Ágnes Mócsy - RBRC 1 Ágnes Mócsy Quarkonium Correlators and Potential Models DESY, Hamburg, Oct 17-20, 2007

Ágnes Mócsy - RBRC 2 Content of this talk  Why interested in quarkonia at finite temperature  Finite T lattice quarkonia studies  Potential models, use of lattice data to constrain potential  Spectral functions & correlators  Upper bound on quarkonium dissociation temperatures  Conclusions

Ágnes Mócsy - RBRC 3 Quarkonia at Finite Temperature “unambiguous signature of QGP formation” binding in quarkonium reduced dissociation: D  r Quarkonium Deconfinement at high temperatures formation of QGP (quark-gluon plasma) chromo-electric screening large increase in number of d.o.f. Matsui,Satz,PLB 86 RBC-Bielefeld Coll.07

Ágnes Mócsy - RBRC 4 Sequential Suppression Hierarchy in binding energy T 0.9 fm0.7 fm 0.4 fm 0.2 fm J/  (1S)  c (1P)  ’(2S)  b (1P)  b ’(2P)  (1S)  ’’(3S) Quarkonia melting as QGP thermometer Karsch,Mehr,Satz 88 Satz 06 Karsch,Mehr,Satz 88 Satz 06

Ágnes Mócsy - RBRC 5 PHENIX

Ágnes Mócsy - RBRC 6 Experimental J/  suppression NA50 at SPS (0<y<1) PHENIX at RHIC (|y|<0.35) Bar: uncorrelated error Bracket : correlated error Global error = 12% is not shown In heavy ion collisions - dilepton rates PHENIX Preliminary J/  suppression measured SPS RHIC LHC talk by C. Laurenco O. Drapier but still not understood

Ágnes Mócsy - RBRC 7 Theoretical Tools Quarkonium studies at T  0 Potential Models Matsui,Satz PLB 86 Karsch,Mehr,Satz Z.Phys C 88 Digal,Petreczky,Satz PLB 01, PRD 01 Shuryak,Zahed PRD 04 Wong PRC 05 Alberico et al PRD 05 Blaschke EurPJ 05 Mocsy,Petreczky EurPJ 05, PRD 06 Mannarelli, Rapp PRC 05, Nucl.Phys A 06 Cabrera, Rapp 06, EurPJ 07 Alberico et al PRD 07 Wong,Crater PRD 07 Mocsy,Petreczky PRL 07 Umeda et al EurPJ 05 Asakawa,Hatsuda PRL 04 Datta et al PRD 04 Iida et al PRD 06 Jakovac et al PRD 07 Aarts et al 07 Lattice QCD

Ágnes Mócsy - RBRC 8 Lattice QCD at Lattice QCD at T  0 directly calculated Euclidean-time correlatorSpectral function extracted from correlators using Maximum Entropy Method large uncertainties T-dependence of correlators spectral fct unchanged  G/G rec =1 G/G rec  1  modified spectral fct G/G rec =1  unchanged spectral fct Data Interpretation: ?

Ágnes Mócsy - RBRC 9 Lattice Correlators Charmonium correlators Initial interpretation: flat correlator = quarkonium survival dissociation T = where deviation significant Jakovác et al, PRD cc cc J/  and  c survive up to 1.5-2T c  c melts by 1.1 T c gluon plasma Bound states in the deconfined medium ? Shuryak,Zahed, PRD 04

Ágnes Mócsy - RBRC 10 Lattice Correlators  b same size as the J/ , so why are the  b and J/  correlators so different ? bb bb Bottomonium Correlators Jakovác et al, PRD07 Initial interpretation: flat correlator = quarkonium survival dissociation T = where deviation significant  and  b survive well above 2T c  b melts by 1.1 T c

Ágnes Mócsy - RBRC 11 Lattice Spectral Functions talk by G.Aarts WARNING: broad peak large uncertainties likely contaminated by excited states & lattice artifacts often interpreted as 1S ground state survives above T C Jakovác et al, PRD 07 Aarts et al, [hep-lat]

Ágnes Mócsy - RBRC 12 Lattice Screening … yet still some quarkonium states would survive unaffected? Strong screening seen in lattice QCD Entropy contribution - not the potential ! N f =2+1 RBC-Bielefeld Coll.07 Free energy of a static Q-antiQ : no T effects strong screening r med = distance where exponential screening sets in talk by O. Kaczmarek

Ágnes Mócsy - RBRC 13 Potential Models  Assume potential model works at finite T Potential model valid if interaction instantaneous t gluon  t QantiQ  Construct a T-dependent potential  Calculate the spectral function Unified treatment of bound-, scattering states, threshold effects  Determine the correlators G  Compare G/G rec to lattice data Prescription: T-matrix Cabrera,Rapp,07

Ágnes Mócsy - RBRC 14 Spectral Function NR Green’s function  ~ M QantiQ and s 0 S-wave P-wave NR Green’s function + pQCD Bound states/ResonancesContinuum above threshold s 0 +   s 0 smooth matching details do not influence the result Mócsy,Petreczky, [hep-ph] potential see also talk by R.Rapp

Ágnes Mócsy - RBRC 15 Potential at Finite T talk by M.Laine Derived from pQCD Using lattice data on free and internal energy We don’t know what it is Digal,Satz,Wong,Manarelli,Rapp,Mocsy, Petreczky,Alberico …  ladder resummation  effective theory approach NRQCD,pNRQDC resummed pQCD

Ágnes Mócsy - RBRC 16 Construct Potential at T>T c Assume to share general features with the free energy Potential constrained by lattice data negative entropy contribution Megias,Arriola,Salcedo,PRD 07 also motivated by

