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LATTICE QCD is FUN

LATTICE QCD is FUN. [1] Lattice QCD basics [2] Nuclear force on the lattice (  dense QCD) [3] In-medium hadrons on the lattice (  hot QCD) [4] Summary. Tetsuo Hatsuda, Univ. Tokyo Second Berkeley School on Collective Dynamics May 21-25, 2007. QGP. QGP. c SB.

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LATTICE QCD is FUN

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  1. LATTICE QCD is FUN [1] Lattice QCD basics [2] Nuclear force on the lattice ( dense QCD) [3] In-medium hadrons on the lattice ( hot QCD) [4] Summary Tetsuo Hatsuda, Univ. Tokyo Second Berkeley School on Collective Dynamics May 21-25, 2007

  2. QGP QGP cSB cSB CSC CSC mB In-medium Hadrons ●Asakawa & Yazaki, Nuc. Phys A504 (‘89) 668 ●Yamamoto, Tachibana, Baym & T.H.,Phys. Rev. Lett. 97 (2006)122001

  3. a 1/T L continuum limit 1/T fixed, Nt/Ns small, Nt large  “a” small Lattice setup at finite T 1/T = Nt a L = Ns a

  4. Order of the transition 2nd order (u,d; m=0) 1st order (u,d,s; m=0) crossover (real world) Critical temperature Tc： 160 – 190 MeV ～ 1012 [K] Critical energy density εc： ～　2 GeV/fm3 ～ 10 εnm Bulk Thermodynamics in full QCD MILC Coll., hep-lat/061001 (2+1)-flavor, O(a2) improved action, Ns/Nt=2

  5. Karsch, hep-lat/0608003 Wuppertal-Budapest Coll., hep-lat/0510084 stout, Ccond/Cnt correction by hand Ns/Nt=3

  6. n-th order transition: non-analiticity starts from e.g. 1st order: P smooth, dP/dT=s discontinuous 2nd order: P smooth, dP/dT=s smooth, (d/dT)2P=ds/dT=cV/T divergent crossover: P(K) is everywhere analytic Susceptibilities What is Phase Transition ?

  7. Fluctuation: chiral susceptibility cm/T2 cm/T2 1/T Wuppertal-Budapest Coll., Nature 443 (2006) Order of the transition in full QCD (Nf=2+1)

  8. 2nd order transition • Relation between c and x, e.g. (3-dimension)

  9. Wuppertal-Budapest Coll., Nature 443 (2006)

  10. n-th order transition: non-analiticity starts from e.g. 1st order: P smooth, dP/dT=s discontinuous 2nd order: P smooth, dP/dT=s smooth, (d/dT)2P=ds/dT=cV/T divergent crossover: P(K) is everywhere analytic Intrinsic ambiguity to define Tpc cm/T2 Pseudo critical temperature Tpc

  11. [MeV] [MeV] Tpc (a 0) in full QCD (Nf=2+1) from cm/T2 Staggered fermion MILC Coll., hep-lat/0405029 169(12)(4)(5) MeV Asqtad, Nt=4,6,8, Ns/Nt=2, r_1=0.317(7) fm RBC-Bielefeld Coll., hep-lat/0608013 192(7)(4) MeV P4fat3, Nt=4,6 Ns/Nt=2-4, r_0=0.469(7) fm Wuppertal-Budapest Coll., hep-lat/0609068 151(3)(3) MeV + 9 MeV stout, Nt=6,8,10, Ns/Nt=4, F_K scale WHOT-QCD Coll., preliminary 175(4)(2) MeV (Nf=2, Nt=6, Polyakov-loop sus.) clover, Nt=4, 6, Ns/Nt=3-4, m_V scale Wilson fermion

  12. Sommer scales r0=0.469 (7) fm,HPQCD-UKQCD Coll. hep-lat/0507013 from bottomonium mass splitting (Nf=2+1, staggered) r0=0.516 (21) fm, CP-PACS-JLQCD Coll., hep-lat/0610050 from ρ-meson mass (Nf=2+1, Wilson) Tpc on the lattice from chain rule

  13. de Forcrand and Phillipsen, hep-lat/0607017 Nf=2+1, Nt=4, standard staggered QGP cSB CSC Critical point Cf. Asakawa & Yazaki, NPA504 (1989) 668 Klimt, Lutz & Weise, PLB249 (’90) 386

  14. Spectral Properties of Hot QCD Shear viscosity in quenched QCD pz h/s pQCD ΛQCD py px AdS/CFT What are the elementary excitations in the plasma? DeTar’s conjecture Phys.Rev.D32 (1985) 276 T T/Tc Quenched Lattce QCD: 24x24x24x8 Nakamura & Sakai, Phys.Rev.Lett.94:072305,2005 & hep-lat/0510100

  15. Dynamic probe Static probe Matsui & Satz, PLB178 (’86)Miyamura et al., PRL57 (’86) Gluon matter (quenched QCD) Quark-gluon matter (full QCD) Heavy probes

  16. r g,u,d,s Singlet free energy in full QCD (Nf=2+1) 163x4, p4fat3 action, mud/ms=0.1 RBC-Bielefeld Coll., hep-lat/0610041

  17. 5 4 free Matsui & Satz, PLB178 (’86)Miyamura et al., PRL57 (’86) r (GeV-1) 3 r g T/Tc=1.53 0.5fm T/Tc=0.93 2 t (GeV-1) Charmonium “wave function”（quenched QCD) QCD-TARO Coll., Phys. Rev. D63 (’01)

  18. ~ Dynamic correlation & The spectral function (SPF) Real-time (Retarded) correlation Imaginary-time (Matsubara) correlation

