1. What Can We Learn from Charm Production at RHIC? James Nagle University of Colorado at Boulder c _c_c

2. Heavy Ion Collisions Au-Au reactions at RHIC releases ~ 10,000 gluons, quarks and anti-quarks from the nuclear wavefunction. We want to study this strongly interacting partonic system with self-generated probes - such as charm.

3. Default Charm Picture Transparent medium. D meson c _c_c Charm produced via gluon fusion. Charm fragments outside the medium.

4. Induced Gluon Radiation Z. Lin et al., Phys. Rev. C 57, 899, 1992. Baier, Dokshitzer, Mueller, Schiff, hep-ph/9907267 Gyulassy, Levai, Vitev, hep-pl/9907461 X.N. Wang, nucl-th/9812021 D meson c _c_c

5. Theory Calculations Z.Lin, R.Vogt,X.N.Wang, nucl-th/9705006 Energy Loss dE/dx = 2 GeV/fm D  electron I have used their charm quark spectra to calculate D meson and resulting electron (D  eK ) spectra using Peterson fragmentation functions, decay kinematics and correcting to 10% central AuAu collisions at 130 GeV. (with energy loss) p T (GeV)

6. Experimental Results D  e K  conversion  0   ee    ee, 3  0   ee,  0 ee   ee,  ee   ee  ’   ee K. Adcox et al., Phys. Rev. Lett. 88, 192303, 2002. PHENIX experiment measures single electrons. After subtracting electrons from Dalitz decays, conversions,… remaining signal expected from charm and beauty. D  e K  B  e D

7. Transparent Medium? PYTHIA model is tuned to match lower energy charm production data. PYTHIA shows good agreement with charm production that scales with the number of binary collisions. No indication of energy loss effect. (with energy loss)

8. Dead Cone Effect Charm quarks at moderate pT~3 GeV have velocity ~0.92 c Very forward gluon emission violates causality, leading to a dead-cone effect. This reduction of induced gluon radiation may explain the data. However, recent calculations by Djordjevic indicate this effect is not large enough to explain the data. They suggest an additional effect of suppression of vacuum energy loss below the plasma frequency. Y.L.Dokshitzer and D.E. Kharzeev, hep-ph/0106202 M. Djordjevic and M. Gyulassy, nucl-th/0302069 c

9. Alternative Picture Perhaps charm is swallowed up by the medium and D mesons form via recombination, not fragmentation. If charm quarks lose substantial energy via scattering or radiation, they may hadronize inside the medium. cc D meson c _c_c

10. Medium and Hydrodynamics If charm becomes thermalized with the system, there can be both positive and negative feedback on charm. Hydrodynamics assumes local thermal equilibrium (zero mean-free-path limit) and solves equations of motion for fluid elements (not particles).

11. Hydrodynamic Success Hydro calculations: P. Huovinen, P. Kolb and U. Heinz Ansatz of zero mean free path hydrodynamics. Start with Equation-of-State from lattice QCD. Common velocity field yields larger p T boost for more massive particles. Good agreement with experimental data.

12. Pressure Gradient Hadronic re-scattering is insufficient to describe the data. Implies strong partonic re-scattering and high initial density.  = 20 GeV/fm 3 and  = 0.6 fm/c Non-central collisions have spatial anisotropy in the density gradient. Pressure via re-scattering leads to a momentum space anisotropy. STAR

13. Heavy Hydrodynamics Ansatz of zero mean free path hydrodynamics including heavy quarks. No new parameters introduced. Large momentum boost (positive feedback) from system leads to D meson agreement with PYTHIA pQCD up to p T ~ 3 GeV and for B meson up to p T ~ 5 GeV.

14. Positive and Negative Feedback Z.Lin et al. calculation assumes charm only loses energy to the system. If p T ~ T then it is “thermalized part.” Our calculation assumes complete loss of energy and then positive boost in hydrodynamic picture.

15. Transparent vs. Opaque S. Batsouli, S. Kelly, M. Gyulassy, JN, Phys. Lett. B 557, pp 26-32. Transparent system with charm fragmenting outside the system shows good agreement with PHENIX electron data. Opaque system with charm boosted via re-scattering and hadronizing in the medium shows good agreement with the PHENIX electron data. Amazing ambiguity!

16. Conclusions D meson c _c_c Opaque Medium + Hydrodynamics Transparent Medium + Fragmentation

17. Conclusions++ Higher statistics electron measurements with higher p T reach may help discriminate models. However, that would not rule out hydrodynamics for lower p T. Hydrodynamics has a specific prediction for momentum anisotropy (v 2 ) for D mesons and J/ . In contrast, a transparent system would produce no anisotropy. Not easy to measure, but a good experimental test of the two pictures.

18. Scaling of Cross Section

19. Fragmentation Functions Light quarks (u,d) blue = Fields-Feynman black dash = Lund fragmentation z dN/dz * z Heavy quarks (c,b) red = Peterson function black dash = Lund fragmentation Bowler correction not shown  (1-z) is obvious For charm quarks, the Peterson and Lund fragmentation roughly agree and give an average ~ 0.8.

20. Minimum Bias Comparison

21. PHENIX 200 GeV Data

22. PHENIX 200 GeV Data II

23. Question on Ansatz? Low and medium p T (0-4 GeV/c) D mesons may be formed inside the system and re-scattering with surrounding particles may lead to collective behavior. Interactions with other hadrons are relatively weak  (  D)~10 mb Ziwei Lin, C. M. Ko, Bin Zhang, Phys. Rev. C 61, 024904 (2000). Ziwei Lin, C. M. Ko, Bin Zhang, preprint [nucl-th/9905007] However there is a very large abundance of  (for T~170MeV) Alternatively, charm quarks may undergo significant re-scattering in the partonic medium and participate in hydrodynamic type expansion then either fragment into D mesons or coalesce with co-moving spectators of low relative momentum to form D mesons. No calculation yet proves the validity of this ansatz. However, it should be noted that this is also true for light quarks as well (D. Molar, M. Gyulassy).