1. Duke University 野中 千穂 Hadron production in heavy ion collision: Fragmentation and recombination in Collaboration with R. J. Fries (Duke), B. Muller (Duke), S. A. Bass (Duke & RIKEN) PRL90,202303(2003), nucl-th/0306027, nucl-th/0308051 2003 年 9 月 9 日＠日本物理学会 ２００３年秋季大会、宮崎

2. C.NONAKA 2 OutlineOutline Introduction Hadronization mechanism Experimental data Elliptic Flow, Proton Puzzle, R AA Hadronization mechanism Recombination + Fragmentation Model Comparison with Experimental data Hadron Spectra, Hadron ratio, R AA, Centrality dependence of hadron spectra Elliptic Flow Summary

3. C.NONAKA 3 Hadronization mechanism Relativistic Heavy Ion Collision Schematic sketch (ex. Hydro) Experiments t hydrodynamical expansion hadronizationthermalizationcollision QGP production hadron phase phase transition freezeout hadron production We have to find the hints about hadronization in experimental data.

4. C.NONAKA 4 Au+Au at sqrt(s NN )=200GeV r.p. |  |=3~4 min. bias Experimental Data ( I ) Saturation in v 2 of baryon occurs at higher P T than one of meson. PHENIX : nucl-ex/0305013 (STAR : nucl-ex/0306007) Hydro : Huovinen et al., PLB503,58(2001) At low P T At Low P T Hydro works well

5. C.NONAKA 5 Experimental Data ( II ) Proton Puzzle at RHIC p/  ratio ~ 1 (P T >2 GeV) in central collisions (PHENIX:nucl-ex/0307022) Hadronization from Fragmentation at high P T g qq : KKP fragmentation function p/  ratio << 1 p/ 

6. C.NONAKA 6 Experimental Data ( III ) Sorensen@SQM2003 There are some correlations between R AA and v 2. Suppression in R AA of baryon occurs at higher P T than one of meson. Nuclear modification factor Intermediate P T # of valence quarks High P T Fragmentation Hints from experimental data

7. C.NONAKA 7 Recombination + Fragmentation Model Recombination at moderate P T Recombination occurs in an instant. The parton spectrum is shifted to higher p T in the hadron spectrum. Entropy and energy conservation No gluon dynamics Fragmentation at high P T The parton spectrum has a power law tail (quarks and gluons) from pQCD. The parton spectrum is shifted to lower p T in the hadron spectrum. recombining partons: p 1 +p 2 =p h fragmenting parton: p h = z p, z<1 Recomb. Frag.

8. C.NONAKA 8 Formalism of Recombination ( I ) Number of meson Effective wave function Covariant form on hadronizaion hypersurface  meson parton Integral over q in terms of light cone coordinates : phase space distribution of parton : degree of freedom of meson : Wigner function : Meson states with momentum P : density matrix for systems of parton

9. C.NONAKA 9 Formalism of Recombination ( II ) Recombination from thermal phase Baryon/Meson ratio Input: This depends on hadron momentum ! ex. ratio ~ 2 mass effect superposition with fragmentation ratio ~ 1 (2 < P T < 4 GeV) Meson: Baryon: Important feature

10. C.NONAKA 10 Recombination vs. Fragmentation Fragmentation : KKP fragmentation function Recombination exponential parton spectrum Fragmentation power law parton spectrum i. Parton spectrum: ii. Parton spectrum:(power law) (exponential) Recomb. Frag. Important feature

11. C.NONAKA 11 Input for Quantitative Calculation Recombination Fragmentation K=1.5 :roughly account for higher order corrections C, B,  are taken from a leading order pQCD calculation Energy Loss :  a : fugacity factor,  rapidity width f(  transverse distribution T=175 MeV,  fm, v T =0.55 Spectrum of parton

12. Comparison with Experimental Data I Hadron spectra, Hadron ratio, Central dependence of hadron spectra

13. C.NONAKA 13 Hadron Spectra ( I ) R + F R F R F

14. C.NONAKA 14 Hadron Spectra ( II ) R + F R F R F

15. C.NONAKA 15 Hadron Ratios vs. P T R + F R Statistical model Thermal Recomb. Frag Up to 4 GeV, thermal model describes data well. supports transition from recomb to fragmentation at intermediate P T.

16. C.NONAKA 16 Centrality dependence The values of Ncoll(b) are given by PHENIX collaboration Fragmentation Energy loss Recombination Transverse area of the overlap zone

17. C.NONAKA 17 Centrality dependence nucl-th/0306027 Centrality dependence of In peripheral collision, fragmentation becomes more and more important. p/  0

18. C.NONAKA 18 Nuclear Modification Factors ( I ) Nuclear modification factor Central collision Both results are consistent with data. Peripheral collision Uncertainty in pQCD is large. Jet quenching effects are much weaker.

19. C.NONAKA 19 Nuclear Modification Factors ( II ) Nuclear modification factor R F 2 < P T < 4 GeV R CP (baryon) > R CP (meson) Recombination 4 < P T < 6 GeV steep drop Transition from Recom. to Frag. High P T suppression Fragmentation

20. Elliptic Flow Comparison with Experimental data II

21. C.NONAKA 21 Elliptic Flow ( I ) Recomb. Frag. Elliptic flow is sensitive to initial geometry. Total elliptic flow At moderate P T recombination At high P T fragmentation Pressure gradient Collision plane > Perpendicular plane r(p t ): relative weight of the recombination contribution in spectra Energy loss Perpendicular plane > Collision plane

22. C.NONAKA 22 How to construct v 2 of hadrons ? (STAR:nucl-ex/0306007) up to intermediate P T Input: Parton Ouput: Hadron : relative weight of recombination in hadron yield Parton number scaling v 2 of parton v 2 of hadron R F

23. C.NONAKA 23 Elliptic Flow ( I ) Consistent with experimental data. Small deviation between full calculation and  -function approximation. v 2 of baryons saturates at a higher value than for mesons. At high P T, v 2 is dominated by fragmenta- tion. v 2 of baryon and meson is identical. We do not take into account bounding energy at low P T.

24. C.NONAKA 24 Elliptic Flow ( II ) Mesons Baryons Hydrodynamical model v 2 of  is almost the same as that of K. We use the same fragmentation functions of K (  ) for that of  (  ). input For saturation feature, the mass effect in v 2 is negligible. Hadrons with high mass may be disfavored by the fragmentation process. # of valence quarks

25. C.NONAKA 25 Comparison with Hydrodynamical Model # of valence quarks Universal v 2 curve Low P T Intermediate P T High P T Mass effect Fragmentation Saturation feature (Blast wave model) Hydrodynamical Model Model Recombination + Fragmentation v 2 is sensitive to hadron structure !

26. C.NONAKA 26 Summary We can reproduce the experimental data. PTPT Hydro, thermal model Recombination Fragmentation Hadron spectra Hadron ratio Centrality dependence High P T suppression of R AA and R CP Elliptic Flow Recombination + Fragmentation Model provides the solution of understanding RHIC data ! # of valence quark Intermediate P T High P T Fragmentation +