Che-Ming Ko Texas A&M University

1. Relativistic Heavy Ion Collisions and Hot Dense Matter Che-Ming Ko Texas A&M University • Introduction: concepts and definitions - Quark-gluon plasma (QGP) - Heavy ion collisions (HIC) • Experiments and theory - Signatures of QGP - Experimental observations at RHIC - Future experiments at LHC and FAIR References: C.Y. Wong, “Introduction to High Energy Heavy Ion Collisions”, World Scientific (1994); K. Yagi, T. Hatsuda, and Y. Miaki, “Quark-Gluon Plasma”, Cambridge University Press (2005)

2. Big Bang

3. Relativistic Heavy Ion Collisions: little bang

4. A quark-gluon plasma is expected to be produced during initial stage

5. Phases of nuclear matter Courtesy of Roy Lacey

6. QCD phase transition at zero baryon chemical potential • Energy density and pressure of free massless quarks and gluons Energy density and pressure of pion gas Bag constant B1/4~220 MeV

7. Quantum Chromodynamics f1 (1285) a1 (1260) • (782) • (770) σ(400-1200) P-S and V-A splittings in physical vacuum p (140) • Similar to QED but • SU(3) gauge symmetry in color space → gluon self-interaction • Approximate chiral symmetry in the light sector and is spontaneously broken in vacuum → • → Eight goldstone bosons (π, K, η) and absence of parity doublets

8. Confinement at large distance → V(r) ~ k r • Asymptotic freedom at short distance → αs=g2/4π decreases • with momentum transfer

9. Lattice QCD QCD can be solved in a discrete space Lattice QCD is the algorithm to evaluate Z in the space-time → static at finite temperature via Time dimension is thus regulated by temperature e.g., for gluon field, the action becomes

10. Phase transition in lattice GCD Karsch et al., NPA 698, 199 (02) 530 MeV 410 210 0 • Soft equation of state (p< e/3) • ec ~ 6Tc4 ~ 0.66 GeV/fm3 • Appreciate interaction energy • Tc ~ 170 MeV

11. Chiral symmetry restoration • Verified by lattice QCD at finite temperature and zero baryon chemical potential • Expect either appearance of parity doublets or similarity • of their spectral functions, e.g, ρ and a1

12. QCD phase diagram probed by HIC AGS SPS RHIC We do not observe hadronic systems with T > 170 MeV (Hagedon prediction)

13. Au+Au STAR The RHIC experiments

14. 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

15. Rapidity distributions • Rapidity • Transverse mass • Pseudirapidity

16. 99% of particles Transverse momentum distributions • Soft (< 2 GeV/c) - exponential spectrum - bulk particle production - described phenomenologically, e.g., string fragmentation through Schwinger mechanism with z= light-cone momentum fraction of produced hadron wrt that of fragmenting string • Hard (> 2 GeV/c) • - power law spectrum • - described by pQCD

17. c a b d hadrons High pT particle production Mini jet production Hadron prodution from empirical fragmentation function determined from e+e- annihilation ph= zpc, z<1

18. Energy Density Particle streaming from origin For Au+Au @ 200 GeV at RHIC R~1.18 A1/3~ 7 fm, dET/dy~ 720 GeV Taking particle formation time τ~0.6 fm/c, then

19. Radial collective flow Slope of transverse momentum spectrum is due to folding temperature with radial collective expansion <βT> Absence Slopes for hadrons with different masses allow to separate thermal motion from collective flow Tf ~ (120 ± 10) MeV <βT> ~ (0.5 ± 0.05)

20. Statistical model Assume thermally and chemically equilibrated system of non-interacting hadrons and resonances with density Determine chemical freeze out temperature Tch and baryon chemical potential μB by fitting experimental data after inclusion of feed down from short lived particles and resonances decay. Tch~Tc

21. Hydrodynamic model Kolb & Heinz; Teany & Shuryak; Hirano, …….. HydrodynamicEquations Energy-momentum conservation Charge conservations (baryon, strangeness,…) For perfect fluids without viscosity e: energy density p: pressure uμ: four velocity Equation is closed by the equation of state p(e) Cooper-Frye instantaneous freeze out dσ is an element of space-like hypersurface

22. Transverse momentum spectra from hydrodynamic model Kolb & Heinz, nucl-th/0305084 Initial flow efo=0.45 Gev/fm-3 0.075 Gev/fm-3 Initial Ti=340 MeV, ei=25 GeV/fm3 Freezeout Tf=128 MeV

23. Parton cascade Bin Zhang, Comp. Phys. Comm. 109, 193 (1998) D. Molnar, B.H. Sa, Z. Xu & C. Greiner • Using αs=0.5 and screening mass μ=gT≈0.6 GeV at T≈0.25 GeV, • then <s>1/2≈4.2T≈1 GeV, and pQCD gives σ≈2.5 mb and a • transport cross section • σ=6 mb → μ≈0.44 GeV, σt≈2.7 mb • σ=10 mb → μ≈0.35 GeV, σt≈3.6 mb

