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The strongly coupled Quark-Gluon Plasma

The strongly coupled Quark-Gluon Plasma. Edward Shuryak Department of Physics and Astronomy State University of New York Stony Brook NY 11794 USA. Outline:. The Little Bang, not a firework of minijets Collective flows: radial and elliptic, systematics: => viscosity

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The strongly coupled Quark-Gluon Plasma

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  1. The strongly coupled Quark-Gluon Plasma Edward Shuryak Department of Physics and Astronomy State University of New York Stony Brook NY 11794 USA

  2. Outline: • The Little Bang, not a firework of minijets • Collective flows: radial and elliptic, systematics: => viscosity • Where the energy of jets go? A ``sonic boom” • What does the ``strong coupling” mean? • Quasiparticles and Potentials at T>Tc • The phase diagram and few puzzles • Hadronic bound states at T>Tc • Colored bound state and EoS • Strongly coupled atoms • Strongly coupled N=4 SUSY YM and AdS/CFT correspondence

  3. Big Bang is an explosion which created our Universe. Entropy is conserved. Hubble law v=Hr for distant galaxies. H is isotropic. “Dark energy” (cosmological constant) seems to lead to accelerated expansion Little Bang is an explosion of a small fireball created in high energy collision of two nuclei. Also entropy is well conserved Hubble law, but anisotropic (see below) The ``vacuum pressure” works against expansion (And that is why it was so difficult to produce it) The Big vs the Little Bang

  4. The vacuum is very complicated, dominated by ``topological objects” Vortices, monopoles and instantons Among other changes it shifts its energy down compared to an “empty” vacuum, known as The Bag terms, p=#T^4-B Epsilon=#T^4+B The QGP, as any plasma, screens them, and is nearly free from them So, when QGP is produced, the vacuum tries to expel it (recall here pumped out Magdeburg hemispheres By von Guericke in 1656 we learned at school) The vacuum vs the QGP

  5. Magdeburg hemispheres 1656 We cannot pump the QCD vacuum out, but we can pump in something else, namely the Quark-Gluon Plasma

  6. The map: the QCD Phase Diagram The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland) T Theory prediction (numerical calculation, lattice QCD, Karsch et al) the pressure as a function of T (normalized to that for free quarks and gluons) p= #T^4 – B, the vacuum pressure Chemical potential mu

  7. Collective flows: bits of history

  8. Early days • L.D.Landau, 1953 => first use of hydrodynamics • L.D.Landau, S.Z.Belenky 1954 Uspechi => compression shocks => resonance gas (Delta just discovered) • G.A.Milekhin 1958 => first numerical solution for the transverse flow

  9. My hydro • Hydro for e+e- as a spherical explosion PLB 34 (1971) 509 => killed by 1976 discovery of jets in e+e- • Looking for transverse flow at ISR, ES+Zhirov, PLB (1979) 253 =>Killed by apparent absence of flow in pp • ES+Hung, prc57 (1998) 1891, radial flow at SPS with correct freezeout surface, Tf vs centrality dependence predicted

  10. QM99 predictions for v2(with D.Teaney) Our hydro/ cascade RQMD HIJING

  11. Main findings at RHIC • Partciles are produced from matter which seems to be well equilibrated (by the time it is back in hadronic phase), N1/N2 =exp(-(M_1-M_2)/T) • Very robust collective flows were found, indicating very strongly coupled Quark-Gluon Plasma (sQGP) • Strong quenching of large pt jets: they do not fly away freely but are mostly (up to 90%) absorbed by the matter. The deposited energy seem To go into hydrodynamical motion (conical flow)

  12. Reminder Statistical Model Works well with just two parameters Hadro-chemistry seems to be all done at the critical line

  13. Hydrodynamics is simple and very predictive, but one has to understand few things,and so not all hydros are the same EoS from Lattice QCD Local Energy-momentum conservation: Conserved number: • Dynamic Phenomena • Expansion, Flow • Space-time evolution of • thermodynamic variables Caveat: Why and when the equilibration takes place is a tough question to answer

