1. Che-Ming Ko Teaxs A&M University  Introduction: concepts and definitions - Quark-gluon plasma (QGP) - Heavy ion collisions (HIC)  Experiments and theory - Signatures of QGP - Experimental observations Searching for the Quark-Gluon Plasma in Relativistic Heavy Ion Collisions Largely based on slides by Vincenzo Greco

2. Big Bang Hadronization ( T~ 0.2 GeV, t~ 10 -2 s ) Quark and gluons Atomic nuclei ( T~100 KeV, t ~200s ) “chemical freeze-out” opaque but matter opaque to e.m. radiation e. m. decouple ( T~ 1 eV, t ~ 3. 10 5 ys ) “thermal freeze-out “ We’ll never see what happened at t < 3. 10 5 ys (hidden behind the curtain of the cosmic microwave background) HIC can do it! Bang

3. Freeze-out Hadron Gas Phase Transition Plasma-phase Pre-Equilibrium Little Bang finite  t “Elastic”

4. Bag Model Heuristic QGP phase transition Pressure exceeds the Bag pressure -> quark liberation Extension to finite     B 1/4 ~ 210 MeV  T c ~ 145 MeV Free massless gas

5. Quantum ChromoDynamics Similar to QED, but much richer structure Similar to QED, but much richer structure:  SU(3) gauge symmetry in color space  Approximate Chiral Symmetry in the light sector which is broken in the vacuum.  U A (1)  iral  Scale Invariance broken by quantum effects

6. Phase Transition in lattice QCD Enhancement of the degrees of freedom towards the QGP Noninteracting massless partons Gap in the energy density (I st order or cross over ?)

7. QCD phase diagram From high   regime to high T regime We do not observe hadronic systems with T> 170 MeV (Hagedon prediction) AGS SPS RHIC

8. Definitions and concepts in HIC Kinematics Observables Language of experimentalist

9. The RHIC Experiments STAR Au+Au

10. Soft and Hard Small momentum transfer Bulk particle production –How ? How many ? How are they distributed? Only phenomenological descriptions available ( pQCD doesn’t work ) SOFT ( non-pQCD) string fragmentation in e + e    pp … or (p T <2 GeV) string melting in AA (AMPT, HIJING, NEXUS… ) QGP HARD minijets from first NN collisions phenomenology Independent Fragmentation : pQCD + phenomenology 99% of particles

11. Collision Geometry - “Centrality” 0 N_ part 394 15 fm b 0 fm Spectators Participants For a given b, Glauber model predicts N part and N binary S. Modiuswescki

12. Kinematical observables Additive like Galilean velocity Angle with respect to beam axis PHOBOS Transverse mass Rapidity -pseudorapidity

13. Energy Density Energy density a la Bjorken: dE T /dy ~ 720 GeV Estimate  for RHIC: Time estimate from hydro:  T initial ~ 300-350 MeV Particle streaming from origin

14. Some definitions I: radial collectiv flows Slope of transverse momentum spectrum is due to folding temperature with radial collective expansion from pressure. Slopes for hadrons with different masses allow to separate thermal motion from collective flow Absence T f ~ (120 ± 10) MeV ~ (0.5 ± 0.05)

15. Collective flow II: Elliptic Flow Anisotropic Flow x y z pxpx pypy v2 is the 2 nd Fourier coeff. of particle transverse moment distribution Fourier decomposition of particle momentum distribution in x-y plane Measure of the pressure gradient Good probe of early pressure

16. Anisotropic flow v n Sine terms vanish because of the symmetry  in A+A collisions Initial spatial anisotropy Anisotropic flows Pressure gradient anisotropy  x Anisotropic flow

17. Yield MassQuantum Numbers TemperatureChemical Potential Statistical Model Hydro adds radial flow & freeze-out hypersurface for describing the differential spectrum Is there a dynamical evolution that leads to such values of temp. & abundances? Yes, but what is Hydro? Maximum entropy principle

18. HYDRODYNAMICS Local conservation Laws 5 partial diff. eq. for 6 fields (p,e,n,u) + Equation of State p(e,n B )  No details about collision dynamics (mean free path  0)

