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Static/Dynamic Correlations in Hot QCD -- Tickling the QCD Vacuum --

RHIC (2000- ). WMAP (2001-). Static/Dynamic Correlations in Hot QCD -- Tickling the QCD Vacuum --. T. Hatsuda (Univ. Tokyo). Two major experiments to probe the early Universe. Big Bang. Little Bang. Present (13.7 x 10 9 years). RHIC data. WMAP data (3x10 5 years).

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Static/Dynamic Correlations in Hot QCD -- Tickling the QCD Vacuum --

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  1. RHIC (2000- ) WMAP (2001-) Static/Dynamic Correlations in Hot QCD -- Tickling the QCD Vacuum -- T. Hatsuda (Univ. Tokyo) Two major experiments to probe the early Universe

  2. Big Bang Little Bang Present (13.7 x 109 years) RHIC data WMAP data (3x105 years) Hot Era QGP Inflation CGC

  3. Contents • [1] Origin of Masses • -- one of the big questions in modern physics • [2] QCD Phase Structure • -- similarity to High Tc superconductivity • – anomaly induced critical point at high density • [3] Dynamics of QCD Phase Transition • -- climbing the Hagedorn slope • [4] Strongly Correlated QCD Plasma ? • -- electric/magnetic screening and viscosity • -- heavy flavor as a probe • [5] Summary

  4. Origin of Masses

  5. “Origin of masses” Structure of the vacuum quark baryons bare quark quark Universe baryon Cosmological constant “Chiral” condensate “Higgs” condensate Einstein (1917) Nambu (1960) Anderson (1963) Englert-Brout, Higgs (1964) WMAP (2001-), Planck (2007-) RHIC (2000-), LHC (2007-) LHC(2007-)

  6. 4He 3He QCD Phase Structure

  7. QGP (Quark-Gluon Plasma) cSB (Chiral Symmetry Breaking) CSC (Color Superconductivity)

  8. strong residual force • pre-formed pairs • Hatsuda & Kunihiro, • Phys.Rev.Lett. 55 (1985) • DeTar, PRD32 (1985) Asymptotic freedom + Debye screening  deconfinement Collins & Perry, Phys.Rev.Lett. 34 (1975) QGP T cSB CSC mB & • quark - anti-quark pairing • chiral instability • Nambu & Jona-Lasinio, • Phys.Rev. 122 (1961) quark-quark pairing  Cooper instability Bailin & Love, Phys.Rep.107 (1984) Origin of each “phase”

  9. QGP Bi2Sr2CaCuO8+δ Highly undedoped cSB CSC 1. Competing order parameters 2. strong coupling effect  pre-formed pairs in Tc < T < T* Tc = decoherence temp. T* = dissociation temp. underdoped optimally doped HTS – BEC – QCD connection ? • Babaev, PRD (’00) • Abuki, Itakura & Hatsuda, PRD (’02) • Kitazawa, Koide, Kunihiro & Nemoto, PRD (’02) • Chen, Stajic, Tan & Levin, Phys. Rep. (’05) Similarity with high Tc superconductivity

  10. Most General Ginzburg-Landau Potential with the symmetry: + … QGP QGP CP-T Emergence of a high-density critical point (CP-D) CP Yamamoto, Tachibana, Baym & Hatsuda, hep-ph/0605018 cSB cSB CSC+cSB CP-D Hadron-quark continuity Schafer & Wilczek (’99) cSB+CSC CSC Anomaly Induced Critical Point

  11. QGP cSB CSC Dynamics of QCD phase transition

  12. T (MeV) Hagedorn regime Yukawa regime

  13. E * Laplace transform of s = partition function Z QCD Level Density and Hagedorn slope * QCD in a finite box : V

  14. E • s(e) ∝ lns(E,V) ~ e3/4 • ~ e/T0 • ~ e3/4 s(e) III II I e = E/ V Information of the Phase Transition is encoded in the QCD leverl density s(E,V) Hagedorn (1965) Ejiri & Hatsuda, hep-lat/0509119

  15. Full QCD Quenched QCD Integration : Monte Carlo with importance sampling Lattice Thermodynamics hypercube slab

  16. Nf =0 1st order Tc = 271±2 MeV Equation of State (EoS) on the lattice

  17. Strongly Correlated QCD Plasma ?

  18. Relativistic plasma : Inter-particle distance Electric screening Magnetic screening Debye number : 1/g2T 1/gT 1/T “Coulomb” coupling parameter : S. Ichimaru, Rev. Mod. Phys. 54 (’82) 1071 QGP for g << 1 ( T >> 100 GeV )

