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

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

4. The vacuum vs the QGP The vacuum is very complicated, dominated by ``topological objects” The vacuum is very complicated, dominated by ``topological objects” Vortices, monopoles and instantons Among other changes it shifts its energy down compared to an Among other changes it shifts its energy down compared to an “empty” vacuum, known as The Bag terms, p=#T^4-BEpsilon=#T^4+B The QGP, as any plasma, screens them, and is nearly free from them The QGP, as any plasma, screens them, and is nearly free from them So, when QGP is produced, the vacuum tries to expel it 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)

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 T The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland) Chemical potential mu 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

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) RQMD HIJING Our hydro/ cascade

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) 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) 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%) 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 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 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 Dynamic Phenomena Expansion, Flow Space-time evolution of thermodynamic variables Caveat: Why and when the equilibration takes place is a tough question to answer Local Energy-momentum conservation: Conserved number:

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

15. Understanding of the freezeouts (which some hydro groups forgot) Chemical freezeout at Tch means that at T 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. hydro describes both radial and elliptic flows (from Phenix) v_2= hydro describes both radial and elliptic flows (from Phenix) v_2= protonpion Hydro models: Teaney (w/ & w/o RQMD) Hirano (3d) Kolb Huovinen (w/& w/o QGP) nucl-ex/0410003

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

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

19. More on Elliptic Flow 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)) STAR, PRC66(’02)034904 Hydro: P.Huovinen et al.(’01) PHENIX, PRL91(’03)182301.

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 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 v 2 hydrodynamical for all secondaries? (PHENIX, R.Lacey) Scaling from (nucl-th/0402036) Scaling from (nucl-th/0402036) we then define a “fine structure” variable

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

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. 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 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 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=> M.Miller, QM04 flow of matter normal to the Mach cone seems to be observed! See data from STAR,  +/- 1.23=1.91,4.37

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 at 180 degr., with a value Consistent with background

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

30. away dependence on angle (STAR,preliminary) away dependence on angle (STAR,preliminary) Preliminary (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 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 1 st 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  ? (Zahed and ES,2003) Quark-antiquark bound states don’t all melt at Tc (charmonium from lattice known prior to that…) Quark-antiquark bound states don’t all melt at Tc (charmonium from lattice known prior to that…) Many more colored channels Many more colored channels all q,g have strong rescattering qqbar  meson 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 amplitudes for quasiparticles Scattering amplitudes for quasiparticles M. Mannarelli. and R. Rapp hep-ph/05050080

36. 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” The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a Micro-Bang ! (O’Hara et al, Duke )

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 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: There is no need to specify constituents or a mean free path: Hydro: damping of sound waves can provide a definition 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 = const hbar /  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 T The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland) Chemical potential mu 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 ?

42. How strong is strong? For a screened Coulomb potential, Schr.eqn.=>a simple condition for a bound state (4/3)  s (M/M D ebye ) > 1.68 M(charm) is large, M Debye is about 2T If  (M d ) indeed runs and is about ½-1, it is large enough to bind charmonium till about T=3T c (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 states ES+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/p SB 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 rate ES+Zahed, hep-ph/0406100 Smaller than radiative loss if L>.5-1 fm Smaller than radiative loss if L>.5-1 fm Is there mostly near the zero binding lines, Is there mostly near the zero binding lines, Thus it is different from both radiative and elastic looses, which are simply proportional to density 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) Relates to non-trivial energy dependence of jet quenching (smaller at 62 and near absent at SPS) dE/dx in GeV/fm vs T/T c for a gluon 15,10,5 GeV. Red-elastic, black -ionization

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

51. A gift by the string theorists: AdS/CFT correspondence The viscosity/entropy => 1/4Pi is very small and about as observed at RHIC (D.Son et al 2003)

52. QCD vs CFT: let us start with EoS (The famous.8 explained!)

53. Bound states in AdS/CFT (ES and Zahed, PRD 2004) The quasiparticles are heavy M_q =O(sqrt(lambda) T) >> T But there are light binary bound states with the mass = O(M_q/sqrt(lambda))=O(T) Out of which the matter is made of!

54. A complete ``gravity dual” for RHIC from 10-d GR? (ES,Sin,Zahed, in progress) Black Holes + Howking rad. Is used to mimic the finite T How black hole is produced can be calculated from GR (tHooft … Nastase) Entropy production => black hole formation, falling into it is viscosity Moving brane => hydro expansion

55. Conclusions QGP as a “matter” in the usual sense, not a bunch of particles, has been produced at SPS/RHIC QGP as a “matter” in the usual sense, not a bunch of particles, has been produced at SPS/RHIC It shows very robust collective flows. The EoS is as expected: the vacuum pressure of about.5 GeV/fm3 observed. It shows very robust collective flows. The EoS is as expected: the vacuum pressure of about.5 GeV/fm3 observed. QGP seems to be the most ideal fluid known QGP seems to be the most ideal fluid known eta/hbar s=.1-.2 <<1 eta/hbar s=.1-.2 <<1 All of this hints that QGP is a liquid, in a strong coupling regime All of this hints that QGP is a liquid, in a strong coupling regime Interesting analogies with other strongly coupled systems Interesting analogies with other strongly coupled systems ``quantum gases” ``quantum gases” AdS/CFT AdS/CFT Strongly coupled e/m plasmas Strongly coupled e/m plasmas