19. Non-relativistically Transport Model Follows time evolution of particle distribution from initial non-equilibrium partonic phase drift mean field collision To be treated: - Multiparticle collision (elastic and inelastic) - Quantum transport theory (off-shell effect, … ) - Mean field or condensate dynamics Relativistically at High density gg  gggg  gg

20. Spectra still appear thermal Elliptic Flow Hydro Transport rapidity

21. Chemical equilibrium with a limiting T c ~170MeV Thermal equilibrium with collective behavior - T th ~120 MeV and ~ 0.5 Early thermalization (  < 1 fm/c,  ~ 10 GeV/fm 3 ) - very large v 2 We have not just crashed 400 balls to get fireworks, but we have created a transient state of plasma A deeper understanding of the system is certainly needed!

22. Signatures of quark-gluon plasma  Dilepton enhancement (Shuryak, 1978)  Strangeness enhancement (Meuller & Rafelski, 1982)  J/ψ suppression (Matsui & Satz, 1986)  Pion interferometry (Pratt; Bertsch, 1986)  Elliptic flow (Ollitrault, 1992)  Jet quenching (Gyulassy & Wang, 1992)  Net baryon and charge fluctuations (Jeon & Koch; Asakawa, Heinz & Muller, 2000)  Quark number scaling of hadron elliptic flows (Voloshin 2002)  ……………

23. - Dilepton spectrum at RHIC MinBias Au-Au thermal Low mass: thermal dominant (calculated by Rapp in kinetic model) Inter. mass: charm decay No signals for thermal dileptons yet

24. Strangeness Enhancement Basic Idea:  Production threshold is lowered in QGP Hadronic channels:  Equilibration timescale? How much time do we have? In the QGP:

25. Decreasing threshold in a Resonance Gas To be weighted with the abundances npQCD calculation with quasi particle picture and hard-thermal loop still gives t~5-10 fm/c QGP Scenario Hadronic Scenario

26. How one calculates the Equilibration Time Reaction dominated by gg 6 fm/c  (pQCD) Equilibration time in QGP t eq ~10 fm/c > t QGP  Hadronic matter t eq ~ 30 fm/c Similarly in hadronic case but more channels

27. Experimental results e + e - collisions Schwinger mechanism Strangeness enhancement 1 Strangeness enhancement 2

28. J /  suppression In a QGP enviroment: Color charge is subject to screening in QGP  qq interaction is weakened Linear string term vanishes in the deconfined phase  (T)  0 deconfinement q q q,q,g distribution modified Coulomb  Yukawa  =0 doesn’t mean no bound !

29. Screening Effect Abelian Non Abelian ( gauge boson self-interaction ) One loop pQCD Bound state solution  Bound is not T c ! In HIC at √s ~ SPS, J/  should be suppressed !

30. Lattice result for V channel (J/  ) J/  ( p  0 ) disappears between 1.62T c and 1.70T c A(  )   2  (  )

31. Associated suppression of charmonium resonances  ’  c, … as a “thermometer”, like spectral lines for stellar interiors For light quarks r Bohr ~ 4 fm >> D, dissociation is more effective but of course also recombination B quark in similar condition at RHIC as Charmonium at SPS J/  Initial production Dissociation In the plasma Recombine with light quarks Suppression respect to extrapolation from pp

32. NUCLEAR ABSORBTION pre-equilibrium cc formation time and absorbtion by comoving hadrons HADRONIC ABSORBTION rescattering after QGP formation DYNAMICAL SUPPRESSION (time scale, g+J/   cc,…) pA (models)  abs ~ 6 mb

33. gluon-dissociation, inefficient for m  ≈ 2 m c * “quasifree” dissoc. [Grandchamp ’01] Fireball dynamical evolution Dynamical dissociation J/  + g c + c + X

34. RHIC central: N cc ≈10-20, QCD lattice: J/  ’s to  ~2T c Regeneration in QGP / at T c J/  + g c + c + X → ← - If c-quarks thermalize: [Grandchamp +Rapp ’03]

35. dominated by regeneration sensitive to: m c *, open-charm degeneracy Charmonia in URHIC’s RHIC SPS

