1. Quark Matter ’05 Budapest Aug 3-9, 2005 Marzia Nardi Centro Fermi (ROME) / CERN - TH J/  suppression

2. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 2 Outline Introduction Normal suppression in nuclear matter : preresonance absorption Anomalous suppression : –QGP (percolation, thermal dissociation) –Normal hadronic interactions (comovers) Discussion : SPS and RHIC Conclusions

3. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 3 Normal suppression General definition : J/  suppression in p-A collisions is well described by a probabilistic formula z b p A

4. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 4 From a fit of experimental p-A data (NA38,NA50):  abs =4.18 +- 0.35 mb ( hep-ex/0412036 ) In S-U collisions the same suppression is observed The normal suppression is interpreted as the absorption, in the nuclear environment, of the c-cbar pair before the J/  (or  ’ or  ) formation : preresonance absorption.

5. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 5 Anomalous suppression In peripheral Pb-Pb collisions the (J/  )/DY ratio is consistent with the normal suppression pattern In central Pb-Pb collisions (b<8- 8.5 fm) a much stronger suppression is observed: Anomalous suppression New In-In data follow the same pattern ! (NA60) NA38/NA50

6. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 6 The anomalous suppression is the candidate as the signal for deconfinement. There are two ways to prove it : –compare to absorption in a hadronic gas: less trivial extrapolation of p-A and S-U. “Known” parameters. Negative approach. –formulate a reasonnable model for a deconfinement scenario: define critical variable(s). Unknown parameters. Positive approach. More difficult !

7. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 7 Feed-down Only a fraction (~60%) of the observed J/  ’s are directly produced. The rest come from the decay of higher excited states (~30% from , ~10% from  ’). The feed-down has been studied in pN and  N interactions. The medium (confined / deconfined) affects differently the different charmonium states. Different properties (binding energy, size,…) implies different dissociation temperatures or different cross- sections for interactions with hadrons.

8. Models: suppression by hadron interactions Models: suppression by hadron interactions

9. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 9 Comover interactions After the normal absorption in the nuclear environment, the survived J/  ’s interact with secondary hadrons: J/  +h->DD. Crucial parameter : J/  -hadron inelastic cross-section, (   h inel ) a very uncertain parameter ! Theoretical estimates :   h inel ~0.1-1 mb Common assumptions: isoentropic, longitudinal expansion of the hadron gas (Monte Carlo calculations include transverse expansion); the density decreases as 1/  ; the interactions stop at the freeze-out.

10. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 10 From p-A and S-U to Pb-Pb Constraints from p-A and S-U data : the cross- section is very small and/or the comover density in these systems is negligible. Can the comover density have such a strong increase in Pb-Pb collisions to produce the observed suppression ? ?

11. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 11 Dual Parton Model [A.Capella et al.,Z.Phys.C3,329,(1980); Phys.Rep.236,225(1994) A.Capella et al.,nucl-th/0303055; hep-ph/0505032] The number of secondary hadrons at the initial (formation) time is given by the sum of two contributions, proportional respectively to the number of participants and to the number of binary N-N collisions (s=coordinate in the transverse plane) : The coefficients C 1 and C 2 are predicted in the DPM. RHIC : shadowing corrections (to moderate the increase of the produced secondaries)

12. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 12 DPM: results A.Capella,D.Sousa,nucl-th/0303055 A.Capella,E.Ferreiro,hep-ph/0505032 SPS: Pb-Pb SPS: In-In RHIC: Au-Au RHIC: Cu-Cu  abs =4.5 mb   h inel =0.65 mb (fitted to Pb-Pb)  abs =4.5 mb   h inel =0.65 mb (fitted to Pb-Pb)

13. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 13 Comover absorption: problems To reproduce the observed suppression in Pb-Pb, the density of comovers must by very high : can a hadron gas exist in these extreme conditions ? Different approach by Maiani et al. [hep=ph/0408150] : the density and temperature of the hadron gas is limited (T=170-180 MeV). The experimental suppression can not be reproduced.

