1. The J/  as a probe of Quark-Gluon Plasma Erice 2004 Luciano MAIANI Università di Roma “La Sapienza”. INFN. Roma.

2. Erice. Sept. 1, 2004.L. MAIANI. Lez.12 Overview Confinement means that the heavy quarks in a c-cbar pair feel a constant attractive force (i.e. a linearly rising potential) In the deconfined phase, the attractive force between c and c-bar is screened by the Quark-Gluon Plasma (QGP) charmonia bound states “melt”, more and more with rising temperature; The onset of J/  suppression in relativistic heavy ion collisions (starting from the J/  s from the decay of higher charmonia) would signal the formation of QGP T. Matsui and H. Satz Phys. Lett. B178, 416 (1986); See R. Vogt, Phys. Rep. 310, 197 (1999).

3. Erice. Sept. 1, 2004.L. MAIANI. Lez.13 Overview (cont’d) However, we must control the “other” sources of absorption (nuclear, hadronic); several calculations of dissociation cross-section have been performed: See e.g.: L. Maiani, F. Piccinini, A.D. Polosa, V. Riquer,hep-ph/0402275; hep-ph/0408150 M.C. Abreu et al., Phys. Lett. B450, 456 (1999); M.C. Abreu et al., Phys. Lett. B477, 28 (2000). Latest analysis: http://na50.web.cern.ch/NA50/ I will report on our calculation: and apply the results to the SPS, NA50 data

4. Erice. Sept. 1, 2004.L. MAIANI. Lez.14 Overview (cont’d) This will be a “bottom up” presentation: from low temperature rising to high temperature (slowly!); 1 st lecture: an elementary introduction to the basic concepts; 2 nd lecture: results of calculations, application to the data. The main question: –DID QGP SHOW UP AT THE SPS? Our analysis says: –YES, MOST LIKELY !! –But we want to know better... –And to study QGP more, at RHIC, LHC,...

5. Erice. Sept. 1, 2004.L. MAIANI. Lez.15 Lecture 1: summary 1.A simple view of the collisions 2.Does the fireball thermalise? 3.Hadron gas 4.Hagedorn gas: limiting temperature vs. phase transition 5.The Polyakov loop and Lattice QCD results 6.Debye screening of charmonia

6. Erice. Sept. 1, 2004.L. MAIANI. Lez.16 time Which is which ? How can we tell ? The energy of the surviving nuclear fragments seen by the Zero Degree Calorimeter in NA50 gives a measure of the impact parameter b ! Wounded nucleons J. Bjorken, Phys. Rev. D27, 140 (1983) U. Wiedemann, CERN Academic Training 2004 1. Snapshots of relativistic heavy ion collision in the c.o.m. before... after...

7. Erice. Sept. 1, 2004.L. MAIANI. Lez.17 Bjorken’s estimate of the energy density of the fireball Nucleon number/unit area (increases with centrality) Longitudinal dimension 1.0 0.6 0.8 fm g(b) for Pb-Pb For central Pb-Pb collision:

8. Erice. Sept. 1, 2004.L. MAIANI. Lez.18 2. Does the fireball thermalize? Average initial density:  1000 particles/100 fm 3 = = 10 fm -3 If the initial particles are pions (?) Cross section:  40mb=4fm -2

9. Erice. Sept. 1, 2004.L. MAIANI. Lez.19 Does the fireball thermalize? (cont’d) Hadrons at freeze-out are thermal, T=170-180 MeV

10. Erice. Sept. 1, 2004.L. MAIANI. Lez.110 Antinori, Quark 2004 Thermal fits on the contrary don’t do badly at all........ relative particle abundances are found to be close to those expected at thermodynamical equilibrium for a grand-canonical system, even for the rare multi-strange particles........we do not seem to be able to observe a system of hadrons with a temperature beyond a maximum value of the order of 170 MeV. Does the fireball thermalize?

