1. A NEARLY PERFECT INK: The quest for the quark-gluon plasma at the Relativistic Heavy Ion Collider Berndt Mueller (Duke University) LANL Theory Colloquium 2 June 2005

2. The Road to the Quark-Gluon Plasma… STAR …Is Hexagonal and 2.4 Miles Long Insights and Scientific Challenges from the RHIC Experiments

3. The quest for simplicity Before the 1975, matter at high energy density was considered a real mess! QCD predicts that hot matter becomes simple – the QGP (not necessarily weakly interacting!). Characteristic features: deconfinement and chiral symmetry restoration. The equation of state of strongly interacting matter according to lattice QCD Quark-gluon plasma T c ≈ 160 MeV

4. The QCD phase diagram BB Hadronic matter Critical endpoint ? Plasma Nuclei Chiral symmetry broken Chiral symmetry restored Colour superconductor Neutron stars T 1 st order line ? Quark- Gluon RHIC TcTc

5. Space-time picture of a r.h.i.c. Equilibration Hadronization Thermal freeze- out

6. RHIC data gathering RHIC has had runs with: Au+Au at 200, 130, 62 GeV Cu+Cu at 200, 62 GeV d+Au at 200 GeV p+p at 200, 130 GeV Charged particle tracks from a central Au+Au collision

7. Frequently Asked Questions How do we know that we have produced equilibrated matter, not just a huge bunch of particles ? What makes this matter special ? How do we measure its properties ? Which evidence do we have that quarks are deconfined for a brief moment (about 10 -23 s) ? Which evidence do we have for temporary chiral symmetry restoration ? What do we still need to learn ? –Translation: When can RHIC be closed down ?

8. FAQ #1 How do we know that we produced equilibrated matter, not just a bunch of particles ? Answer: Particles are thermally distributed and flow collectively !

9. 9 Chemical equilibrium Chemical equilibrium fits work, except where they should not (resonances with large rescattering). RHIC Au+Au @ 200 GeV –T ch = 160  10 MeV –µ B = 24  5 MeV STAR Preliminary Central Au-Au √s=200 GeV

10. Elliptic flow Coordinate space: initial asymmetry Momentum space: final asymmetry pypy Pressure gradient collective flow pxpx x y Two-particle correlations dN/d(  1 -  2 )  1 + 2v 2 2 cos(2[  1 -  2 ])

11. FAQ #2 What makes this matter special ? Answer: It flows astonishingly smoothly ! “The least viscous non-superfluid ever seen”

12. v 2 requires low viscosity Relativistic viscous fluid dynamics: Shear viscosity  tends to smear out the effects of sharp gradients But what is  s ? pQCD: Dimensionless quantity

13. Viscosity must be ultra-low D. Teaney Quantum lower bound on  /s :  /s = 1/4  ( Kovtun, Son, Starinets ) Realized in strongly coupled (g  1) N = 4 SUSY YM theory, also in QCD ?  /s = 1/4  implies f ≈ (5 T) -1 ≈ 0.3 d QGP(T ≈T c ) = sQGP v 2 data comparison with (2D) relativistic hydrodynamics results suggests  /s  0.1 Recent excitement:

14. FAQ #3 How do we measure its properties ? Answer: With hard QCD probes, such as jets, photons, or heavy quarks

15. High-energy parton loses energy by rescattering in dense, hot medium. q q Radiative energy loss: “Jet quenching” = Parton energy loss qq g Scattering centers = color charges L Scattering power of the QCD medium: Density of scattering centers Range of color force

16. Suppression of fast pions (  0 ) Phenix preliminary Central collisons Peripheral collisons

17. Energy loss at RHIC Data are described by a very large loss parameter for central collisions: p T = 4.5 – 10 GeV/c (Dainese, Loizides, Paic, hep-ph/0406201) Larger than expected from perturbation theory ? Pion gas QGP Cold nuclear matter RHIC data sQGP R. Baier

18. Does QCD perturbation theory work? I. Vitev (JRO Fellow – LANL) d+Au Au+Au → What is the appropriate value of QCD coupling  s ? 00

19. FAQ #4 Which evidence do we have that quarks are deconfined for a brief moment (about 10-23 s) ? Answer: Baryons and mesons are formed from independently flowing quarks

20. Suppression Patterns: Baryons vs. Mesons  What makes baryons different from mesons ?

21. Hadronization Mechanisms Fragmentation Recombination This is not coalescence from a dilute medium !

22. Recombination “wins” … … always for a thermal source Baryons compete with mesons Fragmentation still wins for a power law tail

23. Recombination vs. Fragmentation T eff = 350 MeV blue-shifted temperature T = 180 MeV pQCD spectrum shifted by 2.2 GeV R.J. Fries, BM, C. Nonaka, S.A. Bass Baryon enhancement

24. Hadron v 2 reflects quark flow ! Recombination model suggests that hadronic flow reflects partonic flow (n = number of valence quarks): Provides measurement of partonic v 2 !

