Quarkonium Correlators Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Quarkonium Correlators Péter Petreczky in collaboration with : Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506 Á. Mócsy, P.P. arXiv.0705.2559 and arXiv:0706.2183 

Introduction constraints on σ(ω,T) Correlation functions of static Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Correlation functions of static charges indicate strong screening Strong color screening in QGP leads to reduced binding and quarkonium melting above deconfinement Quarkonium suppression (Matsui and Satz) Kaczmarek, Karsch, P.P., Zantow,PLB 543 (02) 41 Quarkonium properties at T>0 are encoded in the spectral functions T=0 qq well defined - width smaller compared to binding energy . at T will become broader and when it is large enough than we should switch from talking instead about individual states rather about spectral function. On the lattice we calculate constraints on σ(ω,T) Introduction

Spectral Function from lattice at T=0 Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti For the spectral function is sensitive to lattice cut-off ; Strong default model dependence in the continuum region Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506 Spectral Function from lattice at T=0

T-dependence of quarkonium correlators Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti temperature dependene of If there is no T-dependence in the spectral function, PS SC in agreement with previous calculations: Datta et al, PRD 69 (04) 094507 T-dependence of quarkonium correlators

Spectral functions from LQCD at T>0 Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti ground state peak is shifted, excited states are not resolved when become small no temperature dependence in the PS spectral functions within errors Spectral functions from LQCD at T>0

Default model dependence at T>0 Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti constant default model default model from the high enetgy part of the T=0 spectral function the shape of the spectral functions depends on the default model the T-dependence of the spectral functions is small for all default models no strong evidence for the resonance peak Default model dependence at T>0

Bottomonium correlators at T>0 Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506 PS SC b b “the b puzzle” - same size as the J/ why are the b and J/ correlators so different Bottomonium correlators at T>0

Spectral Function  bound states/resonances & Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti  bound states/resonances &  continuum above threshold  (GeV) PDG 06  s0 perturbative calculations  ~ MJ/ , s0 : ladder resummation + high energies NR treatment breaks down , but away from threshold perturbative treatment Spectral Function

Spectral Function  bound states/resonances & Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti  bound states/resonances &  continuum above threshold  (GeV) PDG 06  ~ MJ/ , s0 nonrelativistic many gluon exchanges important near threshold re-summation of ladder diagrams : close to the threshold q and antiq move slowly - there is enough time for multiple gluon exchanges since an extra Coulomb gluon exchange is not suppressed by alpha we need to resum ladder diagrams resummation done separately in PS and S channels . but in both cases it reduces to solving scr eq for NR green fct first in vector channel Strassler,Peskin PRD 91 also Casallderey-Solana,Shuryak,04 S-wave nonrelativistic Green’s function P-wave S-wave also Cabrera,Rapp 07 Spectral Function

Spectral Function  bound states/resonances & Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti  bound states/resonances &  continuum above threshold  (GeV) PDG 06  ~ MJ/ , s0 nonrelativistic   s0 perturbative smooth matching details do not influence the result + the nr spf has been smoothly matched onto the perturb relativistic form the details of the matching do not influence the results . perfect for studying quarkonium properties in medium nonrelativistic Green’s function + pQCD Unified treatment: bound- and scattering states, threshold effects together with relativistic perturbative continuum Spectral Function

Constructing the Potential Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Constrain the potential by lattice data what we know: Free energy of static Q-Qbar pair in deconfined phase Kaczmarek, Karsch, P.P., Zantow,PLB 543 (02) 41 no temperature effects strong screening effects and a potential that is physically motivated. Free energy - contains negative entropy contribution - provides a lower limit for the potential V(r,T) Constructing the Potential

Constructing the Potential Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Constrain the potential by lattice data Potential assumed to share general features with the free energy no temperature effects strong screening effects and a potential that is physically motivated. other choices of the potential consistent with lattice results is possible but give very similar results for quarkonium correlators also motivated by Megías,Arriola,Salcedo PRD07 Constructing the Potential

S-wave Charmonium in Gluon Plasma Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Mócsy, Petreczky arXiV.0705.2559[hep-ph] higher excited states gone continuum shifted 1S becomes a threshold enhancement c lattice Jakovác,Petreczky, Petrov,Velytsky, PRD07 resonance-like structures disappear already by 1.2Tc strong threshold enhancement contradicts previous claims this finding S-wave Charmonium in Gluon Plasma

