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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
),(),(),(,)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
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
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
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