1 / 46

Quark-Gluon Plasma and Lattice QCD

Quark-Gluon Plasma and Lattice QCD. T. Hatsuda (Univ. Tokyo). Probing the Early Universe. Simulating the Early Universe. QCDPAX. STAR@RHIC. What have we learned from lattice QCD simulations?. Contents. Brief introduction to QCD – what one can/cannot do in lattice QCD

oneida
Download Presentation

Quark-Gluon Plasma and Lattice QCD

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Quark-Gluon Plasma and Lattice QCD T. Hatsuda (Univ. Tokyo) Probing the Early Universe Simulating the Early Universe QCDPAX STAR@RHIC What have we learned from lattice QCD simulations?

  2. Contents • Brief introduction to QCD • – what one can/cannot do in lattice QCD • QCD phase structure • – equation of state • – liberation of color • Plasma properties at T > Tc • – strong coupling plasma ? • – plasma screening and effective potential • – dynamic structure factor • 4. Cold plasma and color superconductivity • – its mechanism • – BCS-BEC crossover • 5. Summary and outlook

  3. Where to find？ ●Early Universe ( t < 10 -4 sec)：　 High T, low D ● Deep interior of Neutron star：Low T, High D ●Relativistic Heavy Ion Collisions：High T and/or High D How to describe？ Quantum Chromo Dynamics (QCD) Matter under high temperature/pressure Critical Density：1012 kg/cm3 Critical Temperature:1012 K

  4. Color Confinement Effective coupling (αs = ｇ２/４π） αs Asymptotic freedom Energy scale （ＧｅV) Nambu (’66) Gross, Wilczek, Politzer (’73) Wilson (’74) Quantum Chromo Dynamics Chromo- paramagnetism (m > 1)

  5. Heavy quarks Light quarks mc~1.5 GeV mb~5 GeV mt~178 GeV mu~3MeV md~7MeV ms~100MeV Quark flavors

  6. Lattice QCD

  7. Full QCD Quenched QCD Integration : Monte Carlo with importance sampling Basic idea hypercube slab

  8. Continuum and thermodynamic limits 0.1 fm 2-3 fm Why lattice ? • Well defined QM (finite a and L) • Gauge invariant • Fully non-perturbative What one can do in principle • Equation of state of hot plasma • Phase transition (critical temperature, order etc) • Static and dynamic correlations near equilibrium What one cannot do (at present) • Cold degenerate plasma • Phenomena far from equilibrium

  9. Linear confining string Heavy-quark bound states R 2S+1LJ 0.5 fm 1.0 fm Bali, Phys. Rep. 343 (’01) 1 CP-PACS, Phys. Rev. D65 (’02) 094508 Examples (quenched)

  10. 4He 4He H2O λ-line Phase Structure http://boojum.hut.fi/research/theory/typicalpt.html

  11. μB Color Superconductor Quark-Gluon Plasma Triple point ? Hadronic Fluid Critical End point Vacuum T QCD Phase Diagram (full)

  12. Black-body radiation for massless particles : BB limit Nf = 3 Nf = 2+1 Nf = 2 Karsch, Lect.Notes Phys. 583 (’02) 209 Tc~160 MeV ( full)c.f. Tc = 270 MeV (quenched ) Equation of State on the lattice (full)

  13. T=0 Karsch, Laermann, Peikert, Nucl. Phys.B605 (’01) 579 Fate of the color string (full)

  14. Low T Low T low D :Hadronic phase high D :color supercond. ? Quark gluon plasma High T More on QCD Phase Transition at finite T (full) (i) String fluctuation and breaking (ii) Restoration of broken symmetries Pisarski & Wilczek, PRD29 (’84) e.g. Matsuura, Iida, Baym and T.H., PRD69 (’04)

  15. Chiral phase structure from RG Yaffe-Svetizky, (’83) ∞ Pisarski and Wilczek, Phys.Rev.D (’84) m s Nf = 2(ms= ∞, mu,d = 0） 2nd order (O(4) universality) Nf = 3(ms = 0, mu,d = 0) 1st order (fluctuation/instanton induced) 1st 2nd cross over Nf = 2+1(ms >> mu,d ≠0) 1st order or crossover 1st 0 ∞ m u,d Tc from “BCS” lattice QCD 1. Order : consistent with RG 2. Tc= 173±8 MeV (Nf=2) = 154±8 MeV (Nf=3) Kunihiro and T.H., Prog. Theor. Phys. (’85) CP-PACS, Bielefeld

  16. μB QCD Phase Diagram Color superconductor Quark-gluon plasma ~ 1 GeV Hadronic fluid Vacuum ~ 160 MeV T

  17. Static plasma properties at T > Tc

  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. Strong coupling problem g ~ 2 for T=200-400 MeV badly behaved perturbation series B. Non-Abelian magnetic problem soft magnetic gluons are always non-perturbative even if g  0 pertubation theory Problems of high T perturbation

