Energy Loss and Flow in Heavy Ion Collisions

Energy Loss and Flow in Heavy Ion Collisions at RHIC Niels Bohr was almost right about the liquid drop model Jim Thomas Lawrence Berkeley National Laboratory Berkeley, CA University of Notre Dame February 20 th, 2008 Jim Thomas - LBL 1

The Phase Diagram for Nuclear Matter The goal is to explore nuclear matter under extreme conditions – T > m c 2 , r > 10 * r 0 and rnet 0 Jim Thomas - LBL • One of the goals of RHIC is to understand the QCD in the context of the many body problem • Another goal is to discover and characterize the Quark Gluon Plasma • RHIC is a place where fundamental theory and experiment can meet after many years of being apart 2

Who is RHIC and What Does He Do? BRAHMS PHOBOS RHIC • Two independent rings • 3. 83 km in circumference PHENIX h • Accelerates everything, from p to Au s L p-p 500 1032 Au-Au 200 1027 (Ge. V and cm-2 s-1) • Polarized protons Lo Jim Thomas - LBL n sla g. I nd • Two Large and two small detectors were built And for a little while longer, it is the highest energy heavy ion collider in the world 3

The Large Detectors – PHENIX and STAR Jim Thomas - LBL PHENIX 4

STAR is a Suite of Detectors Time Projection Chamber Magnet Coils Silicon Tracker SVT & SSD TPC Endcap & MWPC FTPCs Beam Counters Endcap Calorimeter Central Trigger Barrel & TOF Barrel EM Calorimeter PMD Not Shown: p. VPDs, ZDCs, and FPDs 4. 2 meters A TPC lies at the heart of STAR Jim Thomas - LBL 5

Au on Au Event at CM Energy ~ 130 Ge. V*A Data taken June 25, 2000. The first 12 events were captured on tape! Real-time track reconstruction Pictures from Level 3 online display. ( < 70 m. Sec ) Jim Thomas - LBL 6

Au on Au Event at CM Energy ~ 130 Ge. V*A A Central Event Typically 1000 to 2000 tracks per event into the TPC Two-track separation 2. 5 cm Momentum Resolution < 2% Space point resolution ~ 500 mm Rapidity coverage – 1. 8 < < 1. 8 Jim Thomas - LBL 7

Particle ID using Topology & Combinatorics Secondary vertex: Ks + p + + K g e++e- Ks + + p + - dn/dm K++Kr + + from K+ K- pairs background subtracted m inv dn/dm K+ K- pairs same event dist. mixed event dist. m inv “kinks” K + Jim Thomas - LBL 8

Identified Mesons and Baryons: Au+Au @ 200 Ge. V and p yields. vs. p. T Jim Thomas - LBL Phys. Rev. Lett. 97 (2006) 152301 9

Nomenclature: Rapidity vs xf • xf = pz / pmax – A natural variable to describe physics at forward scattering angles • Rapidity is different. It is a measure of velocity but it stretches the region around v = c to avoid the relativistic scrunch β – Rapidity is relativistically invariant and cross-sections are invariant Rapidity and p. T are the natural kinematic variable for HI collisions ( y is approximately the lab angle … where y = 0 at 90 degrees ) When the mass of the particle is unknown, then y Jim Thomas - LBL 10

Strange Baryons and Mesons: Au+Au @ 200 Ge. V , , and yields. vs. p. T Phys. Rev. Lett. 98 (2007) 060301 Jim Thomas - LBL 11

Transverse Radial Expansion: Isotropic Flow Au+Au at 200 Ge. V Ty pic - al S TA RD ata K- p T ≈ 215 Me. V T ≈ 310 Me. V T ≈ 575 Me. V Slopes decrease with mass. <p. T> and the effective temperature increase with mass. Jim Thomas - LBL The transverse radial expansion of the source (flow) adds kinetic energy to the particle distribution. So the classical expression for ETot suggests a linear relationship 12