  14. partonic hadronic 0.33 0.2 LH Thinking About EoSThe Latent Heat and the ``softest point” (Hung, ES 1995)

  15. Understanding of the freezeouts(which some hydro groups forgot) • Chemical freezeout at Tch means that at T<Tch hadronic matter is indeed chemically frozen => different EoS with nonzero mu’s • Kinetic freezout at fixed Tf is wrong: the larger systems cool to LOWER Tf, one has to calculate the freezeout surface (Hung,ES) or use afterburner (RQMD) (Teaney, ES)

  16. proton pion hydro describes both radial and elliptic flows(from Phenix) v_2=<cos(2 phi)> nucl-ex/0410003 Hydro models: Teaney (w/ & w/o RQMD) Hirano (3d) Kolb Huovinen (w/& w/o QGP)

  17. V2 systematics:it depends on many variables • Particle type => y_t^2 m scaling • Collision energy s –dependence • (pseudo) rapidity (eta) y-dependence • Pt: rapid growth with saturation • Centrality => v2/s2 scaling

  18. A Hydrodynamic Description of Heavy Ion Collisions at the SPS and RHICD. Teaney,J. Lauret,and E.V. Shuryaknucl-th/0110037 v2 6 Dec 2001The dependence on dN/dyhas a growing trend, with a saturation

  19. More on Elliptic Flow STAR, PRC66(’02)034904 PHENIX, PRL91(’03)182301. Hydro: P.Huovinen et al.(’01) • See recent reviews, • P.Huovinen (QM2002) , nucl-th/0305064; • P.Kolb and U.Heinz, nucl-th/0305084; • E.Shuryak, hep-ph/0312227 Hydro: P.Kolb et al.(’99) (Note: Hydro+RQMD gives a better description. D.Teaney et al.(’01))

  20. The (pseudo)rapidity distribution of v2 (from PHOBOS) is not the same as that of the particles

  21. Particle distribution over (pseudo) rapidity • Number of charged particles per unit of pseudorapidity

  22. But the trend roughly follows the (BJ-like) hydro predictions, which is is also about s-independent

  23. Are the fine structure of v2 hydrodynamical for all secondaries? (PHENIX, R.Lacey) • Scaling from (nucl-th/0402036) we then define a “fine structure” variable

  24. data look like hydro! Kolb, et al The data scale as hydro:

  25. Sonic boom from quenched jets Casalderrey,ES,Teaney, hep-ph/0410067; H.Stocker… • the energy deposited by jets into liquid-like strongly coupled QGP must go into conical shock waves, similar to the well known sonic boom from supersonic planes. • We solved relativistic hydrodynamics and got the flow picture • If there are start and end points, there are two spheres and a cone tangent to both

  26. Distribution of radial velocity v_r (left) and modulus v (right).(note tsunami-like features, a positive and negative parts of the wave)

  27. Is such a sonic boom already observed?Mean Cs=.33 time average over 3 stages=> =+/-1.23=1.91,4.37 flow of matter normal to the Mach cone seems to be observed! See data from STAR, M.Miller, QM04

  28. PHENIX jet pair distribution Note: it is only projection of a cone on phi Note 2: more recent data from STAR find also a minimum in <p_t(\phi)> at 180 degr., with a value Consistent with background

  29. Away <pT> vs centrality STAR,Preliminary Away core <pT> drops with centrality faster than corona <pT>. Core hadrons almost identical to medium in central collisions. A punch-though at the highest trigger?

  30. Preliminary away <pT> dependence on angle (STAR,preliminary) <pT> (phi) has a dip structure in central AA. Mach shock wave?

