1. Onset of J/  Melting in Quark- Gluon Fluid at RHIC Taku Gunji Center for Nuclear Study University of Tokyo Paper: Phys. Rev. C 76:051901 (R), 2007 Collaboration with: H. Hamagaki (CNS, Univ. of Tokyo), T. Hatsuda, T. Hirano, Y. Akamatsu (Phys. Dept. Univ. of Tokyo) 1 Quark Matter 2008, Jaipur, India, 2008/2/9

2. Outline Physics Motivation J/  suppression at RHIC Hydro+J/  model Determination of J/  melting temperature J/  suppression in Hot-wind Calculation of J/  v2 Future plan – forward rapidity Summary 2

3. Physics Motivation Quark-Gluon-Plasma (QGP) –New state of QCD matter expected to be created at high temperature (T c = 160-190MeV). Quarkonia suppression in QGP –Color Debye Screening T.Matsui & H. Satz PLB178 416 (1986) –Suppression depends on temperature (density) and radius of QQbar system. T J/  : 1.6Tc~2.0Tc T , T  ’ : ~ 1.1Tc –Serve as the thermometer in QGP. 3 M.Asakawa and T.Hatsuda, PRL. 92, 012001 (2004) A. Jakovac et al. PRD 75, 014506 (2007) G.Aarts et al. arXiv:0705.2198 [hep-lat]. (Full QCD)

4. J/  Suppression at RHIC J/  suppression in A+A Collisions at RHIC (dN/dy) AuAu (dN/dy) pp x R AA = CNM effects Gluons shadowing Nuclear absorption Evaluated from J/ production in d+Au collisions. A.Adare et al. (PHENIX) arXiv:0711.3917 4 Au+Au: A. Adare et al. (PHENIX) PRL 98 232301 (2007) Cu+Cu: A. Adare et al. (PHENIX) arXiv:0801.0220 Au+Au (|y|<0.35) Au+Au (1.2<|y|<2.2) Cu+Cu (|y|<0.35) Cu+Cu (1.2<|y|<2.2) J/  suppression at mid-rapidity at RHIC is compatible to CNM effects except most central Au+Au collisions. Stronger suppression at forward rapidity than CNM effects.

5. J/  Suppression at RHIC Two proposed scenarios: –Gluon dissociation + recombination Dissociation by thermal gluons supplemented by the regeneration of J/  from ccbar coalescence –R. Rapp et al. [EPJC34, 91 (2005), arXiv:0712.2407], L. Yan et al. [PRL97,232301 (2006)], R. Thews [NPA783 301(2007)], A.Andronic et al.[nucl-th/0701079], etc –Need to take into account charm production and its modification in the medium, which are still unclear at RHIC. –Sequential Melting of J/  Absence of the feed down J/  from  c and  ’ (30-40%) just above Tc and melt of direct produced J/ . –F. Karsch et al., PLB 637 (2006) 75 –Feed down fraction is unclear at RHIC (<~40% 90%CL). –This is still in a qualitative level and need to take into account the space-time evolution to study dynamically. 5

6. Hydro+J/  model First attempt for the study of sequential suppression of charmonia at RHIC. –Incorporate J/ ,  c and  ’ into the evolution of matter. Evolution of matter : (3+1)-dimentional relativistic hydrodynamics –T. Hirano and Y. Nara, PRL 91, 082301, (2003) –T. Hirano and Y. Nara, PRC 69, 034908, (2003) –T. Hirano and K. Tsuda, PRC 66, 054905, (2002) –http://tkynt2.phys.s.u-tokyo.ac.jp/~hirano/parevo/parevo.html J/ ,  c and  ’ : impurity traversing through the matter –Assume three kinds of interaction inside QGP. »Free Streaming »Hot-Wind »Complete Thermalization 6 T. Gunji et al. Phys. Rev. C 76:051901 (R), 2007

7. Modeling of J/  suppression Survival Prob. In the medium: Decay Width: Motion of J/  : free streaming Total Survival Prob. Free Parameters: –(T J/ , T , f FD ) J/  x0x0   (p T ) 7 x 0 (Production point) is distributed according to the spatial N col distribution. p T is distributed according to the measured J/ distribution. J/ azimuthal angle, , is flat (0 to 2). T. Song, Y. Park and S. H. Lee Phys.Lett.B659:621-627,2008.