Kinetic freeze-out time Chemical and Kinetic Freeze-out Chemical freeze-out elastic interactions inelastic interactions blue beam • Chemical freeze-out (first) – End of inelastic interactions – Number of each particle species is frozen • Useful data – Particle ratios Jim Thomas - LBL yellow beam • space Kinetic freeze-out (later) – End of elastic interactions – Particle momenta are frozen • Useful data – Transverse momentum distributions – and Effective temperatures 13

Chemical Freeze-out – from a thermal model Thermal model fits Compare to QCD on the (old) Lattice: Tc = 154 ± 8 Me. V (Nf=3) Tc = 173 ± 8 Me. V (Nf=2) (ref. Karsch, various) • The model assumes a thermally and chemically equilibrated fireball at hadro-chemical freeze-out which is described by a temperature T and (baryon) chemical potential : dn ~ e-(E- )/T d 3 p • Works great, but there is not a word of QCD in the analysis. Done entirely in a color neutral Hadronic basis! input: measured particle ratios output: temperature T and baryo-chemical potential B Jim Thomas - LBL 14

Putting RHIC on the Phase Diagram • Final-state analysis suggests RHIC reaches the phase boundary • Hadron spectra cannot probe higher temperatures • Hadron resonance ideal gas (M. Kaneta and N. Xu, Lattice results nucl-ex/0104021 & QM 02) – TCH = 175 ± 10 Me. V – B = 40 ± 10 Me. V Neutron STAR • <E>/N ~ 1 Ge. V (J. Cleymans and K. Redlich, PRL 81, p. 5284, 1998 ) We know where we are on the phase diagram but eventually we want to know what other features are on the diagram Jim Thomas - LBL 15

RHIC Physics is Relativistic Nuclear Physics Jim Thomas - LBL 16

Unlike Particle Physics, the initial state is important • Only a few of the nucleons participate in the collision as determined by the impact parameter • There is multiple scattering in the initial state before the hard collisions take place – Cronin effect • The initial state is Lorentz contracted • Cross-sections become coherent. – The uncertainty principle allows wee partons to interact with the front and back of the nucleus – The interaction rate for wee partons saturates ( ρσ = 1 ) • The intial state is even time dilated – A color glass condensate Jim Thomas - LBL • proton • neutron • delta • pion string 17

Dependent Distributions – Flow • The overlap region in peripheral collisions is not symmetric in coordinate space • Almond shaped overlap region – Larger pressure gradient in the x-z plane drives flow in that direction – Easier for high p. T particles to emerge in the direction of x-z plane • Spatial anisotropy Momentum anisotropy • Perform a Fourier decomposition of the momentum -space particle distribution in the plane – For example, v 2 is the 2 nd harmonic Fourier coefficient of the distribution of particles with respect to the reaction plane Jim Thomas - LBL isotropic directed elliptic 18

Interpreting Flow – order by order n=1: Directed Flow has a period of 2 (only one maximum) – v 1 measures whether the flow goes to the left or right – whether the momentum goes with or against a billiard ball like bounce off the collision zone n=2: Elliptic flow has a period of (two maximums) – v 2 represents the elliptical shape of the momentum distribution isotropic Jim Thomas - LBL directed elliptic higher order terms 19

V 1: Pions go opposite to Neutrons 62 Ge. V Data At low energy, the pions go in the opposite direction to the ‘classical’ bounce of the spectator baryons 200 Ge. V Data At the top RHIC energy, the pions don’t flow (v 1 at =0 ) but at ALICE, v 1 may have a backward wiggle. Reveals the EOS Jim Thomas - LBL • hi 20

Interpreting Flow – order by order n=1: Directed Flow has a period of 2 (only one maximum) – v 1 measures whether the flow goes to the left or right – whether the momentum goes with or against a billiard ball like bounce off the collision zone n=2: Elliptic flow has a period of (two maximums) – v 2 represents the elliptical shape of the momentum distribution isotropic Jim Thomas - LBL directed elliptic 21

V 2 vs. p. T and Particle Mass • v 2 is large • The mass dependence is reproduced by hydrodynamic models – Hydro assumes local thermal equilibrium – At early times – Followed by hydrodynamic expansion PRL 86, 402 (2001) & nucl-ex/0107003 D. Teaney et al. , QM 2001 Proc. P. Huovinen et al. , nucl-th/0104020 Anisotropic transverse flow is large at RHIC Jim Thomas - LBL – 6% in peripheral collisions (for pions average over all p. T ) • Flow is developed very rapidly – Data suggests very early times ~ fm/c • Hydro calculations are in good agreement with the data – Hydro assumes local thermal equilibrium – Followed by hydrodynamic expansion – The mass dependence is reproduced by the models 22

