CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 1 / 26 Collective Expansion in Relativistic Heavy Ion Collisions -- Search for the partonic EOS at RHIC Nu Xu Lawrence Berkeley National Laboratory Many Thanks to Organizers Prof. Weiqing Chao Jinghua Fu, Yugang Ma, Enke Wang J. Castillo, X. Dong, H. Huang, H.G. Ritter, K. Schweda, P. Sorensen, A. Tai, Z. Xu

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 2 / 26Outline  Introduction  Bulk properties - ∂P QCD - hadron spectra - elliptic flow v 2  Summary and Outlook

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 3 / 26 P hase diagram of strongly interacting matter CERN-SPS, RHIC, LHC: high temperature, low baryon density AGS, GSI (SIS200): moderate temperature, high baryon density

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 4 / 26 High-energy Nuclear Collisions Initial Condition - initial scatterings - baryon transfer - E T production - parton dof System Evolves - parton interaction - parton/hadron expansion Bulk Freeze-out - hadron dof - interactions stop jets J/  D      K, K*  p  d, HBT elliptic flow v 2 radial flow  T Q2Q2 time partonic scatterings? early thermalization? T C T ch T fo

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 5 / 26 Identify and study the properties of matter with partonic degrees of freedom. Penetrating probes Bulk probes - direct photons, leptons - spectra, v 1, v 2 … - “jets” and heavy flavor - partonic collectivity - fluctuations jets - observed high p T hadrons (at RHIC, p T(min) > 3 GeV/c) collectivity - collective motion of observed hadrons, not necessarily reached thermalization among them. Physics Goals at RHIC Hydrodynamic Flow Collectivity Local Thermalization = 

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 6 / 26 Equation of State Equation of state: - EOS I : relativistic ideal gas: p =  /3 - EOS H: resonance gas: p ~  /6 - EOS Q: Maxwell construction: T crit = 165 MeV, B 1/4 = 0.23 GeV  lat =1.15 GeV/fm 3 P. Kolb et al., Phys. Rev. C62, (2000). With given degrees of freedom, the EOS - the system response to the changes of the thermal condition - is fixed by its p and T or . Energy density  GeV/fm 3

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 7 / 26 Collision Geometry x z Non-central Collisions Number of participants: number of incoming nucleons in the overlap region Number of binary collisions: number of inelastic nucleon-nucleon collisions Charged particle multiplicity  collision centrality Reaction plane: x-z plane Au + Au  s NN = 200 GeV beam

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 8 / 26 Charged Hadron Density 19.6 GeV 130 GeV 200 GeV Charged hadron pseudo-rapidity  1) High number of N ch indicates initial high density; 2) Mid-y, N ch  N part  nuclear collisions are not incoherent; 3) Saturation model works Initial high parton density at RHIC PRL 85, 3100 (00); 91, (03); 88, 22302(02); 91, (03) PHOBOS Collaboration

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 9 / 26 Suppression and Correlation In central Au+Au collisions: hadrons are suppressed and back-to-back ‘jets’ are disappeared. Different from p+p and d+Au collisions. Energy density at RHIC:  > 5 GeV/fm 3 ~ 30  0 Parton energy loss:Bjorken1982 (“Jet quenching”)Gyulassy & Wang 1992 …

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 10 / 26 Energy Loss and Equilibrium Leading hadrons Medium In Au +Au collision at RHIC: - Suppression at the intermediate p T region - energy loss - The energy loss leads to progressive equilibrium in Au+Au collisions STAR: nucl-ex/

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 11 / 26 Energy Loss (1) Measured spectra show evidence of suppression up to p T ~ 6 GeV/c; (2) Jet-like behavior observed in correlations: - hard scatterings in AA collisions - disappearance of back-to-back correlations ê“Partonic” Energy loss process leads to progressive equilibrium in the medium Next step: fix the partonic Equation of State, bulk properties

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 12 / 26 Pressure, Flow, …  d  = dU + pdV  – entropy; p – pressure; U – energy; V – volume  = k B T, thermal energy per dof In high-energy nuclear collisions, interaction among constituents and density distribution will lead to: pressure gradient  collective flow  number of degrees of freedom (dof)  Equation of State (EOS)  No thermalization is needed – pressure gradient only depends on the density gradient and interactions.  Space-time-momentum correlations!

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 13 / 26 Transverse Flow Observables As a function of particle mass: Directed flow (v 1 ) – early Elliptic flow (v 2 ) – early Radial flow – integrated over whole evolution Note on collectivity: 1)Effect of collectivity is accumulative – final effect is the sum of all processes. 2) Thermalization is not needed to develop collectivity - pressure gradient depends on density gradient and interactions.

