Quark Recombination and Fragmentation

1. Quark Recombination and Fragmentation C. R. Ji In collaboration with Profs. B. Hong and D.-P. Min The 6th Heavy Ion Meeting

2. Motivation of HI Collisions • Quarks and Gluons exist, but not detected individually at T=0. • Temperature Dependence of Confinement • and Chiral Symmetry • High-energy nuclear collisions will compress and heat the heavy nuclei so much that their individual protons and neutrons overlap and lots of pions arise, creating theQuark-Gluon Plasma (QGP) QGPis thought to have existed ten millionths of second after theBig Bang; creating the primordial matter of universe in the laboratory. The 6th Heavy Ion Meeting

3. RHIC obtained distinguished results from CERN SPS. • Jet Quenching and Bulk Hadronization (Winner of recent NSAC meeting). • LHC ALICE (CMS, ATLAS) would need theoretical predictions at energy 30-fold energy increase from RHIC. The 6th Heavy Ion Meeting

4. Outline • Brief Overview on State Changes Chemical and Thermal Freeze-outs • Hadronization Mechanisms Quark Recombination and Fragmentation • Numerical Results Wavefunction Dependence on PT Spectra, Ratio between proton and antiproton, etc... • Discussion and Conclusion BCS-BEC Crossover, Heavy quark systems, etc... The 6th Heavy Ion Meeting

5. Simulation by the Frankfurt Group The 6th Heavy Ion Meeting

6. Heavy Ion Collision • - Hard Scattering and High PT Fragmentation • Formation of QGP • - T ≫ TC ≈ 175 MeV • Expansion and Cooling • - T → TC • Hadronization from QGP • - Intermediate PT (2-5 GeV) Recombination • Chemical Equilibrium and Freeze-out (TC ≈ 175 MeV) • Inelastic Channels (e.g. Δ↔pπ) • Number of each hadron species doesn’t change • Thermal Equilibrium • Elastic Scatterings Dominant • Interaction still exists (MFP > DBP) • Continued Expansion and Thermal Freeze-out • Particle distance gets larger (DBP > MFP) • No further elastic collisions but still heavy particles can decay • into light particles (e.g. Δ→Ρπ): Tfreeze-out≈120 MeV The 6th Heavy Ion Meeting

7. T(MeV) Early Universe (RHIC) Quark-Gluon Plasma RHIC & future LHC explore high temperature & low baryon density partonic matter. ~150 Phase Transition Color Superconductor Neutron Star Hadron Gas SIS explores high baryon density hadronic matter. Atomic Nuclei ~10 Density(n0) Nuclear Phase Diagram The 6th Heavy Ion Meeting

8. Heavy-Ion Accelerators The 6th Heavy Ion Meeting

9. Brookhaven National Lab. in New York • Circumference: 3.83 km • First collision: 2000 • 100A GeV Au+Au(2X1026/cm2/s) • 250 GeV p + p (2X1032/cm2/s) Relativistic Heavy Ion Collider BRAHMS PHOBOS PHENIX STAR The 6th Heavy Ion Meeting

10. Hadronization Mechanisms R.J. Fries, nucl-th/0403036, PRC 68, 044902 (2003) The 6th Heavy Ion Meeting

11. Recombination of a Quark-Antiquark Pair The 6th Heavy Ion Meeting

12. Extended Recombination Formalism The 6th Heavy Ion Meeting

13. β2 (GeV2) = 0.026 0.26 2.6 ψπ k⊥ x ψD k⊥ ψK k⊥ x x Light-Front Wavefunctions The 6th Heavy Ion Meeting

14. Gaussian vs. Power Law The 6th Heavy Ion Meeting

15. - Parameters of the parton distribution function • D.K. Srivastava, et al., PRC 67, 034903 (2003) • - Parameters of the Fragmentation function • B.A. Kniel, et al., NPB 582, 514 (2000) • D. De Florian, et al., PRD 57, 5811 (1998) • R. Baier, et al., JHEP 0109, 033 (2001) • B. Mueller, PRC 67, 061901 (2003) Fragmentation and Jet Quenching The 6th Heavy Ion Meeting

16. Numerical Results • Single Particle Spectra • Particle Ratios • Nuclear Modification Factor Rcp • Wave Function Dependence • Gaussian vs. Power Law • Prediction for D-meson Production at RHIC and LHC The 6th Heavy Ion Meeting

17. Comparison of Single Spectra The 6th Heavy Ion Meeting

18. Comparison of Single Spectra The 6th Heavy Ion Meeting

19. Comparison of Single Spectra The 6th Heavy Ion Meeting

20. Comparison of Single Spectra The 6th Heavy Ion Meeting

21. Comparison of Single Spectra The 6th Heavy Ion Meeting

22. Comparison of Single Spectra The 6th Heavy Ion Meeting

23. Comparison of Single Spectra The 6th Heavy Ion Meeting

24. Comparison of Single Spectra The 6th Heavy Ion Meeting

25. Comparison of Particle Ratios The 6th Heavy Ion Meeting

26. Comparison of Particle Ratios The 6th Heavy Ion Meeting

27. Fries et al., PRC 68, 044902 (2003) Fries et al., PRC 68, 044902 (2003) Comparison of Particle Ratios The 6th Heavy Ion Meeting

28. Comparison of Nuclear Modification The 6th Heavy Ion Meeting

29. Comparison of Nuclear Modification The 6th Heavy Ion Meeting

30. Gaussian vs. Power Law The 6th Heavy Ion Meeting

31. Heavy Quark Distribution Function RHIC The 6th Heavy Ion Meeting

32. Heavy Quark Distribution Function LHC The 6th Heavy Ion Meeting

33. Prediction of D-Meson Spectra The 6th Heavy Ion Meeting

34. Conclusions and Outlook • Extended the formulation of the recombination model • Intrinsic transverse momentum effect • Light-Front wavefunction • Gaussian vs. Power Law • Found the sensitivity of the wavefunction dependence • Recombination is favored by the larger size hadrons • Different results on the yield ratios of K-/K+ and pbar/p • Jet quenching effect is included • Our extended formulation may be useful for the analysis of the QGP nature • Possible formation of the binary system • Crossover between BCS and BEC via Feshbach resonances • Plan to investigate • Heavy hadron production • Elliptic flow The 6th Heavy Ion Meeting

35. Food for Thoughts:Binary Bound States in QGP The 6th Heavy Ion Meeting

36. Effective Mass Pressure T/Tc The 6th Heavy Ion Meeting

37. Bose-Einstein Condensation Hydrodynamical Expansion of Trapped Atoms Analogous to Elliptic Flows in RHIC Data The 6th Heavy Ion Meeting

38. Crossover between BCS and BEC The 6th Heavy Ion Meeting

39. Controlling Parameters • High Tc Superconductors: Doping Holes • Ultracold Trapped Atoms: Applying Magnetic Fields • RHIC: Changing sNNand Projectiles, etc. The 6th Heavy Ion Meeting