Elliptic Flow: in ultra-cold A Simulation ofan Elliptic Flow Fermi-Gas Li-atoms released from an optical trap exhibit elliptic flow analogous to what is observed in ultra-relativistic heavy-ion collisions – Elliptic flow is a general feature of strongly interacting systems! Jim Thomas - LBL 23

v 2 at high p. T shows meson / baryon differences Bulk PQCD Hydro Jim Thomas - LBL Asym. p. QCD Jet Quenching qn Coalescence 24

-meson Flow: Partonic Flow -mesons are special: - they show strong collective flow and - they are formed by coalescence of thermalized s-quarks ‘They are made via coalescence of seemingly thermalized quarks in central Au+Au collisions, the observations imply hot and dense matter with partonic collectivity has been formed at RHIC’ Phys. Rev. Lett. 99 (2007) 112301 and Phys. Lett. B 612 (2005) 81 Jim Thomas - LBL 25

The Recombination Model ( Fries et al. PRL 90 (2003) 202303 ) The flow pattern in v 2(p. T) for hadrons is predicted to be simple if flow is developed at the quark level p. T → p. T /n v 2 → v 2 / n , n = (2, 3) for (meson, baryon) Jim Thomas - LBL 26

Elliptic flow scales with the number of quarks Implication: quarks, not hadrons, are the relevant degrees of freedom at early times in the collision history Jim Thomas - LBL 27

Hints of Elliptic Flow with Charm • D e +X Single electron spectra from PHENIX show hints of elliptic flow Is it charm or beauty? • The RHIC upgrades will cut out large photonic backgrounds: g e+eand reduce other large stat. and systematic uncertainties Shingo Sakai, QM 2006 PRL 98, 172301 (2007) Better if we can do direct topological identification of Charm Jim Thomas - LBL 28

Constituent Quark Scaling? • Hadrons are created by the recombination of quarks and this appears be the dominant mechanism for hadron formation at intermediate p. T • Baryons and Mesons are produced with equal abundance at intermediate p. T • The collective flow pattern of the hadrons appears to reflect the collective flow of the constituent quarks. Partonic Collectivity Jim Thomas - LBL 29

Lets look at some collision systems in detail … Initial state Final state Au + Au d + Au p + p Jim Thomas - LBL 30

Partonic energy loss via leading hadrons Energy loss softening of fragmentation suppression of leading hadron yield Binary collision scaling Jim Thomas - LBL p+p reference 31

Au+Au and p+p: inclusive charged hadrons PRL 89, 202301 p+p reference spectrum measured at RHIC Jim Thomas - LBL 32

PHENIX data on the suppression of 0 s lower energy Pb+Pb lower energy a+a Factor ~5 suppression for central Au+Au collisions Jim Thomas - LBL 33

The Suppression occurs in Au-Au but not d-Au No quenching d+Au Quenching! Au+Au Jim Thomas - LBL 34

Heavy Flavor Energy Loss … RAA for Charm • Heavy Flavor energy loss is an unsolved problem Theory from Wicks et al. nucl-th/0512076 v 2 – Gluon density ~ 1000 expected from light quark data – Better agreement with the addition of inelastic E loss – Good agreement only if they ignore Beauty … • Beauty dominates single electron spectra above 5 Ge. V Where is the contribution from Beauty? Jim Thomas - LBL • RHIC upgrades will separate the Charm and Beauty contributions 35

Partonic energy loss No quenching d+Au Quenching! Au+Au Energy loss suppression of leading hadron yield The jet can’t get out! Binary collision scaling Jim Thomas - LBL p+p reference 36

Jet Physics … it is easier to find one in e+e. Jet event in e+e- collision Jim Thomas - LBL STAR Au+Au collision 37

