Helen Caines Yale University Gordon Research Conference – New London, NH– June 2006 Collisions at RHIC are very strange Outline Bulk matter Equilibrium Enhancement Beyond the bulk Intermediate p T

Helen Caines GRC – New London - June RHIC - a strange particle factory

Helen Caines GRC – New London - June Are we in thermal/chemical equilibrium? 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 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

Helen Caines GRC – New London - June Canonical vs Grand Canonical –Canonical (small system i.e. p-p): Quantum Numbers conserved exactly. Computations take into account energy to create companion to ensure conservation of strangeness. Relative yields given by ratios of phase space volumes P n /P n’ =  n (E)/  n’ (E) –Grand Canonical limit (large system i.e. central AA): Quantum Numbers conserved on average via chemical potential Just account for creation of particle itself. The rest of the system “picks up the slack”. Not new idea pointed out by Hagedorn in 1960’s (and much discussed since)

Helen Caines GRC – New London - June Comparison to data Canonical ensemble Au-Au √s NN = 200 GeV STAR Preliminary p-p √s = 200 GeV STAR Preliminary  B 45 ± 10 MeV  S 22 ± 7 MeV T168 ± 6 MeV s s 0.92 ± 0.06 T171 ± 9 MeV s s 0.53 ± 0.04

Helen Caines GRC – New London - June Centrality and energy dependence ● , K,p ● , K,p, ,  ● , K,p ● , K,p, ,  Small N ch dependence of  s Chem. equilibrium ! Close to net-baryon free T ch flat with centrality Energy dependence of  B T LQCD ~ MeV and 62 GeV STAR preliminary Au+Au at √s NN =200GeV

Helen Caines GRC – New London - June Centrality dependence STAR Preliminary We can describe p-p and Au-Au average ratios. Can we detail the centrality evolution? Look at the particle enhancements. E(i) = Yield AA /Npart Yield pp /2 Au-Au √s NN = 200 GeV Transition described by E(i) behaviour There is an enhancement E(  ) > E(  )

Helen Caines GRC – New London - June Strangeness phase space suppression -  s Canonical suppression increases with strangeness decreases with volume Canonical system – p-p Small system Lack of phase space available Strangeness suppressed Grand Canonical system – central A-A Large system Large phase space available Strangeness saturated

Helen Caines GRC – New London - June Model description of centrality dependence STAR Preliminary K. Redlich Correlation volume: V= (A NN ) ·V 0 A NN = N part /2 V 0 = 4/3  ·R 0 3 R 0 = 1.1 fm proton radius/ strong interactions T = 170 MeVT = 165 MeV Seems that T=170 MeV fits data best – but shape not correct Au-Au √s NN = 200 GeV

Helen Caines GRC – New London - June Varying T and R Calculation for most central Au-Au data Correlation volume: V 0  R 0 3 R 0 ~ proton radius strong interactions Rapid increase in E(i) as T decreases SPS data indicated R = 1.1 fm K. Redlich Au-Au √s NN = 200 GeV

Helen Caines GRC – New London - June N part dependence STAR Preliminary K. Redlich Correlation volume: V= (A NN )  ·V 0 A NN = N part /2 V 0 = 4/3  ·R 0 3 R 0 = 1.2 fm proton radius/ strong interactions T = 165 MeV  = 1 T = 165 MeV  = 2/3 T = 165 MeV  = 1/3 N part is NOT directly correlated to the strangeness volume. Au-Au √s NN = 200 GeV

Helen Caines GRC – New London - June PHOBOS: Phys. Rev. C70, (R) (2004) More on flavour dependence of E(i) PHOBOS: measured E(ch) for 200 and 19.6 GeV Enhancement for all particles? Yes – not predicted by model STAR Preliminary s quark content determines E Au-Au √s NN = 200 GeV

Helen Caines GRC – New London - June Moving from the bulk /s inel p+p p+p cross section Compare Au+Au with p+p Collisions  R AA Nuclear Modification Factor: R < 1 at small momenta R = 1 baseline expectation for hard processes R > 1 “Cronin” enhancements (as in pA) R < 1: Suppression A+A yield

Helen Caines GRC – New London - June R cp vs R AA Effect increases as strange content of baryon increases. Canonical suppression in p+p R cp  R AA √s NN = 200 GeV STAR Preliminary √s NN = 200 GeV STAR Preliminary

Helen Caines GRC – New London - June Parton recombination at medium p T Parton p T distribution is ~exponential+power-law 7 GeV particle via : Fragmentation from high p T Meson - 2 quarks at ~3.5 GeV Baryon - 3 quarks at ~2.5 GeV Recombination - more baryons than mesons at medium p T

