1. Results from RHIC Measurements of High Density Matter Thomas S. Ullrich Brookhaven Nation Laboratory and Yale University January 7, 2003 Introduction Soft Physics Hard Physics

2. 2 Thomas Ullrich, BNL (QCD) Phase Diagram of Nuclear Matter T >>  QCD : weak coupling  deconfined phase (Quark Gluon Plasma) T <<  QCD : strong coupling  confinement  phase transition at T~  QCD ? e.g. two massless flavors (Rajagopal and Wilczek, hep-ph/-0011333)

3. 3 Thomas Ullrich, BNL Lattice QCD at Finite Temperature Coincident transitions: deconfinement and chiral symmetry restoration Recently extended to  B > 0, order still unclear (2 nd, crossover ?) F. Karsch, hep-ph/0103314 Critical energy density: T C ~ 175 MeV  C ~ 1 GeV/fm 3 Ideal gas (Stefan- Boltzmann limit ) q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q

4. 4 Thomas Ullrich, BNL The Phase Transition in the Laboratory Chemical freezeout (T ch  T c ) : inelastic scattering stops Kinetic freeze-out (T fo  T ch ): elastic scattering stops e.m. probes (l  l   ) hard (high-p T ) probes soft physics regime

5. 5 Thomas Ullrich, BNL RHIC @ Brookhaven National Laboratory h Long Island Relativistic Heavy Ion Collider 2 concentric rings of 1740 superconducting magnets 3.8 km circumference counter-rotating beams of ions from p to Au STAR PHENIX PHOBOS BRAHMS 2000 run: Au+Au @  s NN =130 GeV 2001 run: Au+Au @  s NN =200 GeV (80 mb -1 ) polarized p+p @  s=200 GeV (P ~15%, ~1 pb -1 )

6. 6 Thomas Ullrich, BNL Geometry of Heavy Ion Collisions Number of participants (N part ): number of incoming nucleons (participants) in the overlap region Number of binary collisions (N bin ): number of equivalent inelastic nucleon-nucleon collisions Reaction plane x z y Non-central collision “peripheral” collision (b ~ b max ) “central” collision (b ~ 0) N bin  N part

7. 7 Thomas Ullrich, BNL Peripheral Event From real-time Level 3 display. STAR color code  energy loss

8. 8 Thomas Ullrich, BNL Mid-Central Event From real-time Level 3 display. STAR

9. 9 Thomas Ullrich, BNL Central Event From real-time Level 3 display. STAR

10. 10 Thomas Ullrich, BNL Charged Particle Multiplicity dN ch /d   19.6 GeV130 GeV200 GeV PHOBOS Preliminary Central Peripheral Central at 130 GeV: 4200 charged particles ! Total multiplicity per participant pair scales with N part

11. 11 Thomas Ullrich, BNL For the most central events: PHENIX EMCAL R2R2 Energy Density at RHIC  Bjorken ~ 4.6 GeV/fm 3 ~30 times normal nuclear density ~1.5 to 2 times higher than at SPS (  s = 17 GeV) ~ 5 times above  critical from lattice QCD Bjorken formula for thermalized energy density time to thermalize the system (  0 ~ 1 fm/c) ~6.5 fm What is the energy density achieved? How does it compare to the expected phase transition value ? 130 GeV

12. 12 Thomas Ullrich, BNL Hydrodynamics: Modeling High-Density Scenarios Assumes local thermal equilibrium (zero mean-free-path limit) and solves equations of motion for fluid elements (not particles) Equations given by continuity, conservation laws, and Equation of State (EOS) EOS relates quantities like pressure, temperature, chemical potential, volume  direct access to underlying physics Works qualitatively at lower energy but always overpredicts collective effects - infinite scattering limit not valid there  RHIC is first time hydro works! lattice QCD input

13. 13 Thomas Ullrich, BNL RHIC Spectra - an Explosive Source data: STAR, PHENIX, QM01 model: P. Kolb, U. Heinz various experiments agree well different spectral shapes for particles of differing mass  strong collective radial flow mTmT 1/m T dN/dm T light heavy T purely thermal source explosive source T,  mTmT 1/m T dN/dm T light heavy very good agreement with hydrodynamic prediction

14. 14 Thomas Ullrich, BNL Single Particle Spectra and Radial Flow Au+Au @ 130 GeV, central and peripheral (STAR, PHENIX): Hydrodynamics even works for peripheral collisions up to b ~ 10 fm! (Heinz & Kolb hep-ph/0204061) Problem with pions at low p T     > 0 required  = 0.6 fm/c, e max (b=0) = 24.6 GeV/fm 3, (  =1 fm/c) = 5.4 GeV/fm 3 T max (b=0) = 340 MeV, T ch = 165 MeV, T fo = 130 MeV    K+K+ p    

15. 15 Thomas Ullrich, BNL T fo and vs.  s  r   increases continously T fo  saturates around AGS energy Strong collective radial expansion at RHIC  high pressure  high rescattering rate  Thermalization likely Slightly model dependent here: blastwave model (Kaneta/Xu)