Angular Distribution: Peripheral Au+Au data vs. pp+flow Ansatz: A high p. T triggered Au+Au event is a superposition of a high p. T triggered p+p event plus anisotropic transverse flow v 2 from reaction plane analysis “A” is fit in non -jet region (0. 75<| |<2. 24) Jim Thomas - LBL 38

Angular Distribution: Jim Thomas - LBL Central Au+Au data vs. pp+flow 39

Lessons learned – Dark Matter … its opaque • The backward going jet is missing in central Au-Au collisions when compared to p-p data + flow • The backward going jet is not suppressed in d-Au collisions • These data suggest opaque nuclear matter and surface emission of jets Jim Thomas - LBL Surface emission Suppression of back-to-back correlations in central Au+Au collisions 40

Where does the Eloss go? PHENIX Away-side jet p+p Au+Au Trigger jet Lost energy of away-side jet is redistributed to rather large angles! Jim Thomas - LBL 41

Mach Cone: Theory vs Experiment STAR preliminary 0 -12% 200 Ge. V Au+Au mach cone near deflected jets near • Hint of a Mach Cone? Jim Thomas - LBL Medium away 42

Nuclear Fluid Dynamics. . . with friction • The energy momentum tensor for a viscous fluid • Conservation laws: and where • The elements of the shear tensor, , describe the viscosity of the fluid and can be thought of as velocity dependent ‘friction’ • Simplest case: scaling hydrodynamics – – – assume local thermal equilibrium assume longitudinal boost-invariance cylindrically symmetric transverse expansion no pressure between rapidity slices conserved charge in each slice • Initially expansion is along the Z axis, so viscosity resists it – Conservation of T means that energy and momentum appear in the transverse plane … viscosity drives radial flow • Viscosity is velocity dependent friction so it dampens v 2 – Viscosity ( /z ) must be near zero for elliptic flow to be observed Jim Thomas - LBL 43

Ad. S/CFT correspondence (from H. Liu) Maldacena (1997) Gubser, Klebanov, Polyakov, Witten N = 4 Super-Yang-Mills theory with SU(N) A string theory in 5 -dimensional anti-de Sitter spacetime anti-de Sitter (Ad. S) spacetime: homogeneous spacetime with a negative cosmological constant. N = 4 Super-Yang-Mills (SYM): maximally supersymmetric gauge theory scale invariant A special relative of QCD The value turns out to be universal for all strongly coupled QGPs with a gravity description. It is a universal lower bound. Jim Thomas - LBL 44

PHENIX PRL 98, 172301 (2007) • RAA of heavy-flavor electrons in 0%– 10% central collisions compared with 0 data and model calculations 0 • V 2 of heavy-flavor electrons in minimum bias collisions compared with 0 data and the same models. • Conclusion is that heavy flavor flow corresponds to /s at the conjectured QM lower bound Jim Thomas - LBL 45

Viscosity and the Perfect Fluid H 2 O N 2 He hadronic partonic The universal tendency of flow to be dissipated due to the fluid’s internal friction results from a quantity known as the shear viscosity. All fluids have non-zero viscosity. The larger the viscosity, the more rapidly small disturbances are damped away. Quantum limit: /s. Ad. S/CFT ~ 1/4 p. QCD limit: ~ 1 At RHIC: ideal ( /s = 0) hydrodynamic model calculations fit to data Caption: The viscosity to entropy ratio versus a reduced temperature. Perfect Fluid at RHIC? ! Lacey et al. PRL 98: 092301(07) hep-lat/0406009; hep-ph/0604138 Csernai et al, PRL 97, 152303(06) Jim Thomas - LBL 46

Old Chinese Proverb Beware of theorists waiting for data – Confusion Jim Thomas - LBL 47

PRL 99, 172301 (2007) … new insights • Romatschke 2 perform relativistic viscous hydrodynamics calculations • Data on the integrated elliptic flow coefficient v 2 are consistent with a ratio of viscosity over entropy density up to /s 0. 16 • But data on minimum bias v 2 seem to favor a much smaller viscosity over entropy ratio, below the bound from the anti –de Sitter conformal field theory conjecture Jim Thomas - LBL 48

