1. 1 Searching for the QGP at RHIC Che-Ming Ko Texas A&M University  Signatures of QGP  Quark coalescence Baryon/meson ratio Hadron elliptic flows and quark number scaling Effects of resonance decays and hadron wave function Charm flow Higher-order anisotropic flow  Summary

2. 2 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)  ……………

3. 3 - 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

4. 4 Enhancement of multistrange baryons But enhancement is even larger in HI collisions at lower energies

5. 5 J/Ψ production at RHIC Au+Au @ 200 GeV Grandchamp, Rapp, Brown, PRL 92, 212301 (04)

6. 6 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

7. 7 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  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 String melting: PRC 65, 034904 (02); PRL 89, 152301 (02)

8. 8  Using α s =0.5 and screening mass μ=gT≈0.6 GeV at T≈0.25 GeV, then 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, σ t ≈2.7 mb  σ=10 mb → μ≈0.35 GeV, σ t ≈3.6 mb Zhang’s parton cascade (ZPC) Bin Zhang, Comp. Phys. Comm. 109, 193 (1998)

9. 9 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)

10. 10 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

11. 11 High P T hadron suppression Parton energy loss due to radiation and reabsorption ε 0 =1.07 GeV/fm, μ=1.5 GeV Wang & Wang, PRL 87, 142301 (01) ¢E ( b ; r ; Á ) ¼ ² 0 ( E = ¹ ¡ 1 : 6 ) 1 : 2 =( 7 : 5 + E = ¹ ) £ Z ¢L ¿ 0 d ¿ ¿ ¡ ¿ 0 ¿ 0 ½ 0 ½ g ( ¿ ; b ; ~ r + ~ n¿ ) Also Gyulassy, Levai & Titev, PRL 85, 5535 (00) Jet quenching → initial energy density → 5-10 GeV/fm 3

12. 12  Fragmentation leads to p/π ~ 0.2  Jet quenching affects both  Fragmentation is not the dominant mechanism of hadronization at p T < 4-6 GeV PHENIX, nucl-ex/0212014 PHENIX, nucl-ex/0304022 Puzzle: Large proton/meson ratio π 0 suppression: evidence of jet quenching before fragmentation

13. 13 Surprise: quark number scaling of hadron elliptic flow Except pions, v 2,M (p T ) ~ 2 v 2,q (p T /2) and v 2,B (p T ) ~ 3 v 2,q (p T /3) consistent with hadronization via quark recombination

14. 14 Unexpected: Appreciable charm flow

15. 15 Coalescence model in heavy ion collisions  Extensively used for light clusters production.  First used for describing hadronization of QGP by Budapest group  Revived by Oregon: Hwa, Yang (PRC 66 (02) 025205), ……… Duke-Minnesota: Bass, Nonaka, Meuller, Fries (PRL 90 (03) 202303; PRC 68 (03) 044902 ) Ohio and Wayne States: Molnar, Voloshin (PRL 91 (03) 092301; PRC 68 (03) 044901) Texas A&M: Greco, Levai, Rapp, Chen, Ko (PRL (03) 202302; PRC 68 (03) 034904)  Most studies are schematic, based on parameterized QGP parton distributions.  Study based on parton distributions from transport models has been developed by TAMU group (PRL 89 (2002) 152301; PRC 65 (2002) 034904 ) and also pursued by D. Molnar (nucl-th/0406066).

16. 16 Coalescence model Quark distribution function Spin-color statistical factor e.g. Coalescence probability function PRL 90, 202102 (2003); PRC 68, 034904 (2003) Number of hadrons with n quarks and/or antiquarks For baryons, Jacobi coordinates for three-body system are used.

17. 17  Thermal QGP  Power-law minijets  Choose Consistent with data (PHENIX) Parton transverse momentum distributions P. Levai et al., NPA 698 (02) 631 L/  T=170 MeV quenched softhard

18. 18  Minijet fragmentation via KKP fragmentation functions (Kniehl, Krammer, Potter, NPB 582, 514 (2000))  Gluons are converted to quark-antiquark pairs with equal probabilities in all flavors.  Quark-gluon plasma is given a transverse collective flow velocity of β=0.5 c, so partons have an additional velocity v(r)=β(r/R).  Minijet partons have current quark masses m u,d =10 MeV and m s =175 MeV, while QGP partons have constituent quark masses m u,d =300 MeV, ms=475 MeV (Non-perturbative effects, Levai & Heinz, PRC 57, 1879 (1998))  Use coalescence radii Δp=0.24 GeV for mesons and 0.36 GeV for baryons Other inputs and assumptions

19. 19 Au+Au @ 200AGeV (central) Pion and proton spectra Similar results from other groups  Oregon: parton distributions extracted from pion spectrum  Duke group: no resonances and s+h but uses harder parton spectrum

20. 20 Baryon/Meson ratio   DUKE OREGON TAMU

21. 21 Elliptic flow Quark v 2 extracted from pion and kaon v 2 using coalescence model

22. 22 Momentum-space quark coalescence model Quark transverse momentum distribution Meson elliptic flow Baryon elliptic flow Quark number scaling of hadron v 2 (except pions): Only quarks of same momentum can coalescence, i.e., Δp=0 same for mesons and baryons

23. 23 Effects of hadron wave function and resonance decays Wave function effect Effect of resonance decays Wave fun.+ res. decays Higher fock states → similar effect (Duke)

24. 24 Charm spectra Charm quark D mesonJ/ψ Bands correspond to flow velocities between 0.5 and 0.65 N J/ψ =2.7. 10 -3 N J/ψ =0.9. 10 -3 T=0.72 GeV T=0.35-0.50 GeV D e-e- Au+Au @ 200 A GeV

25. 25 Greco, Rapp, Ko, PLB595 (04) 202 S. Kelly,QM04 Charmed meson elliptic flow v 2 of electrons Data consistent with thermalized charm quark with same v 2 as light quarks Smaller charm v 2 than light quark v 2 at low p T due to mass effect

26. 26 Charm quark elliptic flow from AMPT  P T dependence of charm quark v 2 is different from that of light quarks.  At high p T, charm quark has similar v 2 as light quarks.  Charm elliptic flow is also sensitive to parton cross sections

27. 27 Charm elliptic flow from AMPT Zhang, Chen & Ko, PRC 72, 024906 (05) Current light quark masses are used in AMPT. Charmed meson elliptic flow will be larger if constituent quark masses are used. 15 10 5 0 -5

28. 28 Higher-order parton anisotropic flows Including 4 th order quark flow Meson elliptic flow Baryon elliptic flow Kolb, Chen, Greco, Ko, PRC 69 (2004) 051901

29. 29 Data can be described by a multiphase transport (AMPT) model with large parton cross sections. Data Parton cascade gives v 4,q ~v 2,q 2 Higher-order anisotropic flows

30. 30 Summary on quark coalescence  Quark coalescence can explain observed Large baryon/meson ratio at p T ~ 3GeV Quark number scaling of hadron v 2 → signature of deconfinement?  Coalescence of minijet partons with thermal partons is significant → medium modification of minijet fragmentation.  Scaling violation of pion v 2 can be explained by resonance decays.  Coalescence of thermalized charm quarks can explain preliminary charmed meson spectrum and v 2 as well as J/ψ yield.  Required quark v 2 is consistent with that from parton cascade.  Appreciable parton v 4 is seen in parton cascade.  Entropy violation (~16%) is not as large as one naively thinks and is related to corresponding energy violation.

31. 31 Summary on QGP search  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.