1. GOING WITH THE FLOW What the data from RHIC have taught us so far Berndt Mueller (Duke University) 大阪大学, 14 October 2005

2. The quest for simplicity Before 1975, nuclear 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 (i.e. quarks lose their dynamically generated mass).           ’’  aa  ff aa  Hadronic resonance gas Quark-gluon plasma u d _ u _ d _ u _ s _ d u d s g g g g g g g

3. 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

4. QCD equation of state 20% Free massless particle limits Lattice gauge theory provides a model independent answer (for  B =0). Tc = 175  10 MeV

5. The space-time picture Equilibration Hadronization Thermal freeze- out

6. The path to the Q-G plasma… STAR …Is Hexagonal and 2.4 Miles Long The Relativistic Heavy Ion Collider at Brookhaven National Laboratory

7. RHIC data collection RHIC has had runs with: Au+Au at 200, 130, 62 and 19.6 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

8. 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 ?

9. 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 !

10. 10 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

11. The “elliptic” flow (v 2 ) 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 ])

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

13. v 2 requires low viscosity Relativistic viscous fluid dynamics: Shear viscosity  tends to smear out the effects of sharp gradients pQCD: Dimensionless quantity

14. 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:

15. An sQGP liquid? For realistic g E, perturbative quasiparticles are short-lived: Similar relationship for quarks:  /m* ≈ 1.3 Suggestive scenario:  As T  T c +0,  /m* increases, QGP quasiparticles (gluons, quarks, plasmons, plasminos) become broad and short-lived.  As T  T c -0,  /m* increases, hadrons (mesons, baryons) become broad and short-lived resonances.

16. Schematic scenario sHad  sQGP liquid TcTc HGQGP Hadrons exchange quarks rapidly and become short-lived resonances Quarks and gluons collide frequently and form short- lived “resonances” T Hagedorn????

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

18. High-energy parton loses energy by rescattering in dense, hot medium. q q Radiative energy loss: Parton energy loss (aka: jet quenching) qq g Scattering centers = color charges L Scattering power of the QCD medium: Density of scattering centers Range of color force

19. Pions vs. photons Deviation from binary NN collision scaling: Photons Hadrons

20. 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

21. Test case: R AA for charm …experiment ( STAR, PHENIX ) observe strong suppression up to R AA ~ 0.2 observed in most central events. Is collisional energy loss much larger than expected? Heavy quarks (c, b) should lose less energy by gluon radiation, but…

22. 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

23. Baryons vs. mesons  What makes baryons different from mesons ?

24. Hadronization mechanisms Fragmentation Recombination Meson Baryon from dense system Meson

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

26. Recombination - 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

27. 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 !

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

29. Strangeness at RHIC (sss) (qss) (qqs) Flavor Mass (MeV) QCD mass disappears

30. FAQ #6: 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 ? What do we still need to (or want to) learn ?

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

32. from  and s Eliminate T from  and s : Lower limit on requires lower limit on s and upper limit on . BM & K. Rajagopal, hep-ph/0502174

33. 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.  dS/dy = 5100 ± 400 for Au+Au (6% central, 200 GeV/NN)  Yields: s = (dS/dy)/(  R 2  0 ) = 33 ± 3 fm -3 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.

34. Where does E loss go? p+pAu+Au Lost energy of away-side jet is redistributed to rather large angles! Trigger jetAway-side jet

35. Wakes in the QGP Mach cone requires collective mode with  (k) < k : J. Ruppert and B. Müller, Phys. Lett. B 618 (2005) 123 Colorless sound ? Colored sound = longitudinal gluons ? Transverse gluons pQCD (HTL) dispersion relation

36. Collective modes in medium Cherenkov-like gluon radiation into a space-like transverse gluon branch: I. Dremin A. Majumder, X.-N. Wang, hep-ph/0507062 Mach cone structures from a space- like longitudinal plasmon branch: J. Ruppert & B. Müller, Phys. Lett. B 618 (2005) 123 Mach cone from sonic boom: H. Stoecker J. Casalderrey-Solana & E. Shuryak “Colored” sound Longitudinal (sound) modes Transverse modes Normal sound

37. Jet-Medium Interactions Renk & Ruppert. hep-ph/0509036 Angular distribution and size of off-jet axis peak depends on:  Energy fraction in collective mode  Propagation velocity  Collective flow pattern Note: f = 0.9 is a very large collective fraction requiring an extremely efficient energy transfer mechanism!

38. Outlook The “discovery phase” of RHIC has already uncovered several surprises: near-ideal liquid flow, valence quark number scaling of v 2 ; very large partonic energy loss. Several important observables are still waiting to be explored. Run-4 and -5 data (just coming out!) are beginning to provide some of the needed information. The RHIC data are posing many well defined theoretical challenges, such as:  Structure of QCD matter near T c ?  Thermalization mechanisms in gauge theories ?  Transport coefficients in gauge theories ?  A new window of calculable hadronization ?

39. Special thanks to… Jörg Ruppert Thorsten Renk Chiho Nonaka Steffen Bass Rainer Fries Yuki Asakawa