Did a meteor impact on the Yucatan kill the Dinosaurs? Jim Thomas - LBL 49

Conclusions About Nuclear Matter at RHIC • Its hot – Chemical freeze out at 175 Me. V – Thermal freeze out at 100 Me. V • Its fast – Transverse expansion with an average velocity greater than 0. 55 c – Large amounts of anisotropic flow (v 2) suggest hydrodynamic expansion and high pressure at early times in the collision history • Its opaque – Saturation of v 2 at high p. T – Suppression of high p. T particle yields relative to p-p – Suppression of the away side jet • There are hints that it is thermally equilibrated – Excellent fits to particle ratio data with equilibrium thermal models – Excellent fits to flow data with hydrodynamic models that assume equilibrated systems – Hints of heavy flavor flow • And it has nearly zero viscosity and perhaps a Mach cone – Perhaps it is at or below the quantum bound from the Ad. S/CFT conjecture Jim Thomas - LBL Niels Bohr was almost right … he just didn’t know about q and g 50

STAR Tth [Ge. V] STAR Preliminary PHENIX < r> [c] Kinetic Freezeout from Transverse Flow <ßr> (RHIC) = 0. 55 ± 0. 1 c TKFO (RHIC) = 100 ± 10 Me. V Thermal freeze-out determinations are done with the blast-wave model to find <p. T> Jim Thomas - LBL Explosive Transverse Expansion at RHIC High Pressure 51

3<pt, trigger<4 Ge. V pt, assoc. >2 Ge. V Au+Au 0 -10% preliminary Jim Thomas - LBL 52

The Development of a Weibal Instability Jim Thomas - LBL 53

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Charm Cross Sections at RHIC 1) Large systematic uncertainties in the measurements 2) Theory under predict by a factor ~ 2 and STAR ~ 2 x PHENIX 3) Directly reconstructed charm hadrons Upgrades Jim Thomas - LBL 56

A p. QCD Study - At RHIC energy, baryons are mostly from gluons and pions are mostly from quark jets. - Observation at high p. T : RCP( ) ~ RCP (p) RCP (K) ~ RCP ( ) - p. QCD color factor effects: E(g)/ E(q) ~ 9/4 �A clear challenge to p. QCD predictions! �Future tests with charm hadrons(quarks) and meson(gluon). STAR: nucl-ex/0703040. Phys. Lett. B, in print Nu Jim Thomas - LBL 57

Inclusive cross-section (jets, 0, ±, p±) Mid-y jets, 0, ± and p± productions are well reproduced by NLO p. QCD calculations over many orders of magnitude 1) powerful tool for analyzing spin physics. 2) reliable reference for study high-energy nuclear collisions. 161(06) Jim Thomas - LBL Nu STAR: PRL 97, 252001(06); PL B 637, 58

Hadron Spectra from RHIC p+p and Au+Au collisions at 200 Ge. V ud ss uud sss more central collisions 0 -5% Multi-strange hadron spectra are exponential in their shapes. STAR white papers - Nucl. Phys. A 757, 102(2005). Jim Thomas - LBL 59

Current State of Affairs • A theory is something nobody believes, except the person who made it. • An experiment is something everybody believes, except the person who made it. – attributed to Albert Einstein Jim Thomas - LBL 60

Recombination Tested The complicated observed flow pattern in v 2(p. T) d 2 n/dp. Td ~ 1 + 2 v 2(p. T) cos (2 ) is predicted to be simple at the quark level under p. T → p. T / n , v 2 → v 2 / n , n = 2, 3 for meson, baryon if the flow pattern is established at the quark level Compilation courtesy of H. Huang Jim Thomas - LBL 61

Quark Coalescence q At low pt: mass ordering hydrodynamics q At larger pt: Baryons – mesons S. A. Voloshin, Nucl. Phys. A 715, 379 (2003). quark coalescence Z. Lin et al. , Phys. Rev. Lett. , 89, 202302 (2002). q We need v 2 of f and r Jim Thomas - LBL 0 R. Fries et al. , nucl-th/0306027. D. Molnar and S. A. Voloshin, PRL 91, 092301(2003). 62