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 14 / 26 mid-rapidity, p+p and Au+Au collisions at 200 GeV Hadron Spectra from RHIC mid-rapidity, p+p and Au+Au collisions at 200 GeV centrality 5% 10-20% 20-40% 40-60% 60-80% Results from BRAHMS, PHENIX, and STAR experiments (sss)(ssd) (usd) (ss)

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 15 / 26 Compare with Model Results Model results fit to , K, p spectra well, but over predicted for multi-strange hadrons - Do they freeze-out earlier? Phys. Rev. C (04); Phys. Rev. Lett. 92, (04); 92, (04); P. Kolb et al., Phys. Rev. C (03)

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 16 / 26 Thermal model fit Source is assumed to be: –Local thermal equilibrated –Boosted radially random boosted E.Schnedermann, J.Sollfrank, and U.Heinz, Phys. Rev. C48, 2462(1993)

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 17 / 26 Thermal fits: T fo vs. 1) , K, and p change smoothly from peripheral smoothly from peripheral to central collisions. to central collisions. 2) At the most central collisions, reaches collisions, reaches 0.6c. 0.6c. 3) Multi-strange particles ,  are found at higher T fo  are found at higher T fo (T~T ch ) and lower (T~T ch ) and lower  Sensitive to early partonic stage!  Sensitive to early partonic stage!  How about v 2 ?  How about v 2 ? STAR: NPA715, 458c(03); PRL 92, (04); 92, (04). 200GeV Au + Au collisions Chemical Freeze-out: inelastic interactions stop Kinetic Freeze-out: elastic interactions stop

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 18 / 26 y x pypy pxpx coordinate-space-anisotropy  momentum-space-anisotropy Anisotropy Parameter v 2 Initial/final conditions, EoS, degrees of freedom

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 19 / 26 v 2 at Low p T - At low p T, hydrodynamic model fits well for minimum bias events indicating early thermalization in Au+Au collisions at RHIC! - More theoretical work needed to understand details: v 2 centrality dependence; consistency between v 2 and spectra… P. Huovinen, private communications, 2004

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 20 / 26 v 2 at All p T v 2, the spectra of multi- strange hadrons, and the scaling of the number of constituent quarks  Partonic collectivity has been attained at RHIC!  Deconfinement, model dependently, has been attained at RHIC! Next question is the thermalization of light flavors at RHIC: - v 2 of charm hadrons - J/  distributions !! PHENIX: PRL91, (03) STAR: PRL92, (04) Models: Greco et al, PRC68, (03)

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 21 / 26 Nuclear Modification Factor 1) Baryon vs. meson effect! 2) Hadronization via coalescence 3) Parton thermalization (model) - (K 0,  ): PRL92, (04); NPA715, 466c(03); - Greco et al, PRC68,034904(03);PRL90, (03) - R. Fries et al, PRC68, (03); ), Hwa, nucl-th/

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 22 / 26 Bulk Freeze-out Systematics The additional increase in  T is likely due to partonic pressure at RHIC. 1) v 2 self-quenching, hydrodynamic model works at low p T 2) Multi-strange hadron freeze-out earlier, T fo ~ T ch 3) Multi-strang hadron show strong v 2

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 23 / 26 Partonic Collectivity at RHIC 1) Copiously produced hadrons freeze-out: T fo = 100 MeV,  T = 0.6 (c) >  T (SPS) 2)* Multi-strange hadrons freeze-out: T fo = MeV (~ T ch ),  T = 0.4 (c) 3)** Multi-strange v 2 : Multi-strange hadrons  and  flow! 4)*** Constituent Quark scaling: Seems to work for v 2 and R AA (R CP ) Partonic (u,d,s) collectivity at RHIC!

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 24 / 26 Summary & Outlook (1) Charged multiplicity - high initial density (2) Parton energy loss - QCD at work (3) Collectivity - pressure gradient ∂P QCD  Deconfinement and Partonic collectivity Open issues - partonic (u,d,s) thermalization - heavy flavor v 2 and spectra - di-lepton and thermal photon spectra

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 25 / 26 CERN-SPS, RHIC, LHC: high temperature, low baryon density AGS, GSI (SIS200): moderate temperature, high baryon density P hase diagram of strongly interacting matter GSI RHIC LHC

CCAST, Beijing, China, 2004 Nu Xu //Talk/2004/07USTC04/NXU_USTC_8July04// 26 / 26 Future readings: Quark Matter conference proceedings 2002 Nucl.Phys. A715, 1c(2003). - Quark Matter conference proceedings 2001 Nucl.Phys. A698, 1c(2002). - “Introduction to High Energy Heavy Ion Collisions’’ - By C.Y. Wong (Oak Ridge), Singapore, Singapore: World Scientific (1994) 516 p. - “Introduction to Relativistic Heavy Ion Collisions’’ - By L.P. Csernai (Bergen U.), Chichester, UK: Wiley (1994) 310 p. - Recent discussions on the QGP discovery