Quarkonia above Deconfinement and Potential Models

1. QWG Meeting BNL June 27-30 06 Quarkonia above Deconfinementand Potential Models Ágnes Mócsy

2. QWG Meeting BNL June 27-30 06 potential models vs lattice QCD • some features of quarkonia spectral functions agree BUT there are unreconciled inconsistencies • 1st analysis of correlators from potential models • our attempts to understand the discrepancies summary

3. QWG Meeting BNL June 27-30 06 J/(1S) ’(2S) c(1P) 0.9fm 0.7fm 0.4fm T J/ suppression “unambiguous” signal of deconfinement T. Matsui, H. Satz 1986 • in quark-gluon plasma the color Coulomb-force between heavy Q and Q gets Debye-screened Rscreening < RQQquarkonium dissociates • sequential suppression F. Karsch, M. Mehr, H. Satz 1988 • modification of quarkonia properties with temperature could tell about deconfinement it all started in 1986

4. QWG Meeting BNL June 27-30 06 correlationfunctions of hadronic currents reliably calculated spectral function (,T) M E M c0 P. Petreczky et al 2006 also: T. Umeda T. Hatsuda, M. Asakawa S. Datta et al 2004 1P charmonium is gone at 1.16Tc since 2004 from QCD

5. QWG Meeting BNL June 27-30 06 c contradiction with early potential model predictions S. Datta et al 2004 1S charmonium survives up to 1.5Tc correlatorspectral function does not change spectral function properties do not change from

6. QWG Meeting BNL June 27-30 06 • At what temperature do heavy quark bound states disappear? • Can modification of quarkonia properties be understood via a temperature-dependent screened potential? • If yes, what is the potential? • If not, how can we explain quarkonium dissociation? What is the mechanism behind quarkonia melting?

7. QWG Meeting BNL June 27-30 06 heavy Q-Q interactions are mediated by a potential T = 0 V(r) confined • success for spectroscopy • lattice confirmed • obtainable from QCD deconfined J/ T > Tc we don’t know r assume a temperature-dependent potential V(r,T) & solve Schrödinger’s equation to obtain properties of QQ potential MODEL

8. QWG Meeting BNL June 27-30 06 F. Karsch, M. Mehr, H. Satz, 1988 E. Shuryak, I. Zahed, 2004 W. Alberico et al 2005 • screened Cornell potential: • fitted lattice internal energy: • Wong potential: mixture of lattice internal & free energy Common: all could keep the J/ up to 1.5 Tc Is this enough to be consistent with lattice? O. Kaczmarek et al 2004 C. Y. Wong 2005 screened potentials

9. QWG Meeting BNL June 27-30 06 bound states/resonances + continuum ÁM, P. Petreczky, hep-ph/0411262 hep-ph/0512156 hep-ph/0606053  = + Schrödinger eq with V(r,T) Mi(T) bound state mass Fi(T) amplitude asymptotic value of V(r,T) s0(T) threshold I. model spectral function

10. QWG Meeting BNL June 27-30 06 the c0 is gone just above Tc increase in correlator due to continuum qualitative agreement with lattice ÁM, P. Petreczky 2005 S. Datta et al 2004 c0correlator

11. QWG Meeting BNL June 27-30 06 • c correlator does not agree with lattice increase due to continuum, decrease due to amplitude reduction • correlator implies change in spectral function • disagrees with lattice feature for all screened potentials ÁM, P. Petreczky 2005 S. Datta et al 2004 ccorrelator

12. QWG Meeting BNL June 27-30 06 • no assumption for spectral function needed • drastic change in 1S mass & amplitude • inconsistent with lattice • even though 1S survives the spectral function is strongly modified S-wave lattice internal energy A. Jakovác et al 2006 ÁM, P. Petreczky, J. Casalderrey-Solana, in prep. II. nonrelativistic Green’s function

13. QWG Meeting BNL June 27-30 06 • inconsistency with lattice data is even worse how could we - can we - produce agreement with lattice? Wong potential A. Jakovác et al 2006 ÁM, P. Petreczky hep-ph/0606053 Green’s fct. cont.

14. QWG Meeting BNL June 27-30 06 ÁM hep-ph/0606124 no temperature-dependent screening • no modification of the 1S properties - use PDG • melting of 2S and 3S states • melting of the 1P state • continuum threshold s0 reduction T = 0 T Tc   s0 1P s0 1S s0 s0 2S 3S instead consider a toy model

15. QWG Meeting BNL June 27-30 06 c0 c ÁM 2006 • choice of s0 can reproduce lattice correlators • c unchanged & c0 increased • compensate for the melting of higher excited states above Tc with the decrease of the threshold the toy model

16. QWG Meeting BNL June 27-30 06 • maybe works BUT note: “screened” not screened • screening might not be the mechanism governing quarkonia melting tscreening>tQQ “screened” Cornell potential ÁM, P. Petreczky, J. Casalderrey-Solana, in prep. with nonrelativistic Green’s fct.

17. QWG Meeting BNL June 27-30 06 • temperature-dependent screened potentials have problems even though 1S can survive and 1P melts • two different analysis of spectral functions and correlators not consistent with lattice QCD • medium modification cannot be described by a simple Debye screening picture • gluo-dissociation effect  finite width  Green’s fct current investigation conclusion

18. QWG Meeting BNL June 27-30 06 Péter Petreczky Jorge Casalderrey-Solana Dima Kharzeev Helmut Satz my thanks to

19. QWG Meeting BNL June 27-30 06 Rate of J/ escape into the continuum D. Kharzeev, L. McLerran, H. Satz 1995 binding energy • T >> EQQ screening • continuum dominates • all states get modified • T << EQQ gluo-dissociation effect discrete states dominate • ground state unaffected T >Tc gluon sector relevant F. Karsch et al 1996 E. Shuryak 1978 G. Bhanot, M.Peskin 1979