  19. Lattice QCD data “Laplace” kernel P[A|D] ~ P[D|A] P[A] Maximum Entropy Method T. Bayes C.E. Shannon (1702-1761) (1916-2001) Maximum Entropy Method (MEM) Review + proofs : Asakawa, Nakahara & T.H., Prog. Part. Nucl. Phys. 46 (’01) 459

  20. Why MEM is so powerful ? P[A|D] ~ P[D|A] P[A] • No parameterization necessary for A • Unique solution D A • Error estimate for A possible First application of MEM to LQCD: Asakawa, Nakahara & T.H, Phys. Rev. D60 (’99) 091503 Review + proofs : Asakawa, Nakahara & T.H., Prog. Part. Nucl. Phys. 46 (’01) 459

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

  22. MEM: mock data

  23. p Wilson doubler p’ r Wilson doubler r’ MEM for mesons at T=0 Asakawa, Nakahara & T.H., PRD60 (‘99) 091503

  24. JP=1/2+ N N’ WD1 WD2 MEM N* N*’ JP=1/2- WD1 WD2 MEM Sasaki, Sasaki and T. H., Phys. Lett. B623 (’05) 208 MEM for baryons at T=0

  25. J/ψ(3.1GeV) • J/ψ survives • even up to 1.6 Tc • 2. J/ψdisappears • in 1.6 Tc < T < 1.7 Tc Spectral function ρ(ω) Asakawa & T.H., PRL 92 (’04) 012001 • see also, • Umeda et al, hep-lat/0401010 • Datta et al., PRD 69 (’04) 094507 • Jakovac et al., hep-lat/0611017 MEM: charmonium above Tc (quenched)

  26. ηc(3.0GeV) J/ψ(3.1 GeV) Spectral function ρ(ω) J/ψ and ηc above Tc (quenched)

  27. at T/Tc= 1.4 ss-channel mφ(T=0)=1.03 GeV A(ω）/ω2 Light meson spectra in quenched QCD mud << ms~Tc << mc < mb Asakawa, Nakahara & Hatsuda, [hep-lat/0208059]

  28. Possible mechanisms of supporting “hadrons” above Tc • Strong correlations • in JP=0+ (σ) and JP=0-(π) channels • above Tc ? • Kunihiro and T.H., Phys. Rev. Lett. 55 (’85) 88 • Dynamical confinement • in all color singlet channels above Tc ? • DeTar, Phys. Rev. D32 (’85) 276 • Strong Coulomb interaction • in color singlet and non-singlet channels • above Tc ? • Shuryak and Zahed, Phys. Rev. D70 (2004) 054507 • Brown, Lee, Rho and Shuryak, Nucl. Phys.A740 (’04) 171

  29. anisotropic lattice, 323 x (96-32) x=4.0, at=0.01 fm, (Ls=1.25fm) isotropic lattice, 483 x(24-12), a=0.04 fm (Ls=1.9 fm) Asakawa & Hatsuda, hep-lat/0308034 Datta, Karsch, Petreczky & Wetzorke, hep-lat/0312034 g g c J/y c hc J/y hc anisotropic lattice, 243 x (160-34) x=4.0, at=0.056 fm, (Ls=1.34 fm) Jakovac, Petreczky, Petrov & Velytsky hep-lat/0611017 Charmonium spectra in quenched QCD h

  30. g,u,d hc J/y Hamber-Wu, stout, ξ=6, at=0.025fm, 83 x (16,24,32), mp/mr=0.5 Aarts et al., hep-lat/0610065, 0705.2198 [hep-lat] Charmonium spectra in full QCD (Nf=2) Net dissociation rate may even be smaller in full QCD Hatsuda, hep-ph/0509306

  31. g J/Y moving in the plasma in quenched QCD g Datta, Karsch, Wissel, Petreczky & Wetzorke, [hep-lat/0409147] Aarts, Allton, Foley, Hands & Kim, [hep-lat/0610061]

  32. anisotropic lattice, 243 x (160-34) x=4.0, at=0.056 fm, (Ls=1.34 fm) Jakovac, Petreczky, Petrov & Velytsky hep-lat/0611017 Bottomonium spectra in quenched QCD quenched, a = 0.02 fm Datta, Jakovac, Karsch & Petreczky, [hep-lat/0603002]

  33. T High Tc superconductor Chen, Stajic, Tan & Levin, Phys. Rep. (’05) weakly int. q + g plasma viscous fluid 3 pz 10 T c q + g plasma ~ 2T * c T q + g +”extra” plasma ? ΛQCD py perfect fluid T c px Resonance gas f T viscous fluid p Pion gas 0 Hot QCD -- a “paradigm” --

  34. 1. Progress in lattice QCD Improved action, Faster algorithm, Faster computer  simulations of the REAL world RHIC LATTICE AdS/CFT HTS/BEC Summary 2. Progress in bulk thermodynamics Equation of state, Pseudo-critical temperature, Susceptibilities  precision science 3. Progress in spectral analysis elementary excitations in QGP  still exploratory 4. Progress in finite density no conclusion yet

  35. Back up slides

  36. 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 )

  37. A. Linde, Phys. Lett. B96 (’80) 289 EOS : μ ν magnetic screening : “Debye” screening : Kraemmer & Rebhan, Rept.Prog.Phys.67 (’04)351 Non-Abelian magnetic problem QCD is non-perturbative even at T = ∞

  38. soft magnetic gluons are always non-perturbative even if g  0 (T ∞) pertubation theory from O(g6) (wm~ g2T)

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