Ágnes Mócsy - RBRC 17 Free Propagation charmonium 30-40% bottomonium 70%  c (1S)  c (1P) Free case gives upper bound on correlator decrease

Ágnes Mócsy - RBRC 18 S-wave Charmonium Resonance-like structures disappear already by 1.2T c seemingly contradicts previous claims Strong threshold enhancement above free propagation indicates correlation Resonance-like structures disappear already by 1.2T c seemingly contradicts previous claims Strong threshold enhancement above free propagation indicates correlation  higher excited states gone  continuum shifted  1S becomes a threshold enhancement lattice Jakovác et al, PRD07 Mócsy,Petreczky, [hep-ph] cc no hyperfine splitting gluon plasma Pseudoscalar spectral function

Ágnes Mócsy - RBRC 19 S-wave Charmonium height of bump ( and integral under ) in lattice and model are similar: lattice data consistent with threshold enhancement height of bump ( and integral under ) in lattice and model are similar: lattice data consistent with threshold enhancement details cannot be resolved cc

Ágnes Mócsy - RBRC 20 S-wave Charmonium spectral function unchanged across deconfinement or… integrated area under spectral function unchanged N.B.: Unchanged lattice QCD correlators do not imply quarkonia survival: Lattice data consistent with charmonium dissolution just above T c N.B.: Unchanged lattice QCD correlators do not imply quarkonia survival: Lattice data consistent with charmonium dissolution just above T c cc Threshold enhancement in spf compensates for dissolution of states

Ágnes Mócsy - RBRC 21 Other Channels For P-wave look at the derivative constant contribution in the correlator quark number susceptibility Agreement to few% between model and lattice correlators for all states - first time Agreement to few% between model and lattice correlators for all states - first time Pseudoscalar bottomonium Umeda, PRD T c bb cc Scalar quarkonia bb spectral function contains zero mode

Ágnes Mócsy - RBRC 22 >> deconfined confined in free theory charm bottom ideal gas expression susceptibilities explain correlators deconfined heavy quarks carry the quark-number at 1.5 T c ideal gas expression susceptibilities explain correlators deconfined heavy quarks carry the quark-number at 1.5 T c Mócsy,Petreczky, [hep-ph] Indication for deconfined heavy quarks 1.5T c

Ágnes Mócsy - RBRC 23 Alberico et al, [hep-ph] Convergent results from different models

Ágnes Mócsy - RBRC 24 Most Binding Potential need strongest confining effects = largest possible r med r med = distance where exponential screening sets in distance where deviation from T=0 potential starts Explore the uncertainty in the potential Note: still constrained by lattice & in agreement with correlator data

Ágnes Mócsy - RBRC 25  cc spectral fct may show resonance-like structures, but binding energy is small When binding energy drops below T state is weakly bound thermal fluctuations can destroy the resonance

Ágnes Mócsy - RBRC 26 Binding Energy Upper Limits Upsilon remains strongly bound up to 1.6T c Other states are weakly bound above 1.2T c weak binding strong binding Find the upper limit for binding

Ágnes Mócsy - RBRC 27 Thermal Dissociation Widths Estimate the thermal width  (T)  related to the binding energy  Also: NLO pQCD calculation yields similar large width for the Jpsi Park et al PRC 07 Upper limit for thermal width for weak binding E bin <T for strong binding E bin >T Kharzeev,McLerran,Satz, PLB 95

Ágnes Mócsy - RBRC 28 Upper Bounds condition: thermal width > 2x binding energy Mócsy,Petreczky, [hep-ph], to appear in PRL Upper bounds on dissociation temperatures

Ágnes Mócsy - RBRC 29 Sequential Suppression Revisited T TcTc T c 2T c J/  (1S)  b (1P)  ’’(3S)  b ’(2P)  (1S)  ’(2S)  ’(2S)  c (1P) New calibration of the QGP thermometer

Ágnes Mócsy - RBRC 30 Conclusions To Do  finite momentum effects  better lattice data will provide stringent constraint on potential model  effective theory approach for quarkonia at finite T : role of octet channel, better understanding of singlet potential, in-medium quark masses and widths … 1. Potential model can be used to understand quarkonium at finite T. Lattice correlators are explained correctly for the first time, using model based on lattice screening. Unchanged correlators do not imply quarkonia survival: threshold enhancement compensates for dissolution of states. Lattice data consistent with charmonium dissolution just above T c 2. Upper bound estimates on dissociation temperatures All states dissolve by ~1.3T c, except the  and  b New sequential suppression pattern - Implications for heavy ion phenomenology Laine, JHEP 07

Ágnes Mócsy - RBRC 31 ****The END****

Ágnes Mócsy - RBRC 32 spectral function T=0 cc latticemodel Comparing to lattice no hyperfine splitting gluon plasma Jakovác et al, PRD07

Ágnes Mócsy - RBRC 33 T  0 Spectral Function reasonably good agreement between model and data ground state peak, excited states, and continuum identified model lattice Jakovac et al PRD 07 relativistic continuum seen on lattice this contradicts statements made in the recent literature cc

Ágnes Mócsy - RBRC 34 Wong potential  apparent agreement but Wong 05 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

Ágnes Mócsy - RBRC 35 Internal energy

Ágnes Mócsy - RBRC 36 Mócsy,Petreczky EJPC 05 Mócsy,Petreczky PRD 06 modellattice First Indication of Inconsistency simplified spectral function: discrete bound states + perturbative continuum T = 0 T  T c also Cabrera, Rapp 06 It is not enough to have “surviving state” Correlators calculated in this approach do not agree with lattice