36. Pion interferometry STAR Au+Au @ 130 AGeV open: without Coulomb solid: with Coulomb Au+Au @ 130 GeV STAR R o /R s ~1 smaller than expected ~1.5

37. Source radii from hydrodynamic model Fails to explain the extracted source sizes

38. Two-Pion Correlation Functions and source radii from AMPT Lin, Ko & Pal, PRL 89, 152301 (2002) Au+Au @ 130 AGeV Need string melting and large parton scattering cross section which may be due to quasi bound states in QGP and/or multiparton dynamics (gg↔ggg)

39. Emission Function from AMPT Shift in out direction ( > 0) Strong positive correlation between out position and emission time Large halo due to resonance (ω) decay and explosion → non-Gaussian source

40. Jet quenching Decrease of mini-jet hadrons (p T > 2 GeV) yield, because of in medium radiation. Ok, what is a mini-jet? why it is quenched ?

41. hadrons leading particle Jet: A localized collection of hadrons which come from a fragmenting parton Parton Distribution Functions Hard-scattering cross-section Fragmentation Function a b c d High p T (> 2.0 GeV/c) hadron production in pp collisions ~ High p T Particle Production Parton Distribution Functions “Collinear factorization” Hard-scattering cross-section p had = z p c, z <1 energy needed to create quarks from vacuum

42. Jet Fragmentation-factorization AB ab c p/  < 0.2 p h = z p c, z <1 energy needed to create quarks from vacuum B.A. Kniehl et al., NPB 582 (00) 514 a,b,c,d= g,u,d,s….  K, p... AB= pp (e + e  ) Parton distribution after pp collision (+ phenomenological k T smearing due to vacuum radiation) d

43. 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 Known from pp and pA

44. Non-Abelian gauge Energy Loss Static scattering centers assumed Gluon multiple scattering pipi pfpf k a c Color Color makes a difference Transport coefficient thickness pipi pfpf pfpf pipi k ~ Brehmstralung radiation in QED ×× ×

45. Medium Induced Radiation Clearly similar Recursion Method is needed to go toward a large number of scatterings! Ivan Vitev, LANL

46. Non – abelian energy loss Jet Quenching L/  opacity Large radiative energy loss in a QGP medium weak p T dependence of quenching Jet distribution  E/E ~ 0.5 Quenching

47. Energy Loss and expanding QGP In the transverse plane Quenching is angle dependent  Probe the density

48. nucleon-nucleon cross section Nuclear Modification Factor: AA If R = 1 here, nothing new going on Self-Analyzing (High p T ) Probes of the Matter at RHIC How to measure the quenching

49. Centrality Dependence Dramatically different and opposite centrality evolution of Au+Au experiment from d+Au control. Jet suppression is clearly a final state effect. Au + Au Experimentd + Au Control

50. Consistent with L 2 non-abelian plasma behavior Consistent with  GeV (similar to hydro) Is the plasma a QCD-QGP?

51. Baryon-Meson Puzzle   suppression: evidence of jet quenching before fragmentation  Fragmentation p/   Jet quenching should affect both Fragmentation is not the dominant mechanism of hadronization at p T ~ 1-5 GeV !? PHENIX,nucl-ex/0212014 PHENIX, nucl-ex/0304022 pionsprotons

52. Coalescence vs. Fragmentation Coalescence:  partons are already there $ to be close in phase space $  p h = n p T,, n = 2, 3 baryons from lower momenta Fragmentation:  Leading parton p T p h = z p T according to a probability D h (z)  z < 1, energy needed to create quarks from vacuum Parton spectrum B MB M Even if eventually Fragm. takes over …

53. Coalescence  Energy not conserved  No confinement constraint |M qq->m | 2 depends only on the phase space weighted by wave function (npQCD also encoded in the quark masses, m q =0.3 GeV, m s =0.475 GeV) npQCD Our implementation

54. Coalescence Formula f H hadron Wigner function  x =  p coalescence radius In the rest frame f q invariant parton distribution function thermal (m q =0.3 GeV, m s =0.47 GeV) with radial flow  0.5) + quenched minijets (L 

55. E T ~ 700 GeV  (r)  ~ 0.5 r/R T ~ 170 MeV V ~ 900 fm -3  GeV  fm -3 ) L/  T=170 MeV P. Levai et al., NPA698(02)631 quenched softhard Distribution Function REALITY: one spectrum with correlation kept also at p T < 2 GeV Hadron from coalescence may have jet structure (away suppr.)