24. A multiphase transport (AMPT) model Default: Lin, Pal, Zhang, Li & Ko, PRC 61, 067901 (00); 64, 041901 (01); 72, 064901 (05); http://www-cunuke.phys.columbia.edu/OSCAR • Initial conditions: HIJING (soft strings and hard minijets) • Parton evolution: ZPC • Hadronization: Lund string model for default AMPT • Hadronic scattering: ART String melting: PRC 65, 034904 (02); PRL 89, 152301 (02) • Convert hadrons from string fragmentation into quarks and antiquarks • Evolve quarks and antiquarks in ZPC • When partons stop interacting, combine nearest quark and antiquark to meson, and nearest three quarks to baryon (coordinate-space coalescence) • Hadron flavors are determined by quarks’ invariant mass

25. Transverse momentum and rapidity distributionfrom AMPT BRAHMS Au+Au @ 200 GeV

26. What have we learnt? Matter formed in relativistic heavy ion collisions reaches • thermalization early in time τ < 1 fm/c • high initial energy density ε ~ 10 GeV/fm3 • chemical equilibrium with limiting temperature Tc ~ 170 MeV • final thermal equilibrium at Tth ~ 120 MeV with large radial collective flow velocity <βT> ~ 0.5 Is the matter a quark-gluon plasma?

27. 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) • ……………

28. 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

29. Strangeness enhancement • In QGP

30. Strangeness quilibration Time Kinetic equation Equilibrium density 6 fm/c Strangeness equilibration time in QGP from lowest-order QCD teq ~6 fm/c is comparable to lifetime tQGP of QGP in HIC

31. Strangeness production in hadronic matter • In hadronic matter → cross sections ~ a few mb Cross sections are unknow but expected to be a few mb as well Strangeness equilibration time in hadronic matter teq ~ 30 fm/c is longer than hadronic life time thad ~ 15 fm/c

32. e+e- collisions Experimental results Multistrange baryons are significantly enhanced and can be accounted for by the statistical model → Strangeness equilibration

33. J/ψ suppression • Color charge is subject to screening in QGP One loop pQCD

34. Lattice result for J/ψspectral function A(w)=w2r (w) J/ψdisappears between 1.62Tc and 1.70Tc

35. J/ψ absoprtion and production in HIC • Nuclear absorption:J/ψ+N→D+Λc; p+A data → σ~ 6 mb • Absorption and regeneration in QGP: • Absorption and regeneration in hadronic matter: RHIC SPS

36. Hanbury-Brown-Twiss interferometry Two-particle correlation function with • S(x,p) is the emission source function and is given by the phase space distribution at freeze out in the AMPT model • C(K,q) can be evaluated using Correlation After Burner (Pratt, NPA 566, 103c (94))

37. Pion interferometry open: without Coulomb solid: with Coulomb STAR Au+Au @ 130 GeV qinv2=q2-(E1-E2)2 STAR Au+Au @ 130 AGeV Ro/Rs~1 smaller than expected ~1.5

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

39. 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)

40. 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

41. pi pf × × k pi pf High PT hadron suppression Gyulassy, Levai & Vitev, PRL 85, 5535 (00) Wang & Wang, PRL 87, 142301 (01) Parton energy loss due to radiation x x Jet quenching → initial energy density → 5-10 GeV/fm3

42. p/π+ and pbar/π- ratios at high transverse momentum STAR Collaboration, PRL 97, 152301 (07) Same p/π+ and /π- ratios in central and peripheral collisions → Same RAA for gluon and quark jets, which is not expected from radiative energy loss as gluon jets lose more energy than quark jets.

43. Jet conversions in QGP • Quark jet conversion Elastic process: qg→gq Gluon is taken to have a larger momentum in the final state Inelastic process: • Gluon jet conversion: similar to above via inverse reactions

44. Radiative conversion: 2→3 + ………

45. Coalescence + jet quenching + jet conversion

46. 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

47. Elliptic flow from hydrodynamic model Ideal hydro describes very well data at low pT (mass effect) but fails at intermediate pT → viscous effect.

48. Elliptic flow from AMPT Lin & Ko, PRC 65, 034904 (2002) σp= 6 mb • Need string melting and large parton scattering cross section • Mass ordering of v2 at low pT as in hydrodynamic model

49. Surprise: quark number scaling of hadron elliptic flow Except pions, v2,M(pT) ~ 2 v2,q(pT/2) and v2,B(pT) ~ 3 v2,q(pT/3) consistent with hadronization via quark recombination

50. Momentum-space quark coalescence model Only quarks of same momentum can coalescence, i.e., Δp=0 Quark transverse momentum distribution Meson elliptic flow Quark number scaling of hadron v2 (except pions): Baryon elliptic flow same for mesons and baryons