8. Model results Best Fit @ (T J/ , T , f FD ) = (2.00T c, 1.34T c, 10%) Bar: uncorrelated sys. Bracket: correlated sys. Onset of J/  suppression at N part ~ 160. (  Highest T at N part ~160 reaches to 2.0T c.) Gradual decrease of S J/  tot above N part ~160 reflects transverse area with T>T J/  increases. T J/  can be determined in a narrow region. 8 Contour map 11 22

9. Decay width below T J/  Decay width : 9 T. Song, Y. Park and S. H. Lee Phys.Lett.B659:621-627,2008. Suppression pattern is similar up to  < 0.2.   (T=2Tc)<~0.2 GeV

10. Hot-wind scenario Melting temperature depends on the relative velocity between J/ and fluid. 10 H. Liu, K. Rajagopal and U. A. Wiedemann : hep-ph/0607062. (T J/, T , FD) = (2.0T c, 1.34T c, 10%) Magnitude of the suppression in hot wind is similar to the free streaming case. Gradual decrease above 50 is the effect of hot-wind. Next is SAA vs. pT! Free streaming Hot-wind

11. pT dependence of S AA 11 Free streaming Hot-wind 20-30% 0-10% 40-50%50-60% pT dependence of the suppression is greatly different. Suppression is flat in case of free streaming. Suppression is stronger for high pT J/  in case of hot-wind as predicted. Critical pT in hot-wind relates to the achieved temperature in fluid. (T J/, T , FD) = (2.0T c, 1.34T c, 10%)

12. Calculation of J/  v2 12 Free streaming Hot-wind (T J/, T , FD) = (2.0T c, 1.34T c, 10%) 20-30% 0-10% 40-50%50-60% v2 = 3% v2 is small (<1%) in case of free streaming. v2 is larger for higher pT J/  in case of hot-wind (~3% v2). v2 increases above critical pT.

13. Thermalization Scenario Assume that J/ flows in the fluid (T>T fo ). –J/ moves according to fluid velocity (T>T fo ) and freeze-out at T fo. Momentum of J/ is distributed according to Boltzman eq. Then boost J/ according to fluid velocity. 13 10-20% 0-10% 20-30% 40-50% v2 = 30% T fo = 1.0Tc v2 is much larger than that of free streaming and hot-wind case. Large v2 is predicted in low-mid pT since most of J/in low-mid pT are followed by flow of the fluid. Magnitude is similar to the case of coalescence model. But tendency is much different for high pT. Thermalization Free streaming Hot-wind v2 = 30%

14. Future plan – forward rapidity 14 Stronger suppression at forward rapidity : CGC? (M. Nardi ’ s talk Session VI) Further studies will be done in conjunction with CGC.

15. Summary J/  suppression at RHIC was investigated using hydro+J/  model. –Dynamical and quantitative approach to the sequential suppression. Comparison of the experimental survival probability shows: –Observed suppression is described well with T J/  ~2.0T c at mid-rapidity and T J/  can be determined in a narrow region. –Decay width seems to be  (T=2Tc)<0.2 GeV. Hot-wind calculation was done in this model. –Large suppression and ~3% v2 in high pT region can be seen in a scenario with hot-wind. High pT J/psi is important for this model. –Critical pT depends on the achieved temperature in the fluid. Thermalization scenario shows : –larger v2 (10-30%) in low-mid pT region (pT<4 GeV) and small v2 (<5%) in high pT region. Much different from other scenarios. Further studies of stronger suppression in forward rapidity will be done in conjunction with CGC. Effect of recombination will be studied. 15

16. Back Up Slides

17. Feeze-out Temp. Dependence Assume that “ survived ” J/ flows in the fluid. –J/ moves according to fluid (T>T fo ) and freeze-out at T fo. Momentum of J/ is distributed according to Boltzman eq. 18 10-20% 0-10% 20-30% 40-50% v2 = 30% T fo = 1.0Tc T fo = 1.1Tc T fo = 1.2Tc Most of low-mid pT J/y is from flowed J/y. Large v2 is predicted due to the flow of fluid. It depends on the freeze-out temp. of J/y. Magnitude is similar in case of coalescence model. But tendency is Much different.