Multi-Strange Baryons v 2 q Multi-strange baryons flow ! Partonic Collectivity ! Jim Thomas - LBL 63

Summary of Performance Achieved to date • Features of the STAR TPC – – – – – • Good particle separation using d. E/dx 4 meters in diameter, 210 cm drift No field wires in the anode planes Pad readout, Low gain on anodes • Low drift field Very compact FEE electronics Analog Delay with SCA then onboard ADC Data delivered via optic fiber Uniform E and B fields ‘Ex. B’ and most Electrostatic distortions • correctable to 50 – 100 m level • Position resolution – 500 m in the real world with calibration errors – Space point resolution ~ 100 m for select laser events, 250 - 350 m for select tracks – Function of dip angle and crossing angle Jim Thomas - LBL – 6. 5% d. E/dx resolution @ 100 cm – -proton separation : > 1 Ge. V/c 2 -Track resolution – 2. 5 cm for HBT pairs – 1. 5 cm for laser tracks – limited by 3 pad response function and desire for fast algorithms Momentum resolution – 2% minimum at 0. 25 Tesla (half field) – for p. T > 1. 5 Ge. V in 0. 25 T field • dk/k = 0. 016 p. T + 0. 012 (central) • dk/k = 0. 011 p. T + 0. 013 (peripheral) • 2. 9% 3. 3% peripheral/central @ 1. 5 Ge. V STAR performance is excellent and meets essentially all design specifications! 64

TPC Gas Volume & Electrostatic Field Cage 420 CM • Gas: P 10 ( Ar-CH 4 90%-10% ) @ 1 atm • Voltage : - 28 k. V at the central membrane Jim Thomas - LBL 135 V/cm over 210 cm drift path Self supporting Inner Field Cage: Al on Kapton using Nomex honeycomb; 0. 5% rad length 65

Identified Particle Spectra at 200 Ge. V Bose-Einstein fits mt exponential fits + K- +, -, K+, K- spectra versus centrality PRL 92 (2004) 171801 and Phys. Lett. B 595 (2004) 143 Jim Thomas - LBL 66

Anti-Proton Spectra at 200 & 130 Ge. V / N Au + Au p + X p 200 Ge. V data gaussian fits p 130 Ge. V data p and p spectra versus centrality PRL 92 (2004) 171801 and PRL 87 (2001) 262302 Jim Thomas - LBL 67

Anti-Baryon/Baryon Ratios versus s. NN • In the early universe – p / p ratio = 0. 999999 In HI collisions at RHIC, more baryons are pair produced than are brought in by the initial state Jim Thomas - LBL • At RHIC, pair-production increases with s • Mid-rapidity region is not yet baryon-free! • Pair production is larger than baryon transport • 80% of protons from pair production • 20% from initial baryon number transported over 5 units of rapidity 68

Anti-Particle to Particle Ratios K+/K- ratios p/p ratios STAR results on the p/p ratio • p/p = 0. 11 ± 0. 01 @ 20 Ge. V • p/p = 0. 71 ± 0. 05 @ 130 Ge. V • p/p = 0. 80 ± 0. 05 @ 200 Ge. V Jim Thomas - LBL Excellent agreement between experiments at y = 0, s = 130 69

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Equation of State Parameters at RHIC In central Au+Au collisions: - partonic freeze-out: *Tp = 165 ± 10 Me. V p ≥ 0. 2 (c) weak centrality dependence - hadronic freeze-out: *Tfo = 100 ± 5 (Me. V) fo = 0. 6 ± 0. 05 (c) strong centrality dependence Systematic study are needed to understand the centrality dependence of the EOS parameters * Thermalization assumed Jim Thomas - LBL 71

Bjorken Estimate of Initial Energy Density Boost invariant hydrodynamics: Bjorken Estimate of Initial Energy Density ~ 6. 5 fm Cold nuclear matter: r 0 ~ 0. 16 Ge. V/fm 3 t ~ 0. 2 - 1 fm/c time to thermalize the system 30 xr 0 R 2 nucl-ex/0311017 PRL 87 (01) 52301 Jim Thomas - LBL 72