Helen Caines GRC – New London - June R CP - an energy scan √s NN =200 GeV √s NN =62 GeV 0-5% 40-60% 0-5% 40-60% NA57, PLB in print, nucl-ex/ √s NN =17.3 GeV First time differences between  and   B absorption? Baryon meson splitting at all energies

Helen Caines GRC – New London - June STAR Preliminary NA57: G. Bruno, A. Dainese: nucl-ex/ Baryon/meson splitting at SPS and RHIC is the same 62 GeV Au+Au data also follows the same trend Recombination present in all systems? The R cp double ratio

Helen Caines GRC – New London - June Conclusions Thermal models give good description of the data as function of energy and centrality. The enhancement of strangeness as a function of centrality CAN be described– scales with N part 1/3 NOT N part Non-strange particles are enhanced – NOT predicted by phase space models. The phase space effects of p-p extend into high p T regime. Baryon/meson splitting energy independent. ReCo at SPS.

Helen Caines GRC – New London - June BACKUP

Helen Caines GRC – New London - June Predictions from statistical model Behavior as expected

Helen Caines GRC – New London - June m T scaling STAR Preliminary p+p 200 GeV No complete m T scaling Au-Au Radial flow prevents scaling at low m T Seems to scale at higher m T p-p Appears to be scaling at low m T Baryon/meson splitting at higher m T – Gluon jets?

Helen Caines GRC – New London - June Gluon vs quark jets in p-p Quark jets events display mass splitting Gluon jets events display baryon/meson splitting No absolute m T scaling – “data” scaled to match at m T ~1 GeV/c Way to explore quark vs gluon dominance

Helen Caines GRC – New London - June Recombination and v 2 Works for p, , K 0 s, ,  v 2 s ~ v 2 u,d ~ 7% The complicated observed flow pattern in v 2 (p T ) for hadrons is predicted to be simple at the quark level p T → p T /n v 2 → v 2 / n, n = (2, 3) for (meson, baryon)

Helen Caines GRC – New London - June ReCo model and Correlations R. Hwa, Z. Tan: nucl- th/ The ratio of near side yields in central to peripheral collisions is around 3 at 1 GeV/c and decreases with increasing p T assoc This is in good qualitative agreement with ReCo model predictions though there are some differences to the model (trigger p T, centrality) Long range dη correlations are visible in the STAR data and not taken into account in the plot. This is p T dependent and may reduce any slope. 0-10%/40-80% 3 < p T trigger < 6

Helen Caines GRC – New London - June Recent ReCo Model Predictions Premise: Observables: 1)The ratio of Ω/Φ yields should rise linearly with p T 2) Any Ω or Φ di-hadron correlations are swamped by the background and not observed The production of Φ and Ω particles is almost exclusively from thermal s quarks even out to 8 GeV/c Being actively studied, but no results are available as yet

Helen Caines GRC – New London - June Correlations: near side yields STAR Preliminary No trigger particle dependence in the near side yield/trigger in either d+Au or Au+Au d+AuAu+Au STAR Preliminary No definite trigger particle dependence vs centrality but meson triggers appear to be systematically below baryon triggers Reason for increase may be due to longe range correlations in η

Helen Caines GRC – New London - June Strange Correlations in Au+Au ΔΦ correlations per trigger particle 3 < p T trigger < 3.5 GeV/c 1 < p T assoc < 2 GeV/c |η| < 1 Correlations corrected for TPC acceptance and efficiency of associated particles Near side v 2 is then subtracted to give final correlations

Helen Caines GRC – New London - June R AA - A mocked up string picture does well Topor Pop et al. hep-ph/ HIJING/BBar + K T ~ 1 GeV Strong Color Field (SCF) qualitatively describes R AA. SCF - long range coherent fields SCF behavior mimicked by doubling the effective string tension SCF only produced in nucleus- nucleus collisions R AA ≠ R CP Are strong color fields the answer?

Helen Caines GRC – New London - June R AA for central and peripheral data Peripheral and central data both show an enhancement Peripheral data is more enhanced – Cronin effect? Au-Au √s NN = 200 GeV STAR Preliminary Au-Au √s NN = 200 GeV STAR Preliminary

Helen Caines GRC – New London - June Baryons/Mesons The Λ/K 0 S ratio exhibits a peak in the intermediate p T region. The peak high varies with centrality. At higher p T the ratios for all centralities converge again. nucl-ex/ Magnitude and shape of ratio cannot be explained by flow alone.

