1. Workshop on Critical Examination of RHIC Paradigms April 14–17, 2010 The Department of Physics The University of Texas at Austin RHIC paradigms: Early Thermalization and Collectivity - are they achieved in RHIC’s new state of matter ? Rene Bellwied (Wayne State University)

2. Outline Why is it important ? 2

3. What is based on the assumption of thermalization? The phase diagram (transition, critical point, Phase properties) The models (lattice QCD, Hydrodynamics, Statistical hadronization)

4. Basic thermodynamics Energy: dE = T dS – p dV +  dN Free energy: dF = -S dT – pdV +  dN thermal (or kinetic) equilibration: dT = 0 chemical equilibration: dN = 0 chemical equilibration at a fixed T ch and a fixed  thermal equilibration at a fixed T th (lower than T ch ) chem. freeze-out occurs when inelastic collisions cease thermal freeze-out occurs when elastic collisions cease Temperature progression:T c > T ch > T th Measured yields and spectra will only tell us that the hadrons are equilibrated. Basic thermal models are not dynamic, they tell you nothing about the evolution of the system until freeze-out.

5. Statistical evolution of relativistic heavy ion collisions partons hadrons Model: lQCD SHM Blastwave Effect: hadronization chemical f.o. kinetic f.o. Freeze-out surface:T crit T ch T kin (  ) T kin ( ,k,p  ) Temperature (MeV):190 165 160 80 Expansion velocity:  =0.45  =0.6 time: ~4 fm/c ~4 fm/c (nucl-ex/0604019) References: Lattice QCD: hep-lat/0608013 arXiv:0903.4155 Statistical Hadronization: hep-ph/0511094 nucl-th/0511071 Blastwave: nucl-ex/0307024 arXiv:0808.2041 Hydro condition ? Fast equilibration measurements: strangeness enhancement & v2

6. Famous example: Assessing the Initial Energy Density Central Au+Au (Pb+Pb) Collisions: 17 GeV:  BJ  3.2 GeV/fm 3  GeV  BJ  4.6 GeV/fm 3 200 GeV:  BJ  5.0 GeV/fm 3 Lattice  c  Bj ~ 4.6 GeV/fm 3  Bj ~ 23.0 GeV/fm 3 Bjorken-Formula for Energy Density: PRD 27, 140 (1983) – watch out for typo (factor 2)

7. Can it thermalize that fast ? Not through collisions. That takes at least 5 fm/c (big problem) Alternate ideas: ◦ Plasma instabilities (start off with fields instead of particles) ◦ Hawking radiation (start off with extremely high gluon densities) ◦ System born into thermal state ? 7

8. What is the alternative to thermalization ? A system that is not equilibrated, a system that is governed by a non-thermal fragmentation process (jets in pp, overlapping mini-jets in AA) something that generates correlated emission other than decays or HBT Jets that populate the bulk part of the spectrum

9. hadrons leading particle Jet: A localized collection of hadrons which come from a fragmenting parton a b c d Parton Distribution Functions Hard-scattering cross-section Fragmentation Function High p T (> 2.0 GeV/c) hadron production in pp collisions: ~ Hadronization in QCD (the factorization theorem) “Collinear factorization”

10. 10 Intrinsic k T, Cronin EffectParton Distribution FunctionsShadowing, EMC Effect Fragmentation Function leading particle suppressed Partonic Energy Loss c d hadrons a b Hard-scattering cross-section High p T Particle Production in A+A

11. General Comment: fragmentation does not do well with identified particle production or kinematics. It gets the charged particle distributions sort of correct, but any attempt to determine kinematic observables (pt or v2) or even yield for specific particle species correctly have failed until now. This is important because much of the evidence for equilibration (chemical or thermal) relies on the reproduction of exact patterns of identified particle properties. Thermal and chemical patterns are very sensitive to mass and flavor.

12. The basic RHIC paradigms Paradigm 1: Chemical equilibration at the partonic level ◦ Evidence: yields at chemical freeze-out (hadronic), strangeness/charm enhancement Paradigm 2: Kinetic equilibration (thermalization) at the partonic level ◦ Evidence: spectra at thermal freeze-out, validity of hydrodynamics, radial expansion Paradigm 3: Strong partonic collectivity in agreement with near ideal hydrodynamics ◦ Evidence: spectra, v2, HBT Paradigm 4: Hadronization is not dominated by fragmentation even at high pT ◦ Evidence: B/M ratios, quark scaling for v2 and energy loss Paradigm 5: Energy loss is purely partonic ◦ Evidence: lack of color or mass dependence in R AA Paradigm 6: Particle correlations map initial conditions in a thermally expanding partonic system ◦ Evidence: pt and centrality evolution of properties of same-side structure. ‘Anti’ Paradigm: pp is a small AA system ◦ Evidence: momentum conservation corrected spectra and HBT