Slope Parameters RHIC results: Collective motion for multi-strange and charm hadrons! p ≥ 0. 2 c SPS results: No collective motion for multi-strange and charm hadrons! At RHIC, , and J/ show collective motion in 200 Ge. V Au + Au central collisions! PHENIX ( , K, p, J/ ): PRC 69, 034909(04), QM 05; Jim Thomas - LBL STAR ( , , ): QM 05. 73

QCD is a Rich Theory with Many Features We have a theory of the strong interaction Hadron “level” Diagram Low(er) energy nuclear physics uses OPEP or descriptions in terms of a pion gas. These worked because QCD is a theory with a mass gap. This gap is a manifestation of the approximate SU(2)R x SU(2)L chiral symmetry of QCD with pions as the Nambu-Goldstone bosons Jim Thomas - LBL { W. Zajc 74

Something Funny Happens at T > m c 2 An exponentially increasing density of hadronic states suggests – A “limiting temperature” TH – A phase transition(? ) in hadronic matter This was noticed before quarks were identified as the constituents of matter – ( Hagedorn, Nuovo Cimento Supp. , 3 (147) 1965 ) Density of States. vs. Energy Fit this form with TH = 163 Me. V Thermal equilibrium suggests Which requires T < TH Jim Thomas - LBL 75

Three Particle Correlations Conical Emission Δ 2 Δ 2 P/ = cs 2 Mach cone. Data: Unambiguous evidence for conical emission in central Au+Au collisions. Trigger at higher p. T, more statistics are needed. d+Au Δ 1 0 -12% Au+Au jet v 2=0 Δ 1 p. Ttrig=3 -4 Ge. V/c p. Tassoc=1 -2 Ge. V/c J. Ulery, HP 2006, C. Pruneau, QM 2006 =( 1 - 2)/2 Jim Thomas - LBL =( 1 - 2)/2 76

j correlations vs the reaction plane Out-of-plane 3 /4 p. Ttrigger=4 -6 Ge. V/c, 2<p. Tassociated<p. Ttrigger, | |<1 y x in-plane -3 /4 - /4 Back-to-back suppression out-of-plane stronger than in-plane Effect of path length on suppression is experimentally accessible Jim Thomas - LBL 77

Lattice QCD predictions Energy Density Stephan Boltzman limits for a free Quark Gluon gas TC ~ 170 15 Me. V e. C ~ 0. 7 Ge. V/fm 3 e 0 ~ 0. 16 Ge. V/fm 3 Karsch QM 2004 Temperature TC ~ 170 Me. V, was a very stable prediction over time & technologies … until recently when it went up to 190 Me. V Jim Thomas - LBL (F. Karsch, hep-lat/0106019 and M. Cheng et al. , hep-lat/0710. 0354) 78

A Macroscopic many body system: It Flows Spatial anisotropy Momentum anisotropy – For example, v 2 is the 2 nd harmonic Fourier coefficient of the distribution of particles with respect to the reaction plane Jim Thomas - LBL isotropic directed elliptic 79

Suppresion of inclusive hadron yield RAA Au+Au relative to p+p RCP Au+Au central/peripheral nucl-ex/0305015 • central Au+Au collisions: factor ~4 -5 suppression • p. T >5 Ge. V/c: suppression ~ independent of p. T Jim Thomas - LBL 80

Identifying jets on a statistical basis in Au-Au • You can see the jets in p-p data at RHIC • Identify jets on a statistical basis in Au-Au • Given a trigger particle with p. T > p. T (trigger), associate particles with p. T > p. T (associated) Jim Thomas - LBL STAR Data Au+Au @ 200 Ge. V/c 0 -5% most central 4 < p. T(trig) < 6 Ge. V/c 2 < p. T(assoc. ) < p. T(trig) 81

v 2 vs. Centrality • v 2 is large Hydro predictions – 6% in peripheral collisions – Smaller for central collisions • Hydro calculations are in reasonable agreement with the data – In contrast to lower collision energies where hydro overpredicts anisotropic flow PRL 86, (2001) 402 more central Anisotropic transverse flow is large at RHIC Jim Thomas - LBL • Anisotropic flow is developed by rescattering – Data suggests early time history – Quenched at later times 82