16. 16 Thomas Ullrich, BNL Azimuthal Anisotropy of Particle Emission: Elliptic Flow Almond shape overlap region in coordinate space Anisotropy in momentum space AGS SPS, RHIC Interactions v 2 : 2 nd harmonic Fourier coefficient in dN/d  with respect to the reaction plane

17. 17 Thomas Ullrich, BNL Time Evolution: When Does Elliptic Flow Develop? Equal energy density lines P. Kolb, J. Sollfrank, and U. Heinz Elliptic flow observable sensitive to early evolution of system Mechanism is self-quenching Large v 2 is an indication of early thermalization v2v2 Zhang, Gyulassy, Ko, PL B455 (1999) 45 Au+Au at b=7 fm    

18. 18 Thomas Ullrich, BNL Charged Particle v 2 vs. Centrality midrapidity : |h| < 1.0 Hydrodynamic model N ch /N max SPS AGS PRL 86 (2001) 402 V2V2 Hydrodynamical models can describe data at low p T (~2 GeV/c)  compatible with early equilibration Contrast to lower collision energies where hydro overpredicts elliptical flow Peripheral  Central STAR PRL87 (2001)182301

19. 19 Thomas Ullrich, BNL Models to Evaluate T ch and  B : Statistical Thermal Models Compare particle ratios to experimental data Q i : 1 for u and d, -1 for  u and  d s i : 1 for s, -1 for  s g i : spin-isospin freedom m i : particle mass T ch : Chemical freeze-out temperature  q : light-quark chemical potential  s : strangeness chemical potential  s : strangeness saturation factor Particle density of each particle: Statistical Thermal Model F. Becattini; P. Braun-Munzinger, J. Stachel, D. Magestro J.Rafelski PLB(1991)333; J.Sollfrank et al. PRC59(1999)1637 Assume: Ideal hadron resonance gas thermally and chemically equilibrated fireball at hadro- chemical freeze-out Recipe: grand canonical ensemble to describe partition function  density of particles of species  i fixed by constraints: Volume V,, strangeness chemical potential  S, isospin input: measured particle ratios output: temperature T and baryo- chemical potential  B

20. 20 Thomas Ullrich, BNL Statistical Models work well at RHIC

21. 21 Thomas Ullrich, BNL Statistical Models: from AGS to RHIC Different implementation of statistical model Fact: all work well at AGS, SPS and RHIC T ch [MeV]  B [MeV] AGS  s = 2-4 GeV 125540 SPS  s = 17 GeV 165250 RHIC  s = 130-200 GeV 17530 Does the success of the model tell us we are dealing indeed with locally chemically equilibrated systems? this+flow  If you ask me YES! neutron stars Baryonic Potential  B [MeV] early universe Chemical Temperature T ch [MeV] 0 200 250 150 100 50 020040060080010001200 AGS SIS SPS RHIC quark-gluon plasma hadron gas deconfinement chiral restauration Lattice QCD atomic nuclei Slight variations in the models, but roughly:

22. 22 Thomas Ullrich, BNL Summary on “Soft” ( p T < 2 GeV/c) Physics  Particle production is large l Total N ch ~ 5000 (Au+Au  s = 200 GeV)  ~ 20 in p+p l N ch /N participant-pair ~ 4 (central region)  ~2.5 in p+p  Vanishing baryon/antibaryon ratio (0.7-0.8) l close to net baryon-free but not quite (net proton dN/dy~10)  Energy density is high  4-5 GeV/fm 3 (model dependent) l lattice phase transition ~1 GeV/fm 3, cold matter ~ 0.16 GeV/fm 3  System exhibits collective behavior (radial + elliptic flow) l  strong internal pressure that builds up very early  The system appears to freezes-out very fast l explosive expansion (HBT, correlation studies)  Particles ratios suggest chemical equilibrium T ch  170 MeV,  b <50 MeV  near lattice phase boundary  Large system at freeze-out  2  size of nuclei Overall picture: system appears to be in equilibrium but explodes and hadronizes rapidly

23. 23 Thomas Ullrich, BNL Products of parton fragmentation (jet “leading particle”). Early production in parton-parton scatterings with large Q 2. Direct probes of partonic phases of the reaction Sensitive to hot/dense medium: parton energy loss (“jet quenching”). Info on medium effects accessible through comparison to scaled "vacuum" (pp) yields (“binary scaling”): Production yields calculable via pQCD: High-p T Particles @ RHIC – Jet Tomography q q leading particle

24. 24 Thomas Ullrich, BNL Jets in Heavy Ion Collisions e  e   q q (OPAL@LEP) pp  jet+jet (STAR@RHIC) Au+Au  ??? (STAR@RHIC) Hopeless task? No, but a bit tricky…

25. 25 Thomas Ullrich, BNL Partonic Energy Loss: Theory Elastic scattering (Bjorken 1982): Gluon radiation is factor ~10 larger: Thick plasma (Baier et al.): Thin plasma (Gyulassy et al.): Linear dependence on gluon density  glue   measures gluon density  is continuous function of energy density  not a direct signature of deconfinement

