1. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 1 Predictions for Quarkonium Properties Above Deconfinement in collaboration with Péter Petreczky ref: hep-ph/0705.2559 and in preparation Ágnes Mócsy RIKEN-BNL

2. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 2 IntroductionIntroduction Quarkonium properties at high T interesting proposed signal of deconfinement, matter thermometer, possibility of bound states in deconfined medium Quarkonium properties at high T interesting proposed signal of deconfinement, matter thermometer, possibility of bound states in deconfined medium Need to calculate quarkonia spectral function quarkonium well defined at T=0, but can significantly broaden at finite temperature contains all information about a given channel: unified treatment of bound states, threshold effects, and the continuum can be related to experiments Need to calculate quarkonia spectral function quarkonium well defined at T=0, but can significantly broaden at finite temperature contains all information about a given channel: unified treatment of bound states, threshold effects, and the continuum can be related to experiments

3. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 3 Spectral Function  bound states/resonances &  continuum above threshold  (GeV) nonrelativistic Green’s function  ~ M J/ , s 0 nonrelativistic S-wave P-wave medium effects - important near threshold PDG 06 re-sum ladder diagrams first in vector channel Strassler,Peskin PRD 91 also Casallderey-Solana,Shuryak,04 S-wave also Cabrera,Rapp 07

4. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 4 Spectral Function +   s 0 perturbative  bound states/resonances &  continuum above threshold  (GeV) nonrelativistic Green’s function  ~ M J/ , s 0 nonrelativistic PDG 06

5. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 5 Spectral Function Unified treatment: bound- and scattering states, threshold effects together with relativistic perturbative continuum Unified treatment: bound- and scattering states, threshold effects together with relativistic perturbative continuum  bound states/resonances &  continuum above threshold  (GeV) +   s 0 perturbative  ~ M J/ , s 0 nonrelativistic smooth matching details do not influence the result nonrelativistic Green’s function + pQCD PDG 06

6. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 6 Constructing the Potential Constrain the potential by lattice data Free energy of static Q-Qbar pair in deconfined phase what we know: Kaczmarek,Karsch,Zantow,Petreczky, PRD 04 no temperature effects strong screening effects Free energy - contains negative entropy contribution - provides a lower limit for the potential V(r,T)

7. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 7 no temperature effects Constructing the Potential Potential assumed to share general features with the free energy also motivated by Megías,Arriola,Salcedo PRD07 Constrain the potential by lattice data strong screening effects

8. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 8 S-wave Charmonium in Gluon Plasma resonance-like structures disappear already by 1.2Tc strong threshold enhancement contradicts previous claims resonance-like structures disappear already by 1.2Tc strong threshold enhancement contradicts previous claims  higher excited states gone  continuum shifted  1S becomes a threshold enhancement lattice Jakovác,Petreczky, Petrov,Velytsky, PRD07 Mócsy, Petreczky hep-ph/0705.2559 cc

9. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 9 S-wave Charmonium in Gluon Plasma resonance-like structures disappear already by 1.2T c strong threshold enhancement above free case indication of correlation height of bump in lattice and model are similar resonance-like structures disappear already by 1.2T c strong threshold enhancement above free case indication of correlation height of bump in lattice and model are similar Mócsy, Petreczky hep-ph/0705.2559 details cannot be resolved

10. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 10 S-wave Charmonium in Gluon Plasma Mócsy, Petreczky hep-ph/0705.2559 ” spectral function unchanged across deconfinement” LQCD measures correlators N.B.: 1st time 2% agreement between model and lattice correlators for all states at T=0 and T>T c Unchanged LQCD correlators do not imply quarkonia survival: Lattice data consistent with charmonium dissolution just above T c N.B.: 1st time 2% agreement between model and lattice correlators for all states at T=0 and T>T c Unchanged LQCD correlators do not imply quarkonia survival: Lattice data consistent with charmonium dissolution just above T c

11. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 11 S-wave Quarkonium in QGP J/  at 1.1T c is just a threshold enhancement  survives up to ~2T c with unchanged peak position, but reduced binding energy Strong enhancement in threshold region - Q and Qbar remain correlated J/  at 1.1T c is just a threshold enhancement  survives up to ~2T c with unchanged peak position, but reduced binding energy Strong enhancement in threshold region - Q and Qbar remain correlated J/  

12. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 12 Most Binding Potential need strongest confining effects = largest possible r med Find upper limit for binding r med = distance where exponential screening sets in NOTE: uncertainty in potential - have a choice for r med or V ∞, our choices physically motivated all yield agreement with correlator data

13. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 13 Binding Energy Upper Limits When binding energy drops below T state is weakly bound thermal fluctuations can destroy the resonance Upsilon remains strongly bound up to 1.6T c Other states are weakly bound above 1.2T c strong binding weak binding

14. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 14 for weak binding: E bin <T for strong binding E bin >T Kharzeev, McLerran, Satz PLB 95 Thermal Dissociation Widths  Rate of escape into the continuum due to thermal activation:   related to the binding energy weak binding  

15. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 15 ConclusionsConclusions lattice data does not necessarily imply survival of quarkonia all states except  and  b are dissolved by 1.2 T c lattice data does not necessarily imply survival of quarkonia all states except  and  b are dissolved by 1.2 T c Dissociation condition: thermal width > 2 binding energy upper limits Dissociation condition: thermal width > 2 binding energy upper limits Upsilon suppressed at LHC but less suppresed at RHIC Upsilon suppressed at LHC but less suppresed at RHIC J/   ’’ bb 1.2T c 2T c 1.3T c 1.2T c Threshold is enhanced over free propagation =>> correlations between Q-Qbar may remain strong regeneration from primordially correlated, not independent Q-Qbar  survival  J/   survival   Consequences for LHC Karsch et al

16. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 16 ****The END****

17. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 17 Lattice etac Jakovác,Petreczky,Petrov,Velytsky, PRD 07 pseudoscalar spf unchanged up to 1.5T c within errors, but details cannot be resolved cc cc most recent results if spectral function unchanged across deconfinement

18. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 18 Lattice Spectral Function Jakovac,Petreczky,Petrov,Velytsky, PRD 07 pseudoscalar spf unchanged up to 1.5T within errors, but details cannot be resolved most recent results

19. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 19 note on Correlators if spectral function unchanged across deconfinement LQCD measures correlators lattice data from Jakovác,Petreczky,Petrov,Velytsky, PRD 07 bb cc bb

20. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 20 T  0 Spectral Function  gluon plasma with heavy quarks  results for the  c reasonably good agreement between model and data ground state peak, excited states, and continuum identified modellattice Jakovac,Petreczky,Petrov,Velytsky, PRD 07

21. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 21 Most binding Note the reduced binding energy for the J/  already at 1.2 T c ! Even for maximal binding: J/  at 1.6 T c is just a threshold enhancement  survives up to ~2T c with peak position unchanged Also note strong enhancement in threshold region: Q and Qbar remain correlated Note the reduced binding energy for the J/  already at 1.2 T c ! Even for maximal binding: J/  at 1.6 T c is just a threshold enhancement  survives up to ~2T c with peak position unchanged Also note strong enhancement in threshold region: Q and Qbar remain correlated Most binding possibility J/  

22. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 22 lQCD “J/  survival” current knows about the channels Note: no T=0 data for comparison quenched QCD Euclidean correlation function spectral decomposition MEM Peak still present at J/  mass at 1.62T c ! Gone only at higher T Peak still present at J/  mass at 1.62T c ! Gone only at higher T Asakawa, Hatsuda, PRL 04 other features identified with lattice artifacts Spectral function at finite T from Lattice

23. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 23 lQCD Correlators Datta,Karsch,Petreczky,Wetzorke, PRD 04 if spectral function unchanged across deconfinement look directly at the correlator cc cc  c survives to 2T c &  c melts at 1.1T c

24. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 24 lQCD Bottomonium Jakovac,Petreczky,Petrov,Velytsky, PRD 07 “the  b puzzle” - same size as the J/  why are the  b and J/  correlators so different “the  b puzzle” - same size as the J/  why are the  b and J/  correlators so different bb bb

25. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 25 Full LQCD Aarts,Allton,Oktay,Peardon,Skullerud, hep-lat/0705.2198 S-waves survive up to 2T c P-waves melt away below 1.2T c recent full LQCD results show similar behavior

26. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 26 T=0 Continuum in Quenched QCD relativistic continuum seen on lattice G does not depend on the parameters good agreement between model and data this contradicts statements made in the recent literature

27. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 27 BottomoniumBottomonium ground state survives deconfinement other states dissolved medium modification of the 1S peak is small agreement found with lattice correlators

28. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 28 Scalar Channel so look at the derivative following Umeda 07 constant contribution (G i low ) to the correlator at finite T quark number susceptibility 1.5 Tc Threshold enhancement of spf compensates for dissolution of states Agreement with lattice data for scalar charmonium and bottomonium Threshold enhancement of spf compensates for dissolution of states Agreement with lattice data for scalar charmonium and bottomonium

29. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 29 Scalar Channel >> deconfinedconfined in free theory behavior explained using ideal gas expression for susceptibilities: seems to indicate deconfined heavy quarks carry the quark-number at 1.5 Tc behavior explained using ideal gas expression for susceptibilities: seems to indicate deconfined heavy quarks carry the quark-number at 1.5 Tc charm 1.5 Tc bottom 1.5 Tc

30. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 30 With this potential: 1S charmonium peaks found unmodified at 1.2Tc binding energy ( E binding =s 0 -M ) is small so dissociation by thermal fluctuations is likely all states, except 1S bottomonium, are gone by 1.5T c With this potential: 1S charmonium peaks found unmodified at 1.2Tc binding energy ( E binding =s 0 -M ) is small so dissociation by thermal fluctuations is likely all states, except 1S bottomonium, are gone by 1.5T c charmbottom

31. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 31 Internal Energy as Potential

32. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 32 Screened Cornell

33. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 33 Wong Potential  apparent agreement but Wong 05  admixture of free and internal energies 1.) reports 1S charmonium dissociation at 1.62T c binding energy ~ 0.2MeV 2.) assumes only ground state contributes to correlation function 3.) neglects contribution from the wave fct at the origin, which decreases when screened undetectable contrary to lattice findings

34. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 34 hybrid potentials in quenched QCD

35. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 35 internal energy as potential Cabrera, Rapp hep-ph/0611134 Petrov QM06  big jump in the critical region huge increase in mass  no agreement w/ lattice

36. Ágnes MócsyLast Call for LHC Predictions @ CERN 05 31 07 36 etabetab