  19. Running coupling at finite T 2.5 1/(g2T) 2.0 1/(gT) Inter-particle distance 1/T Electric screening length 1.0 Magnetic screening length Scale degeneracy near Tc

  20. T=100GeV T=1 GeV T=0.2 GeV QCD Pressure (Nf=4) QCD Pressure near Tc ・naive perturbation: meaningful only for T>100 GeV ・resummation may improve the situation

  21. electric Quenched SU(3) 20×20×32×6 Lorenz gauge m/T 1/g2T 1/gT 1/T magnetic Nakamura, Saito & Sakai, Phys.Rev.D69 (’04) 014506 T/Tc Screening masses at T>Tc on the lattice

  22. h/s Baym, Monien, Pethick & Ravenhall (’90) Arnold, Moore & Yaffe, (’03) pQCD AdS/CFT Kovtun, Son & Starinets (’04) T/Tc 24x24x24x8 Nakamura & Sakai, Phys.Rev.Lett.94:072305,2005 updated: hep-lat/0510100 Viscosityupdated (quenched QCD)

  23. Dynamic probe Static probe Gluon matter (quenched QCD) Quark-gluon matter (full QCD) Probing QCD plasma By Heavy Flavors Matsui & Satz, PLB (’86) Miyamura et al., PRL (’86)

  24. r [ V(r) - 2mHL ] a g,u,d 0.5fm 1fm 1.5fm Nf= 2, Wilson sea-quarks, 243x40 a= 0.083 fm, L= 2 fm, mp/mr= 0.704 SESAM Coll., Phys.Rev.D71 (2005) 114513 Static Probe at T=0 : heavy-quark potential (full QCD)

  25. g,u,d,s spin ave. 1S energy Nf= 2+1, staggered sea-quarks, 163x48, 203x64, 283x96 a = 0.18, 0.12, 0.086 fm, L= 2.8, 2.4, 2.4 fm MILC Coll., PoS (LAT2005) 203 [hep-lat/0510072] Dynamic Probe at T=0 : charmonia spectra (full QCD) Note: connection between spectroscopy and V(r) through 1/mc expansion: Eichten-Feinberg (’79) Brown-Weisberger(’79)

  26. r g,u,d Nf= 2, staggered sea-quarks, 163x4 ,mp/mr= 0.7 Kaczmarek & Zantow, PoS (LAT2005) 192 [hep-lat/0510094] Heavy Quark Free-energy at Finite T (full QCD) Note: connection between spectroscopy and F(r) not established yet

  27. preliminary preliminary g,u,d Nf= 2, Wilson sea-quarks, 163x4 mp/mr= 0.8 (& 0.65), Coulomb gauge Tsukuba-Tokyo Coll. (Maezawa, Ukita, Ishii, Ejiri, Hatsuda, Aoki, Kanaya, Taniguchi) Heavy-quark free energy at T >Tc in varous channels (full QCD) r singlet g,u,d r anti-triplet quenched, 243x32, Coulomb gauge Nakamura & Saito, Phys. Lett. B621 (’05) 171

  28. 5 4 free r (GeV-1) r g 3 T/Tc=1.53 T/Tc=0.93 2 t (GeV-1) quenched, 162x24x(96,26,22,16) x=3.95, as=0.12 fm, at=0.03 fm Umeda, Katayama, Miyamura & Matsufuru, Int.J.Mod.Phys.A16 (2001) 2215 [hep-lat/0011085] Charmonium “Wave Function” at Finite T (quenched QCD)

  29. Charmonium Spectral Function at Finite T PDG(’04)

  30. Lattice data Spectral Function All information on hadronic correlations at T=0 and T≠0 “Laplace” kernel • No parameterization necessary for A • Unique solution D A • Error estimate for A possible Advantages of MEM ・　First applications of MEM to lattice QCD: Asakawa, Nakahara & Hatsuda, Phys. Rev. D60 (’99) 091503 Prog. Part. Nucl. Phys. 46 (’01) 459 MEM (Maximum Entropy Method)

  31. Image reconstruction by MEM D = K×A D A D A

  32. MEM : Examples at T=0 (quenched QCD) Asakawa, Nakahara & Hatsuda, Phys. Rev. D60 (’99) 091503 JP=1/2+ Sasaki, Sasaki & Hatsuda, Phys.Lett.B623 (’05) 208

  33. g hc J/y MEM applied to Charmonia at Finite T (quenched QCD) quenched, anisotropic lattice, 323 x (96,54,46,40,32) x=4.0, as=0.04 fm, at=0.01 fm, (Ls=1.25fm) Asakawa and Hatsuda, Phys.Rev.Lett.92 (2004) 012001.