56. Pion & Proton spectra V. Greco et al., PRL90 (03)202302 PRC68(03) 034904 R. Fries et al., PRL90(03)202303 PRC68(03)44902 R. C. Hwa et al., PRC66(02)025205 Au+Au @200AGeV (central)  Proton enhancement due to coalescence!

57. Baryon/Meson ratio  Resonance decays    Shrinking of baryon phase space Fragmentation not included for  Be careful, there are mass effects !

58. Momentum-space coalescence model Including 4 th order quark flow Meson flow Baryon flow Kolb, Chen, Greco, & Ko, PRC 69 (2004) 051901

59. Wave function effects  scaling breaking 10% q/m 5% b/m wave function effect Elliptic Flow from Coalescence Enhancement of partonic v 2 Coalescence scaling

60. Effect of Resonances on Elliptic Flow K, , p … v 2 not affected by resonances! Pions from resonances K & p  coal. moved towards  data nucl-th/0402020 * w.f. + resonance decay

61. Data can be described by a multiphase transport (AMPT) model Data Parton cascade Higher-order anisotropic flows

62. Back-to-Back Correlation ~8% Away Side : quenching has di-jet structure Same Side : Indep. Fragm. equal ( ?! ) to pp Coalescence from s-h leads to away side suppression, While same side is reduced if no further correlation … trigger Assoc. Trigger is a particle at 4 GeV < p Trig < 6 GeV Associated is a particle at 2 GeV < p T < p Trig quenched

63. Unexpected: Appreciable charm flow

64. Does Charm quark thermalize?  v 2 of D meson (single e) coalescence/fragmentation? energy loss?  p T Spectra and Yield of J/  From hard pp collision

65. D meson spectra S. Batsouli,PLB557 (03) 26 Pythia Hydro D mesons B mesons Single electron does not resolve the two scenarios Elliptic flow better probe of interaction No B mes. V. Greco, PLB595 (04) 202 D mesons

66. Charmed Elliptic Flow V 2q from , p,  Coalescence can predict v 2D for v 2c = 0 & v 2c = v 2q V 2 of electrons VGCMKRR, PLB595 (04) 202 S. Kelly,QM04 Flow mass effect Quenching

67. Quark gluon plasma was predicted to be a weakly interacting gas of quarks and gluons The matter created is not a firework of multiple minijets Strong Collective phenomena  Hydrodynamics describes well the bulk of the matter Transport codes needs a quite large npQCD cross section Charm quark interacts strongly in the plasma Recent lattice QCD finds bound states of cc at T>T c Rethinking the QGP at T c < T < 2T c “Strong” QGP

68. Summary  Most proposed QGP signatures are observed at RHIC.  Strangeness production is enhanced and is consistent with formation of hadronic matter at T c.  Large elliptic flow requires large parton cross sections in transport model or earlier equilibration in hydrodynamic model.  HBT correlation is consistent with formation of strongly interacting partonic matter.  Jet quenching due to radiation requires initial matter with energy density order of magnitude higher than that of QCD at T c.  Quark number scaling of elliptic flow of identified hadrons is consistent with hadronization via quark coalescence or recombination.  Studies are needed for electromagnetic probes and heavy flavor hadrons.  Theoretical models have played and will continue to play essential roles in understanding RHIC physics.

69. Conclusions  Matter with energy density too high for simple hadronic phase (  >  c from lattice) Matter is approximately thermalized (T >T c ) Jet quenching consistent with a hot and dense medium described by the hydrodymic approach Hadrons seem to have typical features of recombination Strangeness enhancement consistent with grand canonical ensemble J/  Needed : - Thermal spectrum - Dilepton enhancement

70. A Lot of work to do …  Lattice QCD Effective field theory Transport theory (quantum, field condensate,…) pQCD Scientific approach to an important part of the evolution of the primordial plasma can be achieved Understanding of Non-Abelian Interaction !