Che-Ming Ko Teaxs A&M University

1. Searching for the Quark-Gluon Plasma in Relativistic Heavy Ion Collisions 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 Largely based on slides by Vincenzo Greco

2. Bang Big Bang • e. m. decouple (T~ 1 eV , t ~ 3.105 ys) • “thermal freeze-out “ • but matter opaque to e.m. radiation • Atomic nuclei (T~100 KeV, t ~200s) • “chemical freeze-out” • Hadronization (T~ 0.2 GeV, t~ 10-2s) • Quark and gluons We’ll never see what happened at t < 3 .105 ys (hidden behind the curtain of the cosmic microwave background) HIC can do it!

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

4. Heuristic QGP phase transition B1/4 ~ 210 MeV -> Tc~ 145 MeV Free massless gas Bag Model Pressure exceeds the Bag pressure -> quark liberation Extension to finite mB , mI

5. Quantum ChromoDynamics • 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. • UA(1) ciral • 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 (Ist order or cross over ?)

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

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

9. Au+Au STAR The RHIC Experiments

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

11. 15 fm b 0 fm Collision Geometry - “Centrality” Spectators Participants S. Modiuswescki For a given b, Glauber model predicts Npart and Nbinary 0 N_part 394

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

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

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

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

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

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

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

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

20. Elliptic Flow Hydro Transport Spectra still appear thermal rapidity rapidity

21. Chemical equilibrium with a limiting Tc ~170MeV • Thermal equilibrium with collective behavior - Tth ~120 MeV and <bT>~ 0.5 • Early thermalization (t < 1 fm/c, e ~ 10 GeV/fm3) - very large v2 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/ψsuppression (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. MinBias Au-Au thermal - Dilepton spectrum at RHIC • Low mass: thermal dominant • (calculated by Rapp in kinetic model) • Inter. mass: charm decay No signals for thermal dileptons yet

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

25. QGP Scenario Hadronic Scenario 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

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

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

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

29. Bound state solution Screening Effect • Abelian • Non Abelian • (gauge boson self-interaction) One loop pQCD TBound is not Tc ! In HIC at √s ~ SPS, J/Yshould be suppressed !

30. Lattice result for V channel (J/y) A(w)=w2r (w) J/y (p = 0) disappears between 1.62Tc and 1.70Tc

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

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/Y-> cc,…) pA (models) sabs ~ 6 mb

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

34. If c-quarks thermalize: Regenerationin QGP / atTc J/y + g c + c + X - → ← • RHIC central: Ncc≈10-20, • QCD lattice: J/y’s to~2Tc [Grandchamp +Rapp ’03]

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

36. Pion interferometry open: without Coulomb solid: with Coulomb STAR Au+Au @ 130 GeV STAR Au+Au @ 130 AGeV Ro/Rs~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 (<xout> > 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 (pT> 2 GeV) yield, because of in medium radiation. Ok, what is a mini-jet? why it is quenched ?

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

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

43. High pT Particle Production in A+A Parton Distribution Functions Intrinsic kT , Cronin Effect Shadowing, EMC Effect Hard-scattering cross-section c a Partonic Energy Loss b d hadrons Fragmentation Function leading particle suppressed Known from pp and pA

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

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

46. Jet Quenching Quenching Jet distribution Large radiative energy loss in a QGP medium L/l opacity DE/E ~ 0.5 Non – abelian energy loss weak pT dependence of quenching

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

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

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

50. Is the plasma a QCD-QGP? • Consistent with L2 non-abelian plasma behavior • Consistent with e ~ 10 GeV (similar to hydro)