1. Hadron production @ RHIC at intermediate and high p T Conference on Intersections between Particle and Nuclear Physics New York, NY, May 20-23, 2003 Berndt Müller Duke University The goal of this talk: RHIC physics is simple What this talk is NOT about: Low p T (< 1GeV/c) (Go and listen to the next session!)

2. Suppression of high-p T hadrons in Au+Au collisions PHENIX Data: Identified  0 ? Same side jet Away side jet STAR

3. Centrality scaling of charged particles Relative Yield (Spectra normalized at N part = 65) N part soft physics: particle production scales with N part hard physics: particle production scales with N bin  Why does the charged particle yield at p t ≤4 GeV scale with N part ?

4. Suppression patterns: baryons vs. mesons  What makes baryons different from mesons ?

5. Elliptic flow of K 0 and  Anomalous p /  ratio Central Peripheral

6. Quark recombination ? Fragmentation Recombination S. Voloshin, QM2002

7. v 2 reflects partonic flow!? Recombination model suggests that hadronic flow reflects partonic flow (n = number of valence quarks): Provides measurement of partonic v 2 ! P. Sorensen (UCLA – STAR) Quark v 2 See also: Lin & Ko, PRL 89 (2002) 202302; Molnar & Voloshin, nucl-th/0302014

8. Bulk hadronization … More recent proposals: Net charge and baryon number fluctuations [Asakawa, Heinz, BM, PRL 85 (2000) 2072; Jeon, Koch, PRL 85 (2000) 2076] Balance functions [Bass, Danielewicz, Pratt, PRL 85 (2000) 2689] Recombination / coalescence [Fries, BM, Nonaka, Bass, nucl-th/0301087; Greco, Ko, Levai, nucl-th/0301093; Molnar, Voloshin, nucl-th/0302014] Lopez, Parikh, Siemens, PRL 53 (1984) 1216:Pion charge correlations seen in jet fragmentation will disappear when hadrons are evaporated from a plasma … is not a new idea!

9. Assumptions: Quarks and antiquarks recombine into hadrons locally “at an instant”: Gluons get absorbed into valence quarks before hadronization Competition between fragmentation and recombination; Hadron momentum P much larger than internal momentum  p 2  of the quark wave function of the hadron; Parton spectrum has thermal part (valence quarks) and a power law tail (quarks and gluons) from pQCD. Sudden recombination model  recombinationfragmentation

10. Recombination of thermal quarks Quark distribution function at “freeze-out” Relativistic formulation using hadron light-cone frame: For a thermal distribution Meson Baryon

11. Recombination vs. Fragmentation Fragmentation: … always wins over fragmentation for an exponential spectrum: … but loses at large p T, where the spectrum is a power law ~ (p T ) -b Recombination…Meson Baryon Apparent paradox: At given value of p T … The average hadron is produced by recombination The average parton fragments

12. High-energy parton loses energy by rescattering in dense, hot medium. q q Radiative energy loss: Can be described as medium effect on parton fragmentation: Jet Quenching qq g Scattering centers = color charges L

13. Energy loss in QCD For power law parton spectrum (  p T -v ) energy loss leads to an effective momentum shift for fast partons (BDMS): With expansion: Scattering “power” of QCD medium: Density of scattering centers Property of medium (range of color force)

14. Quenching factor: Analytical model: Surface emission Volume / R = surface   = QCD energy loss parameter:  0.5 ln(…) for gluons;   0.25 ln(…) for quarks partonshadrons  ≤ final dN/dy / volume

15. Away-side jet Q   R/R Quenching mechanism is not strong enough to generate a hadronic v 2 of the observed size, but agrees with the deduced partonic v 2 ! Correlations

16. Model fit to hadron spectrum T eff = 350 MeV blue-shifted temperature pQCD spectrum shifted by 2.2 GeV R.J. Fries, BM, C. Nonaka, S.A. Bass (PRL in print) Corresponds to  ≥ 0.6 !!! Recall:  G  0.5 ln(…)  Q  0.25 ln(…)

17. Hadron Spectra I For more details – see S.A. Bass’ talk tomorrow

18. Hadron Spectra II For more details – see S.A. Bass’ talk tomorrow

19. Hadron dependence of high-p t suppression R+F model describes different R AA behavior of protons and pions Jet-quenching becomes universal in the fragmentation region

20. Charged hadron suppression pQCD-I (XN Wang) fit with energy loss formula  0 = 2 GeV,  0 = 2.04 GeV/fm  Energy loss vanishes below E =3.2 GeV !!! Is R AA (h ± ) = R AA (  0 ) above 6 GeV/c ? Vitev & Gyulassy, PRL 89 (2002) 252301

21. Summary QGP clearly signals its presence at intermediate and high p T : –Hadron formation from a bulk quark phase –Elliptic flow carried by (valence) quarks –Strong energy loss of leading partons Physics of hadron production at RHIC is simple! Unified picture of hadron production at intermediate and high p T emerges: Competition between parton recombination and fragmentation, which naturally explains: –Large p/  ratio at intermediate p T –Lack of suppression of baryons at intermediate p T –Collective flow for baryons persists to higher p T than for mesons and saturates at higher value –“Soft” physics of hadron production up to 4 GeV/c –Energy loss above 6 GeV/c compatible with pQCD estimates

22. Outlook: What we now need… Systematic tests of recombination concept, requiring: Particle ID up to at least 6 GeV/c Measurement of v 2 to highest possible p T Incorporation of quark and hadron masses Realistic calculations of QCD energy loss to determine loss coefficient  Unified framework: recombination as special case of fragmentation in medium  recombinationfragmentation Casalderry-Solana & Shuryak, hep-ph/0305160. No equations!

23. Back-up slides

24. Other high-p T probes Quark-photon back-to-back correlations. In-medium Compton backscattering (qg  q  ) at high p T measures gluon density g  R.J. Fries, BM, D.K. Srivastava, PRL 90 (2003) 132301 Wang, Huang, Sarcevic (1996)

25. pQCD approach to parton recombination AA meson Double parton scattering scales: Single parton scattering and fragmentation scales: T. Ochiai, Prog. Theor. Phys. 75 (1986) 1184