13. Paradigm 1 Chemical equilibration at the partonic level ◦ Evidence: yields at chemical freeze-out (hadronic), strangeness/charm enhancement

14. Statistical Hadronization Models : Misconceptions Model says nothing about how system reaches chemical equilibrium Model says nothing about when system reaches chemical equilibrium Model makes no predictions of dynamical quantities Some models use a strangeness suppression factor,others not Model does not make assumptions about a partonic phase; However the model findings can complement other studies of the phase diagram (e.g. Lattice-QCD)

15. Particle production: Statistical models do well

16. Ratios that constrain model parameters

17. Does it work in elementary collisions ?

18. Equilibration in Elementary Collisions ? Is a process which leads to multiparticle production equilibrated ?  Any mechanism for producing hadrons which evenly populates the free particle phase space will mimic a microcanonical ensemble.  Relative probability to find a given number of particles is given by the ratio of the phase-space volumes P n /P n’ =  n (E)/  n’ (E)  given by statistics only. Difference between MCE and CE vanishes as the size of the system N increases. This type of “thermal” behavior requires no rescattering and no interactions. The collisions simply serve as a mechanism to populate phase space without ever reaching thermal or chemical equilibrium In RHI we are looking for large collective effects.

19. Statistics  Thermodynamics Ensemble of events constitutes a statistical ensemble. Canonical description, i.e. local quantum number conservation (e.g.strangeness) over small volume. T and µ are simply Lagrange multipliers (“Phase Space Dominance”) A+A We can talk about p,T and µ. Grand-canonical description, e.g. percolation of strangeness over large volumes, most likely in deconfined phase if chemical freeze-out is close to phase boundary. PBM et al., nucl-th/0112051) p+p

20. RHIC flavor dependence of yield scaling RHIC flavor dependence of yield scaling participant scaling for light quark hadrons (soft production) strangeness and charm described by SHM up, down strange charm PYTHIA (e + e - ): ◦ D / D s = 7.3 Statistical Hadronization Model (AuAu): ◦ D / D s = 2.8 Measured (e + e - ): ◦ D / D s = 4.8 +- 0.8 Measured (AuAu, STAR prel.): ◦ D / D s = 2.6 +- 0.9

21. The latest numbers from fitting particle yields (Cleymans et al. SQM 2009)

22. Paradigm 2 Kinetic equilibration (thermalization) at the partonic level ◦ Evidence: spectra at thermal freeze-out, validity of hydrodynamics, radial expansion

23. Kinetic freeze-out distributions (particle spectra) N.B. Constituent quark recombination models yield exponential spectra with partons following a pQCD power-law distribution. (Biro et al. hep-ph/0309052)  T is not related to actual “temperature” but reflects pQCD parameter p 0 and n. Alternate: thermal constituent quarks (Chen et al., arXiv:0801.2265)

24. “Thermal” Spectra Invariant spectrum of particles radiated by a thermal source: where:m T = (m 2 +p T 2 ) ½ is the transverse mass  = b  b + s  s is the grand canonical chem. potential T = temperature of source Neglect quantum statistics (small effect) and integrating over rapidity gives: R. Hagedorn, Supplemento al NuovoCimento Vol. III, No.2 (1965) At mid-rapidityE = m T coshy = m T and hence: “Boltzmann”

25. “Thermal” spectra and radial expansion (flow) Different spectral shapes for particles of differing mass  strong collective radial flow Spectral shape is determined by more than a simple T Common flow and temperature: at a minimum T,  T 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

26. Identified Particle Spectra for Au-Au @ 200 GeV BRAHMS: 10% central PHOBOS: 10% PHENIX: 5% STAR: 5% The spectral shape gives us: ◦ Kinetic freeze-out temperatures ◦ Transverse flow The stronger the flow the less appropriate are simple exponential fits: ◦ Hydrodynamic models (e.g. Heinz et al., Shuryak et al.) ◦ give evolution ◦ Hydro-like parameters (Blastwave fits e.g E.Schnedermann et al., PRC48 (1993) 2462 ◦ give freeze-out surface Explains: spectra, flow & HBT

27. Blastwave toy model (Lisa et al.) One gets a common freeze-out T and a common expansion velocity (firmly rooted in the hadronic phase)

28. Hydrodynamics in High-Density Scenarios Ideal hydro: assumes local thermal equilibrium (zero mean-free-path limit) and solves equations of motion for fluid elements (not particles) Ideal hydro: 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) 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 EOS relates quantities like pressure, temperature, chemical potential, volume = direct access to underlying physics Kolb, Sollfrank & Heinz, hep-ph/0006129