Helen Caines GRC – New London - June Particle identification Approx. 10% of a central event a) dE/dx b) RICH c) Topology  Kpd e

Helen Caines GRC – New London - June gluon vs quark jets Has been studied in e + e - collisions at higher energies Quark jets tend to fragment harder than gluon jets We can study this with identified strange hadrons in p+p collisions in STAR

Helen Caines GRC – New London - June

Helen Caines GRC – New London - June p T reach constrained by p+p data Some hint of splitting in the baryons - R AA ≠ R CP HIJING BB predicts such a splitting using Strong Colour Fields... See also the Corona effect in EPOS Identified Particle R AA (TOF) PRC 72:

Helen Caines GRC – New London - June Strange particles at intermediate p T The statistics from Run 4 allow us to go much higher in p T than previously and to study the intermediate p T region in detail Λ K0SK0S

Helen Caines GRC – New London - June Strange Di-hadron Correlations Observed suppression of single particle spectra compared to p+p and d+Au Disappearance of back-to-back jets p, π, Λ, K, Λ Charged Hadrons Baryon/meson puzzle at intermediate p T Particle production mechanisms quark vs gluon jets Identified Hadrons Coalescence/Recombination or Medium modified jets

Helen Caines GRC – New London - June Multiplicity scaling with log(√s) PHOBOS White Paper: Nucl. Phys. A 757, 28, nucl-ex/ If I can describe dN ch /d  as function of  √s Can we describe other observables in terms of dN ch /d η ? dN ch /d η - strongly correlated to the entropy of the system!

Helen Caines GRC – New London - June HBT and dN ch /d  HBT radii ~linear as a function N part 1/3 Even better in (dN ch /d  ) 1/3 power 1/3 gives approx. linear scale nucl-ex/ M.Lisa et al. Scaling works across a large energy range

Helen Caines GRC – New London - June First make a consistency check Require the models to, in principle, be the same. 1.Only allow the least common multiple of parameters: T,  q,  s,  s 2.Use Grand Canonical Ensemble. 3.Fix weak feed-down estimates to be the same (i.e. at 100% or 0%).

Helen Caines GRC – New London - June The results RatioSTAR Preliminary          p/p      p                  1.01± ± ± ± ± ± ±0.005 (7.8±1) (6.3±0.8) (9.5±1) ±0.08 after feed-down increase  s decrease T 1  error Not identical and feed-down really matters Similar T and  s Significantly different errors. Au-Au √s NN = 200 GeV

Helen Caines GRC – New London - June Centrality dependence We can describe p-p and Au-Au average ratios. Can we detail the centrality evolution? Look at the particle enhancements. E(i) = Yield AA /Npart Yield pp /2 STAR Preliminary Solid – STAR Au-Au √s NN = 200 GeV Hollow - NA57 Pb-Pb √s NN = 17.3 GeV

Helen Caines GRC – New London - June Ω : central collisions Motivation Chemistry Dynamics Summary T dec = 164 MeV T dec = 100 MeV Ω - spectra, central Data best reproduced with –T dec ≈ 100 MeV –Same as for π -, K -, p –Agreement holds for entire spectra! Same results at both energies! P.F. Kolb and U. Heinz, nucl-th/ T dec ≈ 164 MeV ( decoupling at hadronization ): not enough radial flow p T = 2 GeV/c Ideal Hydrodynamics

Helen Caines GRC – New London - June Blast wave fits to data 200 GeV Strong centrality dependence on freeze out parameters for light hadrons Multi-strange hadrons freeze out earlier, with a lower Indicative of smaller cross-section for interactions of multiply strange hadrons with lighter species. Is this a signature of partonic collectivity?

Helen Caines GRC – New London - June What interactions can lead to equilibration in < 1 fm/c? Need to be REALLY strong Microscopic picture R. Baier, A.H. Mueller, D. Schiff, D. Son, Phys. Lett. B539, 46 (2002). MPC 1.6.0, D. Molnar, M. Gyulassy, Nucl. Phys. A 697 (2002). Perturbative calculations of gluon scattering lead to long equilibration times (> 2.6 fm/c) and small v 2. v2v2 p T (GeV/c) 2-2 processes with pQCD  = 3 mb Clearly this is not the weakly coupled perturbative QGP we started looking for. s(trong)QGP

Helen Caines GRC – New London - June RHIC BRAHMS PHOBOS PHENIX STAR AGS TANDEMS 1 km v =  c  s NN =200 GeV Relativistic Heavy-Ion Collider (RHIC)