S-wave Charmonium in Gluon Plasma Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Mócsy, Petreczky hep-ph/0705.2559 details cannot be resolved resonance-like structures disappear already by 1.2Tc strong threshold enhancement above free case indication of correlation height of bump in lattice and model are similar this finidng contradicts S-wave Charmonium in Gluon Plasma

S-wave Charmonium in Gluon Plasma Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti N.B.: 1st time 2% agreement between model and lattice correlators for all states at T=0 and T>Tc Unchanged LQCD correlators do not imply quarkonia survival: Lattice data consistent with charmonium dissolution just above Tc Mócsy, Petreczky hep-ph/0705.2559 LQCD measures correlators this finidng contradicts if the spectral function unchanged across deconfinement S-wave Charmonium in Gluon Plasma

Bottomonium ground state survives deconfinement other states dissolved Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti ground state survives deconfinement other states dissolved medium modification of the 1S peak is small agreement found with lattice correlators Bottomonium

Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti constant contribution (Gilow) to the correlator at finite T so look at the derivative following Umeda 07 quark number susceptibility 1.5 Tc Threshold enhancement of spf compensates for dissolution of states Agreement with lattice data for scalar charmonium and bottomonium Scalar Channel

Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti charm 1.5 Tc in free theory bottom 1.5 Tc >> deconfined confined Similar enhancement was observed in the vector correlators P.P., Teaney, PRD 73 (2006) 014508 behavior explained using ideal gas expression for susceptibilities: seems to indicate deconfined heavy quarks carry the quark-number at 1.5 Tc Scalar Channel

Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Lattice data does not necessarily imply survival of quarkonia all states except 1S bottomonia are dissolved by 1.2 Tc Threshold is enhanced over free propagation, correlations between Q-Qbar may remain strong in the plasma The thershold enhancement obtained in potential model with screening togethe with the transport contribution to the spectral function can describe the T-dependence of the quarkonium correlators calculated on the lattice The size of the transport contribution to the correlators seems to be consistent with the expectations based on free quarks Conclusions

Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti ****The END****

Most binding possibility Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Most binding possibility J/  Note the reduced binding energy for the J/ already at 1.2 Tc! Even for maximal binding: J/ at 1.6 Tc is just a threshold enhancement  survives up to ~2Tc with peak position unchanged Also note strong enhancement in threshold region: Q and Qbar remain correlated Most binding

LQCD measures correlators Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti LQCD measures correlators if spectral function unchanged across deconfinement b c b as the temperature is increased the spf will possibly change. this change manifests in the t-dependece of the correlator if spf does not change across the deconf transition this ratio will be independent of the T and = unity lattice data from Jakovác,Petreczky,Petrov,Velytsky, PRD 07 note on Correlators

T0 Spectral Function reasonably good agreement between model and data Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti gluon plasma with heavy quarks results for the c model lattice Jakovac,Petreczky,Petrov,Velytsky, PRD 07 ground state peak, excited states, and continuum identified reasonably good agreement between model and data T0 Spectral Function

c survives to 2Tc & c melts at 1.1Tc Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti look directly at the correlator if spectral function unchanged across deconfinement Datta,Karsch,Petreczky,Wetzorke, PRD 04 c c as the temperature is increased the spf will possibly change. this change manifests in the t-dependece of the correlator if spf does not change across the deconf transition this ratio will be independent of the T and = unity c survives to 2Tc & c melts at 1.1Tc lQCD Correlators

T=0 Continuum in Quenched QCD Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti G does not depend on the parameters good agreement between model and data I show the spf calculated for different values of the parameters the correlator does not depends on the valoes of the param the correct behavior at short distance reproduced with the relativistic form of continuum, the correl obtained with the nr falls well below the data this contradict statements made in the recent literature - that the correlator does not carry info about the continuum relativistic continuum seen on lattice this contradicts statements made in the recent literature T=0 Continuum in Quenched QCD

1S charmonium peaks found unmodified at 1.2Tc Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti charm bottom With this potential: 1S charmonium peaks found unmodified at 1.2Tc binding energy (Ebinding=s0-M) is small so dissociation by thermal fluctuations is likely all states, except 1S bottomonium, are gone by 1.5Tc

Internal Energy as Potential Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Internal Energy as Potential

Péter Petreczky xQCD 2007, August 6-8,2007,Frascatti Screened Cornell