18. R AA (1.2<|y|<2.2) /R AA (|y|<0.35) 1 R AA 0 1 0 Bar: uncorrelated error Bracket : correlated error Forward rapidity Stronger suppression at forward rapidity. –Gluon saturation (CGC)? Leading to suppression of charm production 25  =2 Open charm yield in Au+Au @ 200 GeV  =0 ~60% Suppression pattern due to CGC K. L. Tuchin hep-ph/0402298

19. (T J/ ,T  ) = (2.02T c,1.22T c ) FD = 30% (y=0), FD= (35-50)% (y=2) Forward Rapidity Experimental S J/  tot (y=2) –CNM at y=0 & CGC suppression (y=2/y=0) Model S J/  tot (y=2) –Hydro at y=2 Need larger feed-down fraction at y=2. Onset of suppression at N part ~ 240? 2.02T c is achieved at N part ~240 at y=2? Further analysis is on going. 26 S J/  (y=0) =R AA /CNM (y=0,  abs =1mb) S J/  (y=2) =R AA /R(CGC)/CNM (y=0,  abs =1mb)

20.  c feed-down fraction Feed down fraction –~40% of J/  from  c and  ’ 34 χ,1,2  J/ ~30% ΄  J/ 5.5%

21. Complete Thermalization T>Tc: J/  moves according to fluid velocity vector. T~Tc: J/  freeze-out: –Re-arrange the J/  px, py and pz using Boltzman Eq (in local fluid coordinate). –Then boost J/  according to the fluid velocity vector. 22

22. pT and v2 of flowed J/  J/  participating in the flow of the matter dN/dpT [A.U] v2 23

23. Melting temperature Spectral analysis in quenched lattice. J/  cc cc Datta, Karsch, Petreczky & Wetzorke, hep-lat/0312037 Asakawa & Hatsuda, hep-lat/0308034 T c ~270 MeV J/  may survive up to ~2T c.  c and y’ would melt at ~1T c. T. Hatsuda QM2006 (hep-ph/0702293) 27

24. Melting temperature Spectral analysis in full lattice (N f =2). T. Hatsuda QM2006 (hep-ph/0702293) 28 J  cc Aarts et al., hep-lat/0610065 Even with the light quarks, J/  may survive up to ~2T c. T c ~170 MeV

25. p T [GeV] Hydro. calculation (3+1) dimensional hydro. ( ,x,y,  s ) –r, T, v(v x,v y ) at ( ,x,y,  s ) –  0 = 0.6 fm/c, T c =170 MeV –Massless parton gas (u,d,s,g) –Tuned to reproduce dN/dh 31  Hydro data are open to public: http://tkynt2.phys.s.u-tokyo.ac.jp/~hirano/parevo/parevo.html T.Hirano and Y.Nara, PRL91,082301(2003); T.Hirano and Y. Nara PRC69,034908(2004); T.Hirano and K.Tsuda, PRC66,054905(2002).

26. Hydro+Jet model Hydro+“hard probe” works. –Identified hadron spectrum –Back-to-back correlation –Pseudo-y dependence of R AA 32 T. Hirano and Y. Nara PRL91 082301 (2003) p T [GeV] T. Hirano and Y. Nara PRC69 034908 (2004) T. Hirano and Y. Nara PRC68 064902 (2003)

27. T J/  comparison This study shows T J/  ~2.02T c. Estimation of T J/  in 3-falvor QCD from quenched lattice QCD. 33 = 1.7= 270/170 Asakawa & Hatsuda, hep-lat/0308034 This coincides with the result obtained in this study.

29. Map of Suppression Example of suppression map –10-20% centrality, T melt = 1.0Tc Production probability map Temperature Field (=0.6 fm/c) Suppression Map (integrated over ) Similar to surface emission! Main component of survival J/psi Small component (gained by large Ncoll ) 9

30. Sensitivity for T J/  & FD T J/  /T c = 1.88, 1.94, 2.00, 2.06, 2.12 9 T J/y can be determined in a narrow region around 2.00T c.

31. Forward-Rapidity Use hydro at y=2 –(T J/y, T , FD) free (2.08Tc, 1.62Tc, 70%) Chi2 = 0.83 –(T J/y, T  ) fixed (T J/y, T  ) = (2.0, 1.34) FD45%, chi2 = 10 15

32. Hot-wind in hydro+J/ model T. Gunji, H. Hamagaki, T. Hatsuda, T. Hirano, Y. Akamatsu : Phys. Rev. C 76:051901 (R), 2007 Parallel talk at QM2008 by T. Gunji, Feb. 9 th SessionXVIII 15:20~15:40 Melting temperatures : (T J/, T  ) = (2.0T c, 1.34T c ) 10% feed-down correction 1: Survival Probability of J/  vs. N part 20-30% N part ~ 170 H. Liu et al. PRL.98:182301,2007 J/  suppression from Hot-wind scenario was calculated in hydro+J/  model. Overall suppression pattern is similar in both cases. Larger suppression and large v2 (~3%) in the high pT region in a scenario with hot-wind. 2: Survival Probability of J/  vs. pT 3: v2 of J/  vs. pT Melting temperature in hot-wind