26. 26 Thomas Ullrich, BNL Energy Loss in Cold Matter Modification of fragmentation functions in e-Nucleus scattering: dE/dx ~ 0.5 GeV/fm for 10 GeV quark Existing data is extensively studied but p+A measurements at RHIC are desperately needed  Run III (2003) d+Au Wang and Wang, hep-ph/0202105

27. 27 Thomas Ullrich, BNL High-p T Hadrons: Au+Au at RHIC Preliminary  s NN = 200 GeV

28. 28 Thomas Ullrich, BNL Measuring Hadron Suppression /  inel p+p N-N cross section 1. Compare Au+Au to nucleon-nucleon cross sections 2. Compare Au+Au central/peripheral Nuclear Modification Factor: If no “effects”: R < 1 in regime of soft physics R = 1 at high-p T where hard scattering dominates Suppression: R < 1 at high-p T

29. 29 Thomas Ullrich, BNL Leading Hadrons in Fixed Target Experiments A Multiple scattering in initial state(“Cronin effect”) p+A collisions: Central Pb+Pb collisions at SPS SPS: any parton energy loss effects buried by initial state multiple scattering, transverse radial flow,…

30. 30 Thomas Ullrich, BNL Hadron Suppression: Au+Au at 130 GeV Phenix: PRL 88 022301 (2002)   and charged hadrons, central collisions STAR: nucl-ex/0206011 Charged hadrons, centrality dependence Clear evidence for high p T hadron suppression in central nuclear collisions

31. 31 Thomas Ullrich, BNL Hadron Suppression: Au+Au at 200 GeV Preliminary  s NN = 200 GeV PHENIX preliminary 200 GeV preliminary data: suppression of factor 4-5 persists to p T =12 GeV/c Phenix    peripheral and central over measured p+p STAR charged hadrons: central/peripheral

32. 32 Thomas Ullrich, BNL Hadron Suppression: Central Au+Au (Data vs. Theory) l Parton energy loss : dE/dx ≈ 0.25 GeV/fm (expanding) dE/dx| eff ≈ 7 GeV/fm (static source) ~ 15 times that in cold Au nuclei Opacities: = L/  ≈ 3 – 4 Gluon densities: dN g /dy ~ 900 S.Mioduszewski PHENIX Preliminary nucl-ex/0210021 All models expect a moderate increase of R AA at higher p T What does it tell us about the medium ?

33. 33 Thomas Ullrich, BNL Elliptic “Flow” at High-p T : Theory Snellings; Gyulassy, Vitev and Wang (nucl-th/00012092) Jet propagation through anisotropic matter (non-central collisions) Finite v 2 : high p T hadron correlated with reaction plane from “soft” part of event (p T <2 GeV/c) Finite asymmetry at high p T sensitive to energy density jet STAR @ 130 GeV STAR @ 200 GeV

34. 34 Thomas Ullrich, BNL Jet core  ×  0.5 × 0.5  study near-side correlations (  ~0) of high p T hadron pairs Complication: elliptic flow  high p T hadrons correlated with the reaction plane (~v 2 2 ) Solution: compare azimuthal correlation functions for  short range   particles in jet cone + background  long range  background only Azimuthal correlation function: Trigger particle p T trig > 4 GeV/c Associate tracks 2 < p T < p T trig Caveat: Away-side jet contribution subtracted by construction, needs different method…  < 0.5  > 0.5 2-Particle Correlations at High-p T : Direct Evidence for Jets Near-side correlation shows jet-like signal in central Au+Au

35. 35 Thomas Ullrich, BNL 2 Particle Correlations at High-p T : Back-to-Back Jets? away-side (back-to-back) jet can be “anywhere”  Ansatz: correlation function: high p T -triggered Au+Au event = high p T -triggered p+p event + elliptic flow + background A: from fit to “non-jet” region  v 2 from reaction plane analysis 0<|  |<1.4 p+p unlike sign like sign p+p measured in RHIC detectors

36. 36 Thomas Ullrich, BNL Suppression of Back-to-Back Pairs Central Au + Au Peripheral Au + Au Near-side well-described Away-side suppression in central collisions Away side jets are suppressed! near side away side STAR Preliminary

37. 37 Thomas Ullrich, BNL High p T phenomena: suppression of inclusive rates, finite elliptic flow, suppression of back-to-back pairs  compatible with extreme absorption and surface emission

38. 38 Thomas Ullrich, BNL Summary ? Soft physics: Low baryon density System appears to be in equilibrium (hydrodynamic behaviour) Explosive expansion, rapid hadronization Hard physics: Jet fragmentation observed, agreement with pQCD Strong suppression of inclusive yields Azimuthal anisotropy at high pT Suppression of back-to-back hadron pairs large parton energy loss and surface emission? Coming Attractions: d+Au: disentangle initial state effects in jet production (shadowing, Cronin enhancement)  resolution of jet quenching picture J/  and open charm: direct signature of deconfinement? (Charm via single electrons: PHENIX, PRL 88, 192303 (2002)) Polarized protons:  G (gluon contribution to proton spin) Surprises …