  34. g MEM applied to Charmonia at Finite T (quenched QCD) quenched, isotropic lattice, 483 x (24,16,12) a=0.04 fm (Ls=1.9 fm) Datta, Karsch, Petreczky & Wetzorke, Phys. Rev. D69 (2004) 094507.

  35. at T/Tc= 1.4 ss-channel mφ(T=0)=1.03 GeV A(ω）/ω2 Is heaviness essential for bound states aboveTc ? mud << ms~Tc << mc < mb Asakawa, Nakahara & Hatsuda, [hep-lat/0208059]

  36. Full QCD ? 0.7Tc 0.7Tc Tc Tc 1.3Tc 1.3Tc Net dissociation rate may even be smaller in full QCD J/y 2Tc 2Tc Hatsuda, hep-ph/0509306 g,u,d hc Nf=2, anisotropic lattice, 83 x (48,32,24,16) x=6.0, as=0.2 fm, at=0.033 fm, (Ls=1.6 fm) mp/mr=0.55 Aarts, et.al., [hep-lat/0511028]

  37. weakly int. q+g plasma pQCD viscous fluid q+g plasma Strongly int. Q+G+PFP plasma LHC, RHIC Lattice QCD perfect fluid Resonance gas SPS Chiral dynamics viscous fluid Pion gas A possible “picture” of hot QCD

  38. Hot QCD is strongly interacting: Tc < T* ? • Just like high Tc superconductor • BEC regime of systems of atomic fermions RHIC LATTICE AdS/CFT HTS/BEC Summary 2. Several critical points in (T,μ)-plane ? Chiral CP at high T, Chiral-super CP at high μ, Liquid-gas CP at low μ 3. Progress in spectral analysis on the lattice Heavy and light bound states above Tc Small viscosity even up to 30 Tc ? Full QCD study is started

  39. (1992-) (2001-) Planck (2007-) Q.G.P. RHIC (2000-) LHC (2007-) SPS (1994-) Big Bang Little Bang

  40. 1. What is quark-gluon plasma Part I. Basic Concept of Quark-Gluon Plasma: 2. Introduction to QCD 3. Physics of quark-hadron phase transition 4. Field theory at finite temperature 5. Lattice gauge approach to QCD phase transitions 6. Chiral phase transition 7. Hadronic states in hot environment Part II. QGP in Astrophysics: 8. QGP in the early universe 9. Compact stars Part III. QGP in Relativistic Heavy Ion Collisions: 10. Introduction to relativistic heavy ion collisions 11. Relativistic hydrodynamics for heavy ion collisions 12. Transport theory for pre-equilibrium process 13. Formation and evolution of QGP 14. Fundamentals of QGP diagnostics 15. Results from CERN-SPS experiments 16. First results from BNL-RHIC 17. Detectors in relativistic heavy ion experiments published, Dec., 2005 (Cambridge Univ. Press) http://utkhii.px.tsukuba.ac.jp/cupbook/index.html

  41. Back up slides

  42. Physics Today, Dec. vol.58 (2005) http://www.lsbu.ac.uk/water/phase.html More on H2O

  43. QGP cSB CSC Scale of each “phase”

  44. Tc in 2-favor lattice QCD Ejiri (’04) Filled:Nt=4, Open:Nt=6 173±8 MeV Small mud

  45. Volume fraction: 1/3 Percolation picture Percolation transition Dilute gas Closely packed T.H., (’97)

  46. Color Confinement Lattice QCD simulations Super Computer: IBM BlueGene at KEK (March, 2006-) 57.3 Tflops

  47. Confining string Heavy bound states R [ V(R) - 2mHL ] a Mass-(spin avaraged 1s) [MeV] Nf= 2, Wilson, 243x40 a= 0.083 fm L= 2 fm mp/mr= 0.704 Nf= 2+1, staggered, 163x48, 203x64, 283x96 a = 0.18, 0.12, 0.086 fm L= 2.8, 2.4, 2.4 fm 1.5fm 0.5fm 1fm R/a MILC Coll., hep-lat/0510072 SESAM Coll., Phys.Rev.D71 (2005) 114513 Examples in full lattice QCD

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