14. Models: suppression by deconfinement Models: suppression by deconfinement

15. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 15 Thermal dissociation Potential extracted from lattice results [Digal et al., hep-ph/0110406; Phys.Rev.D64 ( 2001) 094015] below T c above T c

16. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 16 Thermal dissociation/2 Solve Schroedinger equation to get binding energy (M i (T)) and binding radius r i (T) Below T c : no bound state if M i (T) > V lim (T) Above T c : No bound state if r i (T)>r 0 (T) [Digal et al., hep-ph/0110406; Phys.Rev.D64 ( 2001) 094015]

17. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 17 T diss (  ’) ~ 0.2 T c T diss (  ) ~ 0.7 T c T diss (J/  ) ~ 1.1 T c To compare to the experimental data : introduce the T  b correlation introduce E T b One gets a curve qualitatively similar to the experimental pattern Thermal dissociation/3 J/  suppression pattern: 8%  ’ 57% dir. J/  35% 

18. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 18 Recent lattice calculations ‡ found: ‡ Datta et al., hep-lat/0312037 ; hep-lat/0403017 ¶ Datta et al., hep-lat/0409147 The threshold is lowered if the relative momentum is taken into account ¶. T dependence of the width ? Thermal Dissociation: new developments

19. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 19 New calculation of T diss [W. Alberico et al., hep-ph/0507084 ; C.Y. Wong hep-ph/0408020 ] Extract the internal energy from lattice results and use it in the Schroedinger equation : T diss (  ’) ~ T diss (  ) ~ 1.1 T c T diss (J/  ) ~ 1.7 - 2 T c In good agreement with the dissociation temperatures given by lattice !

20. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 20 Percolation critical phenomenon pre-equilibrium deconfinement prerequisite for QGP applicable to finite-size systems [First works: Baym, Physica (Amsterdam) 96A, 131 (1979) Celik et al., Phys. Lett. 97B (1980) 128]

21. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 21 Circular surface of radius R and N small discs of radius r<<R randomly distributed. R The cluster size increase with increasing n=N/  R 2 s n Percolation/2 ncnc

22. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 22 Cluster formation shows critical behaviour: in the limit of infinite R and N with constant n the cluster size diverges at a critical density n c. Onset of percolation : with  = 43/18 ; n c ~1.12-1.13 Percolation/3

23. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 23 The transverse size r c of the percolating partons is determined by the condition (Q c =1/r c ) : the density of the largest cluster at the percolation point is : with  c =1.72 (local percolation condition) Percolation/2

24. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 24 Percolation/3 For Pb-Pb at SPS: 1/r c ~ Q c ~ 0.7 GeV, N part = 150 (b ~ 8fm) [ S. Digal et al, hep-ph/0310354]

25. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 25 Percolation:results Q(  ) ~ 0.6 GeV Q(  ’) ~ 0.5 GeV  and  ’ are dissociated at the percolation (onset of deconfinement). Directly produced J/  ’s survive because Q(J/  )~1GeV; second threshold at N part =200-300 Results : Data: NA50 Coll.

26. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 26 Percolation: results Predictions for In-In :Predictions for Au-Au :

27. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 27 Regeneration [L. Grandchamp et al., Nucl.Phys.A715 (2003) 545; Phys.Rev.Lett.92 (2004) 212301.] “Two component” model: suppression in hadronic and QGP phase + statistical production at hadronization. In the QGP phase: in-medium properties of open- and hidden-charm states as deduced from lattice calculations. The regeneration is very important at higher energies.

28. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 28 Results At SPS energy the regeneration contribution is small; at RHIC it is the dominant one.

29. Comparison with new data !

30. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 30 Experiment : SPS No direct J/  suppression at SPS, only  and  ’ at onset of the deconfinement !!!! No direct J/  suppression at SPS, only  and  ’ at onset of the deconfinement !!!! L. Ramello, R.Arnaldi

31. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 31 Theory… Thermal model:Percolation :

32. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 32 Experiment : RHIC H. Buesching : More data on p-A are needed to define the normal suppression ! Compatible with regeneration, but… Compatible with regeneration, but…

33. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 33 Lattice and potential models : J/  dissolves at T~2Tc, the corresponding energy density is very high ! RHIC suppression is compatible with the one observed at SPS (?) RHIC data could be explained by the suppression of the  and  ’ components only, without recombination !!!

34. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 34 Improving models… Generally, deconfinement models assume the complete suppression for the charmonium states inside the “QGP” bubble: this is a really extreme assumption ! Finite-size effects can modify the suppression pattern in small systems and in peripheral collisions.

35. Conclusions

36. Marzia Nardi Centro Fermi (ROME) / CERN-TH Quark Matter ’05 – Budapest Aug 3-9, 2005 36 Conclusions The observed J/  suppression at SPS is qualitatively very similar to the pattern expected by deconfinement models. None of the models so far is completely satisfactory in the comparison with data; new effects: finite size, life-time, surface… RHIC data : recombination or higher states suppression ? There is room for work and progress !