Heavy quarks in finite temperature lattice QCD Péter Petreczky Physics Department and RIKEN-BNL

Exploring QCD : Deconfinement etc , Newton Institute, Cambridge, August 20-24, 2007

• Introduction : Deconfinement at high temperature and color screening

• Free energy of static quarks in 2+1 F QCD

• Quarkonium correlators and spectral functions from lattice

• Heavy quark transport and quarkonia correlators

• Conclusions and Outlook

Deconfinement at high temperatures

RBC-Bielefeld collaboration (preliminary)

large increase in number of d.o.f. chromo-electric screening

bindings effects in quarkonium are reduced ( Matsui and Satz )

study spatial correlators of static color charges in LQCD at T>0

potentialmodel

lattice calculations of quarkoniumspectral functions in LQCD

Static quark anti-quark pair in T>0 QCD

QCD partition function in the presence of static pairMcLerran, Svetitsky, PRD 24 (1981) 450

temporal Wilson line:

Polyakov loop: )xTr W()( xL

8133

Separate singlet and octet contributions using projection operators

81 and PP Nadkarni, PRD 34 (1986) 3904

RBC-Bielefeld Collaboration:M. Cheng, N.H. Christ, S. Eijiri, K. Hübner, C. Jung, F., O. Kaczmarek, F. Karsch, E. Laermann, J. Liddle, R. Mawhinney, C. Miao, P. Petreczky, K. Petrov, C. Schmidt, W. Söldner, J. Van der Heide

Static quark anti-quark free energy in 2+1f QCD

preliminary

preliminary

Static quark anti-quark free energy in 2+1f QCD

preliminary

preliminary

),(),(),(,)0,0(),(),,( 3 xxxJJxJexdTpG HHHHxpi

Meson correlators and spectral functions

5,,5,1H

)(),( iDTG

Imaginary time Real time

0 ))2/(sinh(

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

T

TTdTG

)()(Im1

2

)()(

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

Charmonia spectral functions at T=0

Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

For the spectral function is sensitive to lattice cut-off ;Strong default model dependence in the continuum region

If there is no T-dependence in the spectral

function,

0 ))2/(sinh(

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

T

TTdTG

temperature dependene of ),( TG

Charmonia correlators at T>0

in agreement with previous quenched calculations: Datta et al, PRD 69 (04) 094507 Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506 very similar results in full (2 F) QCD : Aarts et al, arXiv:0705.2198

Bottomonium correlators

Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

Charmonia spectral functions in PS channel at T>0

ground state peak is shifted, excitedstates are not resolved when become small

no temperature dependence in thePS spectral functions within errors

Jakovác, P.P., Petrov, Velytsky, PRD 75 (07) 014506

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

Can 1S charmonia state survive deconfinement ?

•resonance-like structures disappear already by 1.2Tc

•strong threshold enhancement

•contradicts lattice results ?

•resonance-like structures disappear already by 1.2Tc

•strong threshold enhancement

•contradicts lattice results ?

higher excited states gonecontinuum shifted1S becomes a threshold enhancement

Mócsy, P. P., arXiV:0705.2559 [hep-ph]

c

What about color screening ? )'(),',()(1 32 rrErrErVm G

NR

E 2Nc

ImGNR

r ,r ', E r

r '0

No !

>>

deconfined confined

charm 1.5 Tc

bottom 1.5 Tc

Scalar and axial-vector correlators

free theory:

quasi-free charm (beauty) carriers

see also Umeda PRD 75 (07) 094502

Vector correlator and heavy quark diffusion

Effective Langevin theory Free streaming :Collision less Boltzmann equation

Interactions

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

P.P., Teaney PRD73 (06) 014508

Conclusions

• Lattice QCD study of free energy of static color charges shows strong color screening at distances comparable to quarkonium sizes

• Quarkonium correlation functions in the PS channel show only very small temperature dependence, the same is true for the derivative of the correlator in the SC channel. MEM is not a reliable tool for extracting the spectral functions at high temperatures • Potential model with screening leads to the dissolution of most quarkonia states above deconfinement, nevertheless are compatible with lattice data on quarkonium correlators => large threshold enhancement

• The observed temperature dependence of the quarkonium correlators is governed by the transport contribution (zero mode contribution) not by threshold (resonance) region of the spectral functions

small thermal velocity of charm quarks

lattice data are not precise yet to constrain the value of heavy quark diffusion constant D

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