  20. j i Static gluon correlation magnetic screening : A. Linde, Phys. Lett. B96 (’80) 289 EOS : “Debye” screening : Kraemmer & Rebhan, Rept.Prog.Phys.67 (’04)351 QCD is non-perturbative even at T = ∞ ( L3x(1/T)  L3 )

  21. Quenched SU(3) 20×20×32×6 Lorenz gauge m = gT Nakamura, Saito & Sakai, Phys.Rev.D69 (’04) 014506 Screening masses at T>Tc (quenched)

  22. T/Tc=3.04 243×6 Lorenz gauge Heavy quark “potentials” at T>Tc (quenched) 0.25fm 0.5fm Nakamura & Saito, Prog.Theor.Phys.111, 112 (’04) hep-lat/0406038, 0404002

  23. Heavy quark “potentials” at T>Tc (quenched)

  24. γ γ * * Dynamic structure factor of the plasma vacuum plasma Dynamic structure factor of the vacuum PDG(’04) Dynamic plasma properties at T > Tc

  25. probe system lattice QCD data known kernel spectral function = dynamic structure factor Maximum Entropy Method Asakawa, Nakahara & T.H, Phys. Rev. D60 (’99) 091503 Prog. Part. Nucl. Phys. 46 (’01) 459 Method in lattice QCD

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

  27. Quark-anti-quark ound state above Tc ? charm strange

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

  29. ssbound state above Tc (quenched) Mφ(T=0)=1.03 GeV T/Tc= 1.4 A(ω）/ω2 Asakawa & T.H., Prog. Theor. Phys. Suppl. 149 (‘03)42

  30. 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 bound states • above Tc • Shuryak and Zahed, Phys. Rev. D70 (2004) 054507 • Brown, Lee, Rho and Shuryak, Nucl. Phys.A740 (’04) 171

  31. Chiral dynamics pQCD Lattice QCD RHIC, LHC Possible hierarchy of QCD plasma Strongly int. Resonance plasma Strongly int. q+g+”extra” plasma Strongly int. q+g plasma weakly int. q+g plasma Weakly int. pion plasma perfect fluid ? viscous fluid ?

  32. Nakamura and Sakai, hep-lat/0406009 Viscous fluid R << 1 Baym, Monien, Pethick & Ravenhall (’90) Arnold, Moore & Yaffe, (’03) 1.0 1.5 2.0 2.5 3.0 Perfect fluid R >> 1 T/Tc Kovtun, Son & Starinets (’04) “Reynolds number” Shear viscosity (quenched)

  33. ？ ？ Dense Plasma and Color Superconductivity 10 km N. Itoh (’70), E. Witten (’84)

  34. QCD Phase Diagram μB Color superconductor Quark-gluon plasma ~ 1 GeV Hadronic fluid Vacuum T ~ 160 MeV

  35. Major differences from BCS 1. Highlyrelativisitic Long range magnetic int. High Tc superconductor Tc/pF ~ 0.1 Compact Cooper pair size ~ 1-10 fm 2. Color-flavor entanglement Variety of phases CFL, 2SC, dSC, uSC Color Superconductivity in Quark Matter

  36. Abuki, Itakura & T.H., PRD65 (’02) dq 40K Cond. of Fermionic-Atom Pairs ξc N0/N = 1% 5% 10% BCS ξc/dq 40K : JILA, PRL 92 (2004) 040403 6Li : Innsbruck, PRL 92 (2004) 120401 MIT, PRL 92 (2004) 120403 to BEC ? pF(MeV) μB Various scenarios possible: seeFukushima, hep-ph/0403091

  37. Summary and outlook • Progress in lattice QCD • – equation of state of hot plasma • – static and dynamic correlations -> strongly coupled plasma ? • Need to be done • – full QCD for small m, small a and large L • – full QCD for dynamic correlations • (viscosity, colored bound states etc) • Computer resources • – massive computers （>10Tflops) + sharing lattice data • (see, Lattice QCD simulations via International Research Network, • Sep. 21-24, 2004,http://www.rccp.tsukuba.ac.jp/workshop/ilft04/) • 4. Need new ideas • – cold degenerate plasma • – far from equilibrium • – ideas to and from QED plasma and atomic condensates

  38. μB QCD Phase Diagram Color superconductor Quark-gluon plasma ~ 1 GeV new regime? Hadronic fluid Vacuum ~ 160 MeV T

  39. (1989-) (2001-) Planck (2007-) sQGP? RHIC (2000-) LHC (2007-) SPS (1987-) Big Bang Little Bang

  40. Back up slides

  41. Bali, Phys. Rep. 343 (’01) 1 0.5 fm 1.0 fm 323 x 56 – 643 x 112 a=0.1-0.05 fm La=3 fm CP-PACS, PRD 67 (’03) 034503

  42. Quark number susceptibility Kunihiro, Phys. Lett. B271 (’92) 395 Hatta-Ikeda, Phys.Rev.D67 (’03) 014028 Ejiri et al. (Bielefeld-Swansea Coll.)

  43. 3He H2O PhaseDiagrams 4He http://boojum.hut.fi/research/theory/typicalpt.html

  44. under heat under pressure

  45. Plasma frequency:

More Related