate from each other;  The CEPs of the two PTs may coincide;Quarkyonic phasemay bea metastable phase. • An improved PNJL model is proposed with the quark chemical potential effect being involved explicitly in the Polyakov-loop potential. • QCD phase transitions are investigated • Thorough investigations are needed . Thanks !!

  14. 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); LYX, Roberts, et al., CTP 58 (2012), 79;  .

  15.  Dyson-Schwinger Equations (DSEs) in 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); C.S. Fischer, JPG 32(2006), R253;  .

  16.  Practical Algorithm at Present  Truncation：Preserving Symm. Quark Eq.  Decomposition of the Lorentz Structure  Quark Eq. in Vacuum : 

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

  18. Cuchieri, et al, PRD, 2008  Models of the effective gluon propagator Commonly Used: Maris-Tandy Model (PRC 56, 3369) (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 arXiv:1209.1974show that the one in 4-D should be infrared constant.

  19. 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)

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

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

  22. 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)

  23. New Crirerion: m2 of mesons Effective Thermal Potential Phase diagram K.L. Wang, L. Chang, Y.X. Liu, C.D. Roberts, et al., Phys. Rev. D 86, 114001 (2012)

  24. 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))

  25.  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

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

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

  28. 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, & C.D. Roberts, Phys. Rev. Lett. 106, 172301 (2011)

  29.  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)

  30.  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)

  31. 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)

  32. T-dependence of some hadrons’ properties in DSE ( Kun-lun Wang, Yu-xin Liu, Lei Chang, C.D. Roberts, & S.M. Schmidt, Phys. Rev. D 87, 074038 (2013) )

  33. 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-M. Oscil., ···

  34. 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).

  35. 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) )

  36. 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) )

  37. T-dependence of some properties of mesonsin the model with contact interaction ( Wei-jie Fu, and Yu-xin Liu, Phys. Rev. D 79, 074011 (2009) ; Kun-lun Wang, Yu-xin Liu, & C.D. Roberts, PRD 87, 074038)

  38. Fluctuation & Correlation of Conserved ChargesRecent Lattice QCD results agree with ours excellently! W.J. Fu, Y.X. Liu, & Y.L. Wu, PRD 81, 014028 (2010)。 HotQCD Collaboration, 1203.0784

  39.  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;

  40.  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)

  41. 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).

  42. V. Summary & Remarks  Dynamical Mass is generated by DCSB;  Phase Diagram is given;  CEP is fixed & Coexisting Phase is discussed; sQGP above but near the Tc is discussed. • DSE, a npQCD approach, is described • QCD phase transitions are investigated via DSE • Some possible observables are discussed .  Far from well established ! Thanks !!

  43.  Experimental Aspects： （1）Relativistic Heavy Ion Collisions (u23u) 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

  44.  Special Topic (1) : Critical EndPoint (CEP) The Existence & Position of CEP is highly debated !  (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);  • Whatsophisticated DSE calculation can give? • 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); 

  45.  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?

  46.  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: • 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?

  47. Ⅳ. Hadrons via DSE Pressure difference provides the bag constant.  Approach 1: Soliton bag model 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)。

  48. 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) )

  49. 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) )

  50. 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)

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