  31. Collective flows =>collisional regime => hydrodynamics The main assumption: l << L (the micro scale) << (the macro scale) (the mean free path) << (system size) (relaxation time) << (evolution duration) I In the zeroth order in l/L it is ideal hydro with a local stress tensor. Viscosity appears as a first order correction l/L, it has velocity gradients. Note that it is inversely proportional to the cross section and thus is (the oldest) strong coupling expansion

  32. Viscosity of QGP QGP at RHIC seem to be the most ideal fluid known, viscosity/entropy =.1 or so water would not flow if only a drop with 1000 molecules be made • viscous corrections 1st order correction to dist. fn.: :Sound attenuation length Velocity gradients Nearly ideal hydro !? D.Teaney(’03)

  33. Theory and phenomenology of sQGP

  34. How to get 20 times pQCD s? (Zahed and ES,2003) • Quark-antiquark bound states don’t all melt at Tc (charmonium from lattice known prior to that…) • Many more colored channels • all q,g have strong rescattering qqbar  meson Resonance enhancements Huge cross section due to resonance enhancement causes elliptic flow of trapped Li atoms

  35. Scattering amplitudesfor quasiparticlesM. Mannarelli. and R. Rapp hep-ph/05050080

  36. The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a Micro-Bang ! (O’Hara et al, Duke ) Elliptic flow with ultracold trapped Li6 atoms, a=> infinity regime The system is extremely dilute, but can be put into a hydro regime, with an elliptic flow, if it is specially tuned into a strong coupling regime via the so called Feshbach resonance Similar mechanism was proposed (Zahed and myself) for QGP, in which a pair of quasiparticles is in resonance with their bound state at the “zero binding lines”

  37. Hydro works for up to 1000 oscillations! The z mode frequency agrees with hydro (red star) at resonance, with universal EoS Viscosity has a strong minimum there

  38. ``Quantum viscosity” <= universality • There is no need to specify constituents or a mean free path: • Hydro: damping of sound waves can provide a definition • For cold T=0 atoms ``quantum viscosity” • =hbar n  • Should be the universal • dimensionless constant • Scattering rate must be -1= consthbar/F

  39. So what is the viscosity? • B.Gelman, ES,I.Zahed nucl-th/0410067 • At the minimum alpha_eta is about .5+- .3 or so => • This liquid is about as perfect as sQGP at RHIC!

  40. Bound states in sQGP

  41. The map: the QCD Phase Diagram The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland) T Theory prediction (numerical calculation, lattice QCD, Karsch et al) the pressure as a function of T (normalized to that for free quarks and gluons) p/psb=0.8 weak or strong coupling? Chemical potential mu

  42. How strong is strong?For a screened Coulomb potential, Schr.eqn.=>a simple condition for a bound state • (4/3)s (M/MDebye) > 1.68 • M(charm) is large, MDebye is about 2T • If (Md) indeed runs and is about ½-1, it is large enough to bind charmonium till about T=3Tc(above the highest T at RHIC) • Since q and g quasiparticles are heavy, M about 3T, they all got bound as well !

  43. Fitting F to screened Coulomb • Fit from Bielefld group hep-lat/0406036 • Note that the Debye radius corresponds to • ``normal” (enhanced by factor 2) coupling, while the overall strength of the potential is much larger • It becomes still larger if V is used • instead of F, see later

  44. Here is the binding and |psi(0)|^2 E/2M Vs T/Tc

  45. Solving for binary bound statesES+I.Zahed, hep-ph/0403127 • In QGP there is no confinement => • Hundreds of colored channels should have bound states as well!

  46. The pressure puzzle is resolved!Masses, potentials and EoS from lattice are mutually consistent M/Tc vc T/Tc and p/pSB vs T/Tc

  47. Can we verify existence of bound states at T>Tc experimentally?Dileptons from sQGP:

  48. Jet quenching by ``ionization”of new bound states in QGP?

  49. Calculation of the ionization rateES+Zahed, hep-ph/0406100 • Smaller than radiative loss if L>.5-1 fm • Is there mostly near the zero binding lines, • Thus it is different from both radiative and elastic looses, which are simply proportional to density • Relates to non-trivial energy dependence of jet quenching (smaller at 62 and near absent at SPS) dE/dx in GeV/fm vs T/Tc for a gluon 15,10,5 GeV. Red-elastic, black -ionization

  50. Theoretical sQGP in N=4 SUSY YM and AdS/CFT

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