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Bulk and Spectral Observables in Lattice QCD

WMAP (2001-). RHIC (2000- ). LATTICE. Bulk and Spectral Observables in Lattice QCD. Tetsuo Hatsuda ( 初田哲男 ) Univ. Tokyo 　 （東京大学）. Three Major Tools to study Early Universe. Contents. [1] Introduction -- lattice approach to hot QCD [2] Bulk properties of hot QCD

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Bulk and Spectral Observables in Lattice QCD

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  1. WMAP (2001-) RHIC (2000- ) LATTICE Bulk and Spectral Observables in Lattice QCD Tetsuo Hatsuda(初田哲男) Univ. Tokyo　 （東京大学） Three Major Tools to study Early Universe

  2. Contents [1] Introduction -- lattice approach to hot QCD [2] Bulk properties of hot QCD -- equation of state (precision) -- order of the thermal transition (precision) -- critical temperature (precison) -- critical point at finite density (exploratory) [3] Spectral properties of hot QCD -- heavy probes (exploratory) -- light probes (exploratory) [4] Summary

  3. QGP Asakawa & Yazaki, Nuc. Phys A504 (‘89) 668 cSB CSC mB Yamamoto, Tachibana, Baym & T.H., Phys. Rev. Lett. 97 (2006)122001 Introduction T

  4. Why lattice ? • well defined QM (finite a and L) • gauge invariant • fully non-perturbative What one can do • hadron mass, coupling, form factor etc • scattering (phase shift, potential etc) • hot plasma What one cannot do (at present) • cold plasma • non-equilibrium plasma Lattice QCD

  5. a 1/T L Fermions: staggered, Wilson, Domain-wall, Overlap different way of handling chiral symmetry Improved actions: asqtad, p4, stout, clover … different way of reducing the discretization error Modern algorithms: RHMC, DDHMC … techniques to make the simulations fast and reliable 2+1 flavor, physical quark mass, a 0, L ∞ Lattice thermodynamics Full QCD

  6. To collect 1000 indep. gauge conf. On 243x40, a=0.08 fm lattice (T=0) Clark, hep-lat/0610048.

  7. QCD Cluster @ FNAL PACS-CS @ Tsukuba BlueGene/L @ KEK QCDOC @ RBRC-Columbia ApeNEXT @ Rome

  8. QGP cSB CSC Bulk Properties of Hot QCD

  9. Energy density in full QCD (Nf=2+1) MILC Coll., hep-lat/061001 O(a2) improved action Ns/Nt=2, inexact R-algorithm.

  10. Fluctuation: chiral susceptibility cm/T2 cm/T2 1/T mp=235, 300, 355, 405MeV Wuppertal-Budapest Coll., Nature 443 (2006) Order of the transition in full QCD (Nf=2+1)

  11. n-th order transiton: 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

  12. [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

  13. 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

  14. 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

  15. 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 Nakamura & Sakai, hep-lat/0510100

  16. 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) QCD-TARO Coll., Phys. Rev. D63 (’01) Charmonium “wave function”（quenched QCD)

  17. 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

  18. Net dissociation rate may even be smaller in full QCD Hatsuda, hep-ph/0509306 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 Charmonium spectra in full QCD (Nf=2)

  19. 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]

  20. 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]

  21. 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]

  22. 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” --

  23. 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 many attempts, no conclusion yet

  24. Back up slides

  25. QGP cSB CSC Scale of each “phase”

  26. T (MeV) Hagedorn regime Yukawa regime

  27. QGP cSB CSC Symmetry of each “phase” (case for small mud with ms=∞)

  28. ~ ・ Ginzburg-Landau Potential (3-flavor, chiral limit) Symmetry: Chiral modes: Diquark modes:

  29. Yamamoto, Tachibana, Baym & Hatsuda, hep-ph/0605018 ・ Ginzburg-Landau Potential (3-flavor, chiral limit) = U(1)A breaking terms =

  30. 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

  31. 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 )

  32. 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 = ∞

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

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

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

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

  37. 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

  38. Casimir scaling in full QCD (Nf=2) WHOT-QCD Coll., (Maezawa et al.,) In preparation

  39. Casimir scaling in full QCD (Nf=2) quark - anti-quark channel quark-quark channel WHOT-QCD Coll., (Maezawa et al.,) In preparation

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