Quarkonia correlators and spectral functions Péter Petreczky Physics Department and RIKEN-BNL

SQM 2006, March 26-31, 2006

• Meson spectral functions and MEM

• Lattice calculation of charmonium correlators and spectral functions

• Lattice calculation of bottomonium correlators and spectral functions

• Relation of the quarkonium correlators to the heavy quark transport

• Conclusions and Outlook

),(),(),(,)0,0(),(),,( 3 xxxJJxJexdTpG HHHHxpi τψτψτττ Γ== +⋅∫

Meson correlators and spectral functions

μμ γγγγ ⋅=Γ 5,,5,1H

)(),( ττ iDTG −= >

Imaginary time Real time

∫∞ −

=0 ))2/(sinh(

))2/(1(cosh(),(),(

T

TTdTG

ω

τωωωστ

)()(Im1

2

)()( ωσωππ

ωω==

− <>

RDDD

Spectral ( dynamic structure ) function Example : virtual photon

quenched approximationis used !

What are the excitations (dof) of the system ?

Reconstruction of the spectral functions : MEM

data and degrees of freedom to reconstruct

Bayesian techniques: find which maximizes data

Prior knowledgeMaximum Entropy Method (MEM)

Asakawa, Hatsuda, Nakahara, PRD 60 (99) 091503, Prog. Part. Nucl. Phys. 46 (01) 459

Likelyhood function Shannon-Janes entropy:

- default model -perturbation theory

Heavy quarkonia spectral functions

Isotropic Lattice Anisotropic Lattice

space

time

space

Datta, Karsch,P.P. Wetzorke

Umeda et al,Asakawa, Hatsuda,Jakovác, P.P,Petrov, Velytsky

Charmonia spectral functions at T=0

Jakovác, P.P., Petrov, Velytsky, work in progress

For the spectral function is sensitive to lattice cut-off ; In the SC channel even the ground state is poorly resolved ;

Charmonia correlators spectral functions at T>0

1S ( ) exists at

cJ ηψ ,/ 1P ( ) is dissolved at cχ

Datta, Karsch, P.P , Wetzorke, PRD 69 (2004) 094507

G(T)/G(T=0)=1

Correlators do not agree with potential model with screening ! (see talk by Á. Mócsy )

Charmonia correlators: models vs. lattice

Lattice data : Datta, Karsch, P.P , Wetzorke, PRD 69 (2004) 094507

Potential model with screening : Á. Mócsy, P.P, hep-ph/0512156

Potentia

l model

with sc

reening does

not agree

with

lattic

e data

!

Charmonia spectral functions at T>0 from anisotropic lattice

no temperature dependence in thePS spectral functions within errors

Jakovác, P.P., Petrov, Velytsky, work in progress

1P state is melted

See poster by A. Velytsky at SQM 2006, on Thursday, March 30, 2006

1S states are dissolved only at :

1P states are dissolved at :

Bottomonia spectral functions on anisotropic lattices

expected survive till

Jakovác, P.P., Petrov, Velytsky, hep-lat/0509138

Vector correlator and heavy quark diffusion

Effective Langevin theory

Free streaming :Collision less Boltzmann equation

1S charmonium states survies

Interactions

P.P., Petrov, Velytsky, Teaney, hep-lat/0510021

Transport contribution to the Euclidean correlators

P.P. and D. Teaney, PRD 73 (06) 014508

Lattice data ( Datta et al, ) :

Conclusions

• 1S charmonia states ( ) survive till unexpectedly high temperatures • indications for melting of 1P charmonia states ( ) • indications for melting of 1P bottomonia states ( ) Unexpected !

• The temperature dependence of the correlators and the spectral functions is inconsistent with screening and potential models (see talk by Á. Mócsy )

• Euclidean correlators calculated on the lattice are sensitive to transport contribution to the spectral functions Better lattice data are required but no indication for DT<1 from the current lattice data

Charmonia spectral functions at T=0 (cont’d)

Reconstruction of an input spectral function : Lattice data in PS channel for:

Removing lattice artifacts in the spectral functions

Free spectral functions

Wilson fermions Highly improved (HYP) fermions