11. Erice. Sept. 1, 2004.L. MAIANI. Lez.111 3. Bottom up approach: the hadron gas All free particles. Interaction is introduced in the form of new particles, e.g.  etc. +: fermions; -: bosons. Boltzmann limit: exps <<1 lnz ≈ e  e 

12. Erice. Sept. 1, 2004.L. MAIANI. Lez.112 Resonance gas N eff Not only pions !! In spite of higher mass, higher resonances contribute to the energy density at temperatures around 150 MeV because of increasing multiplicities 3 N eff (see later)

13. Erice. Sept. 1, 2004.L. MAIANI. Lez.113 4. In the prehistory of modern hadron theory... Exponentially increasing density of hadronic levels

14. Erice. Sept. 1, 2004.L. MAIANI. Lez.114 Hagedorn bootstrap leads to an exponentially increasing density of hadronic levels T H =Hagedorn temperature ≈ maximum p T observed in hadronic high-energy reactions ≈ 150 MeV; K=3 preferred; Z cannot exist for T>T H ; Hadron matter cannot exist at temperatures >T H Exponentially rising density of hadronic resonances is also a property of the (confined) quark model, e.g. Bag Model What about experiment?

15. Erice. Sept. 1, 2004.L. MAIANI. Lez.115 J. Letessier and J. Rafelski, “Hadrons and Quark Gluon Plasma”, Cambridge Monogr. Part. Phys. Nucl. Phys. Cosmol. 18 (2002). Hagedorn’s thermodynamics NOTE:

16. Erice. Sept. 1, 2004.L. MAIANI. Lez.116 Varying the Hagedorn Temperature C= 0.7, mo= 0.66 GeV, T=158 MeV, or C= 1.66, mo= 0.88 GeV, T=173 MeV give very similar results for m<1.5 GeV T H must be consistent with observed temperatures at freeze-out!!

17. Erice. Sept. 1, 2004.L. MAIANI. Lez.117 Interpretation of the Hagedorn temperature N. Cabibbo and G. Parisi, Phys. Lett. 59B, 67 (1975) (and Erice ’75). Use non-relativistic, Boltzmann approx.: critical behaviour is determined by the high masss part of the spectrum, m>>T  c =1/T H E 0 >> m 0 reg.= terms regular at  c In conclusion: Rather than a limiting temperature...a second order phase transition!

18. Erice. Sept. 1, 2004.L. MAIANI. Lez.118 5. Order parameter for deconfinement The order parameter for the deconfinement transition is the Wilson- Polyakov loop F= free energy of a pair of static point sources (heavy quarks) at distance r confinement: F~ r  ∞, L  0 (T<Tc) de-confinement: F  0, L  0 (T<Tc) F. Karsch, Lattice QCD at High Temperature and Density arXiv:hep-lat/0106019 Chiral symmetry restored too

19. Erice. Sept. 1, 2004.L. MAIANI. Lez.119 Finite Temperature Lattice QCD NOTE:

20. Erice. Sept. 1, 2004.L. MAIANI. Lez.120 6. Debye screening of charmonia

21. Erice. Sept. 1, 2004.L. MAIANI. Lez.121 TDTD

22. Erice. Sept. 1, 2004.L. MAIANI. Lez.122  (1S), M= 3097 MeV  (2S), M= 3686 MeV Above threshold:  (3.77), M= 3770.0  2.4 MeV Y(4.04), M= 4040  10 MeV  c0 (1P), M= 3415 MeV  c1 (1P), M= 3510 MeV  c2 (1P), M= 3556 MeV  =0  = 357 MeV (T=178 MeV)  (3.77)  ’   3.5  2m c =2.64 GeV  = 0.192GeV 2  c =0.471

23. Erice. Sept. 1, 2004.L. MAIANI. Lez.123 Summing up The fireball produced in collisions with low energy density is ~ a pion gas at some T; Increasing , e.g. by increasing c.o.m. energy and/or centrality, T increases and higher resonances are produced; Increasing temperature becomes difficult because more and more energy goes in exciting resonances rather then increasing kinetic energy, i.e. T: dT/d  ~(  -  c ) 3/2, as we approach the limiting Hagedorn temperature; When hadron bags are in contact, bags fuse and quarks and gluon are liberated A cartoon representing this:  /T 4 T T Hag ~T c ~180 MeVHadron gas Quarks & gluons ~  2 /30(16+21/2n f ) ~16 Hagedorn gas  c and  ’ start fusing