25. FAQ #5 Which evidence do we have for temporary chiral symmetry restoration ?

26. Strangeness in Au+Au at RHIC (sss) (qss) (qqs) Flavor Mass (MeV) QCD mass disappears

27. FAQ #6: What do we still need to (or want to) learn ? Number of degrees of freedom: –via energy density – entropy relation. Color screening: –via dissolution of heavy quark bound states (J/  ). Chiral symmetry restoration: –modification of hadron masses via e + e - spectroscopy. Quantitative determination of transport properties: –viscosity, stopping power, sound velocity, etc. What exactly is the “s”QGP ?

28. QCD equation of state 20% Challenge: Devise method for determining from data

29. Alternative method Eliminate T from  and s : Lower limit on requires lower limit on s and upper limit on . BM & K. Rajagopal, hep-ph/0502174 Eur. J. Phys. C (in print)

30. Measuring  and s Entropy is related to produced particle number and is conserved in the expansion of the (nearly) ideal fluid: dN/dy → S → s = S/V. Energy density is more difficult to determine: –Energy contained in transverse degrees of freedom is not conserved during hydrodynamical expansion. –Focus in the past has been on obtaining a lower limit on  ; here we need an upper limit. –New aspect at RHIC: parton energy loss. dE/dx is telling us something important – but what exactly?

31. Entropy Two approaches: 1)Use inferred particle numbers at chemical freeze-out from statistical model fits of hadron yields; 2)Use measured hadron yields and HBT system size parameters as kinetic freeze-out (Pratt & Pal). Method 2 is closer to data, but requires more assumptions (HBT radii = geometric radii, isentropic expansion of hadronic gas). Good news: results agree within errors: –dS/dy = 5100 ± 400 for Au+Au (6% central, 200 GeV/NN)

32. State of the art 6% central s NN 1/2 = 200 GeV Au+Au collisions (  0 = 1 fm/c): –dS/dy = 5100 ± 400 → s = (dS/dy)/(  R 2  0 ) = 33 ± 3 fm -3 –dE T /dy = 650 GeV/fm 3 →  Bj = (dE T /dy)/(  R 2  0 ) = 4.2 GeV/fm 3 –  >  Bj due to longitudinal hydrodynamic work done. PHOBOS estimate is  > 5 GeV/fm 3 at  0 = 1 fm/c. Some examples:  = 5 GeV/fm 3 → = 71 ± 22  = 7 GeV/fm 3 → = 26 ± 8  = 9 GeV/fm 3 → = 12 ± 4 –Improved determination of  must be an immediate goal.

33. Heavy quarks Heavy quarks (c, b) provide a hard scale via their mass. Three ways to make use of this:  Color screening of (Q-Qbar) bound states;  Energy loss of “slow” heavy quarks;  D-, B-mesons as probes of collective flow. RHIC program: c-quarks and J/  ; LHC-HI program: b-quarks and .  RHIC data for J/  are forthcoming (Runs 4 & 5).

34. The Baier plot - again Plotted against , is the same for a  gas and for a perturbative QGP. Suggests that is really a measure of the energy density.  Data suggest that may be larger than compatible with Baier plot.  Better calculations are needed.  One approach (Turbide et al.) based on complete LO HTL transport theory, gets R AA right (hep-ph/0502248) ˆ q ˆ q ˆ q Pion gas QGP Cold nuclear matter RHIC data sQGP

35. J/  suppression ? V qq is screened at scale (gT) -1  heavy quark bound states dissolve above some T d. Karsch et al. Color singlet free energy Quenched lattice simulations, with analytic continuation to real time, suggest T d  2T c ! S. Datta et al. (PRD 69, 094507) Challenge: Compute J/  spectral function in unquenched QCD

36. Di-hadron correlations STAR Data Away-side jet: Q’  (  R/R) 2 Q   R/R Correlations depend on selected momentum windows

37. “Waking” the sQGP v=0.55c v=0.99c

38. Outlook The “discovery phase” of RHIC is just hitting its full stride. Several important observables still waiting to be explored. Run-4 and -5 data are eagerly anticipated. More than 10 9 events will provide many answers and help us to refine the questions. Many well defined theoretical challenges.