29. Many alternative fit functions Alternative question: is it Tsallis or Boltzmann statistics that describes the bulk of the system ? Non-extensive ansatz describes particle spectra from lowest to highest pt (based on correlation length = convolution of mini-jets). No thermalization. Two-component model (soft = Boltzmann, hard = power-law) describes the spectra. Bulk is thermal, fragmentation is not. Very interesting question that requires more data comparison (other than spectra ) Takahashi et al., SQM 2009

30. Paradigm 3 Paradigm 3: Strong collectivity in agreement with near ideal hydrodynamics ◦ Evidence: spectra, v2, HBT

31. Elliptic flow described by fluid dynamics In hydro: Anisotropic flow needs to build up early (80% partonic, 20% hadronic)

32. Hydro is not ideal….. v2/  as a function of centrality does not reach the ideal limit If the system reaches local thermal equilibrium, according to ideal hydro dynamic calculation, v 4 /v 2 2 approaches 0.5 at high p T region STAR preliminary 32 N. Borghini and J.-Y. Ollitraut, Phys. Lett. B 642 227 (2006) STAR preliminary Hydro limit

33.  /s ~ 0  /s = 1/4   /s = 2 x 1/4   /s = 3 x 1/4  …but viscous hydro is doing well

34. Collectivity at early times Strange quark particle have significantly lower hadronic interaction cross section (early development of flow) Heavier particles have lower flow (hydro pattern)

35. Paradigm 4 Hadronization is not dominated by fragmentation even at high pT ◦ Evidence: quark scaling for v2 and energy loss

36. 1977:two distinctly different hadronization processes neither corresponds to parton/hadron duality… More likely in vacuum ? More likely in medium ?

37. Evidence at RHIC: B/M ratio in AA can be attributed to recombination Recombination in medium Fragmentation in vacuum STAR @ SQM 2005 cartoon baryon meson

38. 38 #3:The medium consists of constituent quarks ? (my group’s main contribution) baryons mesons

39. 39 Nuclear Modification Factor R cp 0-5% 40-60% 0-5% 60-80% √sNN=200 GeV Baryon and meson suppression sets in at the same quark pT. √sNN=200 GeV Strange RCP signals range of recombination model relevance Recombination scaling can be applied to RCP as well as v2

40. Paradigm 5 Energy loss is purely partonic Partons always hadronize (fragment) outside the medium ◦ Evidence: lack of color or mass dependence in R AA

41. 41 Formation Time of Hadrons in RHIC / LHC QGP (C. Markert, RB, I. Vitev, 0807.1509) RHIC LHC

42. Nuclear suppression factors of identified particles light quarks (u,d,s): heavy quarks (c,b): non-photonic electrons = B- or D-mesons STAR @ QM 2009 High pt quenching differences between particles could be due to early formation and subsequent color transparency (Brodsky et al., Vitev et al., Markert & RB)

43. Paradigm 6 Particle correlations map initial conditions of a thermally expanding partonic system ◦ Evidence: pt and centrality evolution of properties of same-side structure.

44. Correlations: don’t they tell me when something is not thermalized ? We know of specific processes that cause correlations even in thermal systems (jet fragmentation, resonance decay, HBT, annihilation, v2). But the development of strong correlations across large sections of low-momentum ‘bulk’ particles should hint at non- equilibrium.

45. Number correlations in coordinate space as a f(centrality) Lots of structure in RHIC emissions (STAR preliminary) pp AA A modification of the fragmentation process in pQCD ?

46. Initial conditions plus radial expansion NexSPheRio (color ropes due to nuclear density profile) Hama, Grassi, Kodama, Takahashi et. al. Dumitru, Gelis, McLerran, Gavin, Moschelli et al. CGC &Glasma (flux tubes due to initial gluon profile) Correlations are unrelated to the propagation of a jet through the medium. They are due to a collective push on fluctuating initial conditions

47. STAR preliminary Initial condition model applied to STAR CuCu data (  -width and amplitude of same-side structure) centrality dependence pt dependence STAR preliminary

48. ‘Anti’ Paradigm pp is a small AA system ◦ Evidence: momentum conservation corrected spectra and HBT

49. AA spectra corrected for energy and momentum conservation

50. pp spectra and HBT treated like AA spectra

51. Combined pp and AA fit

52. Summary and Conclusions We have discovered a deconfined phase of nuclear matter (quark scaling, quenching) Although the evidence for the basic RHIC paradigms of early thermalization and strong collectivity is circumstantial, it is based on a variety of many particle identified measurements (yield, spectra, quenching, flow) and is thus the simplest consistent model applicable. The resulting properties from very strong coupling to large correlation structures are unexpected and not readily described by pQCD. This might be an intermediate phase of high collectivity just prior to hadron formation which will subside at even higher initial temperatures (pQCD limit potentially achieved at LHC). Its properties are very relevant to hadron formation in the medium and to structure formation out of the medium. 52