Helen Caines GRC – New London - June Runs so far Run Year Species √s [GeV ]  Ldt Au+Au  b /2 Au+Au  b -1 p+p pb /3 d+Au nb -1 p+p pb /4 Au+Au  b -1 Au+Au 62 9  b /5 Cu+Cu nb -1 Cu+Cu nb -1 Cu+Cu  b -1 p+p pb -1

Helen Caines GRC – New London - June A theoretical view of the collision T c – Critical temperature for transition to QGP T ch – Chemical freeze-out ( T ch  T c ) : inelastic scattering stops T fo – Kinetic freeze-out ( T fo  T ch ): elastic scattering stops ♦ Hadronic ratios. ♦Resonance production. ♦ p  spectra. ♦ Partonic collectivity. ♦ High p  measurements

Helen Caines GRC – New London - June Comparison between p-p and Au-Au T171 ± 9 MeV ss 0.53 ± 0.04 r3.49 ± 0.97 fm Canonical ensemble T168 ± 6 MeV ss 0.92 ± 0.06 r15 ± 10 fm Au-Au √s NN = 200 GeV STAR Preliminary p-p √s = 200 GeV STAR Preliminary

Helen Caines GRC – New London - June Resonances and survival probability Chemical freeze- out Kinetic freeze- out measured lost  K K  K*K* K*K* K   K*K* K measured ♦ Initial yield established at chemical freeze-out ♦ Decays in fireball mean daughter tracks can rescatter destroying part of signal ♦ Rescattering also causes regeneration which partially compensates ♦ Two effects compete – Dominance depends on decay products and lifetime time Ratio to “stable” particle reveals information on behaviour and timescale between chemical and kinetic freeze-out K*K*  K

Helen Caines GRC – New London - June P. Braun-Munzinger et.al.,PLB 518(2001) 41, priv. communication Marcus Bleicher and Jörg Aichelin Phys. Lett. B530 (2002) 81. M. Bleicher and Horst Stöcker J. Phys.G30 (2004) 111. Chemical to kinetic freeze-out Finite time span from T ch to T fo If only rescattering K(892) most suppressed Life-time [fm/c] :     Need rescattering and regeneration to “fix” the picture.

Helen Caines GRC – New London - June Strong collective radial expansion T pure thermal source explosive source T,  mTmT 1/m T dN/dm T light heavy m T = (p T 2 + m 2 ) ½ Au+Au central, √s = 200 GeV Good agreement with hydrodynamic prediction for soft EOS (QGP+HG) T dec = 165 MeV T dec = 100 MeV Different spectral shapes for particles of differing mass  strong collective radial flow T fo ~ 100 MeV  T  ~ 0.55 c Needs “initial kick” mTmT 1/m T dN/dm T light heavy Model (plot) from P.F. Kolb and R. Rapp, Phys. Rev. C 67 (2003)

Helen Caines GRC – New London - June Anisotropic/Elliptic flow Almond shape overlap region in coordinate space Anisotropy in momentum space Interactions/ Rescattering dN/d  ~ 1+2 v 2 (p T )cos(2  ) + ….  =atan(p y /p x ) v 2 =  cos2  v 2 : 2 nd harmonic Fourier coefficient in dN/d  with respect to the reaction plane Elliptic flow observable sensitive to early evolution of system Mechanism is self-quenching Large v 2 is an indication of early thermalization Time –M. Gehm, S. Granade, S. Hemmer, K, O’Hara, J. Thomas - Science (2002)

Helen Caines GRC – New London - June Strong elliptic flow observed Compatible with early equilibration 200 GeV Au+Au STAR preliminary v 2 (p T ) p T (Gev/c) v 2 (K) > v 2 (  ) > v 2 (  ) Hydrodynamical models with soft Equation-of- State describe data well for p T (< 2.5 GeV/c) Although poor statistics even  flows - low hadronic cross-section. Evidence v 2 built up in partonic phase

Helen Caines GRC – New London - June Hydro: small mean free path, lots of interactions NOT plasma-like The perfect fluid First time: hydrodynamics quantitatively describes heavy ion reactions at low p T. Prefers a QGP EOS Hydro without any viscosity. An ideal (perfect) fluid Thermalization time t=0.6 fm/c and  =20 GeV/fm 3

Helen Caines GRC – New London - June Moving away from the bulk...

Helen Caines GRC – New London - June Strangeness in p+p Large statistics data-set allows for the detailed analysis of data NLO calculations show good agreement with non-strange hadrons Agreement with strange hadrons is not as apparent, better for AKK than for Vogelsang Using Pythia (LO) requires changing the K factor to match the data EPOS has very good agreement with all particles, even Xi