1. Quarkonia at finite temperature: lattice results Peter Petreczky
Brookhaven National Laboratory
Introduction : Quarkonium dissolution at finite temperature
Color screening at finite temperature : lattice results
Mesons spectral functions: lattice results
Conclusions
QWG workshop, Beijing, October 15, 2004

2. Quarkonium dissolution at finite temperature
Potential between singlet pair
Coulomb gauge gluon propagator
Matsui and Satz, PLB 178 (1986) 416
No quarkonium binding is possible when
Charmonium suppresseion right after deconfinement
Implicit assumption : instantenous modification of interaction by the medium
Does not hold close to

3. Static quark anti-quark pair in T>0 QCD
QCD partition function in the presence of static pair
McLerran, Svetitsky, PRD 24 (1981) 450
temporal Wilson line:
Polyakov loop:
Separate singlet and octet contributions using projection operators
Nadkarni, PRD 34 (1986) 3904

4. Color singlet free energy:
Color octet free energy:
Fix the Coulomb gauge
transfer matrix can be
defined
Dressed gauge invariant Wilson line
Philipsen, PLB 535 (2002) 138
equivalent
At T=0 equivalent to definition through Wilson loop, Philipsen, PLB 535 (2002) 138

5. Free energy in the pertubative high temperature limit
at leading order
At next to leading order
and the entropy appears:
The internal energy is different from the free energy

6. Color averaged free energy:
Kaczmarek, Karsch, P.P., Zantow, hep-lat/
Singlet contribution
is dominant for rT<<1
Linear rise :
Screening :
long distances rT>>1
T ln 9
Vacuum (T=0) physics, short distances rT<<1

7. The entropy contribution and the internal energy
Numerically:
Negative entropy contribution
1S charmonia states survive
up to
Shuryak, Zahed, hep-ph/
Wong, hep-ph/
Kaczmarek, Karsch, P.P., Zantow, hep-lat/

8. Static free energy in 3 flavor QCD
Improved staggered (Asqtad) action, lattices
Quark masses:
K. Petrov, P.P, hep-lat/
Effective screening radius
String breaking
screening
Vacuum physics

9. decreases, do D,B meson masses decrease ?? Entropy contribution
Digal, P.P. , Satz, PLB 514 (2001) 57
decreases, do D,B meson masses decrease ?? Entropy contribution
K. Petrov, P.P, hep-lat/
Large increase in the entropy and internal energy !

10. Meson correlators and spectral functions
Experiment, dilepton rate
LGT
Imaginary time Real time
Quasi-particle masses and width
KMS condition
MEM

11. Reconstruction of the spectral functions
data and degrees of freedom to reconstruct
Bayesian techniques: find which maximizes
data
Prior knowledge
Maximum Entropy Method (MEM)
Asakawa, Hatsuda, Nakahara, PRD 60 (99) , Prog. Part. Nucl. Phys. 46 (01) 459
Likelyhood function
Shannon-Janes entropy:
- default model
-perturbation theory

12. Lattice set-up Charmonia : Bottomonia :
Non-perturbatively improved Wilson action, isotropic lattices
Charmonia :
Bottomonia :
Anisotropic Fermilab action,

13. Charmonia spectral functions (I)
What do we get at low temperature from lattice calculations ?
Calculations performed on isotropic lattices for 1/a=4.04GeV, 4.86GeV,9.72GeV
1/a=4.04GeV
1/a=4.86GeV
1/a=9.72GeV
Lattice artifacts
by K. Jansen
2nd and 3rd peaks are lattice artfifacts, no 2S state

14. Charmonia spectral functions (II)
The temperature dependence of the correlators x x
If there is no T-dependence in the spectral function,
Datta, Karsch, P.P., Wetzorke, PRD 69 (2004)

15. Charmonia spectral functions (III)
Heavy quarkonia spectral functions from MEM:
Is dissolved at
is dissolved at
Datta, Karsch, P.P., Wetzorke, PRD 69 (2004)
Gradual dissolution of ; screening cannot lead to suppression
what is the thermal width ???

16. Results from anisotropic lattices:
Umeda, Nomura, Matsufuru,
Lattice 2004,
Extended operators
Asakawa, Hatsuda, PRL 92 (2004)
Point operators

17. Temperature dependence of bottomonium correlators
No T-dependence as expected for 1S state
Little supprise ! Expected:
Qualitatively similar T-dependence
for different lattice spacings
Petrov, Velytsky, P.P, work in progress

18. Conclusions non-perturbative even in the deconfined phase
Interaction between quark and anti quark are strong and
non-perturbative even in the deconfined phase
The 1P state charmonia dissolve at
The lattice data support a picture of gradual dissolution of ground
state charmonia starting at and no states are
present at
1P bottomonium state dissolve around What determines the
Dissociation temperature quantum numbers or system size ?
Future challenge : better control of lattice artifatcs,

19. Discussions
Considerable progress in study of quarknium at finite temperature in lattice QCD
but the problem of cut-off effects and systematic errors in MEM is not settled
Completely. Better actions (perfect actions, NRQCD for bottomonium)
Extension to full QCD.
Lattice spacing dependence of

20. Dependence of the spectral functions on number of data points
Resolution problem for bottomonium
NRQCD
What is the thermal width of quarkonium states ?

21. Quarkonium formation in the medium :
Evidence for very large energy density (jet quenching, hydro, multiplicities ),
fast equilibrization (hydro)
Quarkonium may be formed inside a high density medium
 in-medium quarkonium binding has to be understood.
Can be quarkonium used as thermometer ?
Experimental input: measure quarkonium production as function of pT and y
in AA with pp and dA baseline. Measure chi_b ?
To what is extent potential model can be used at T>0 (ok at T=0).
Can one calculate reliably the quarkonium width perturbatively ?
Wong, hep-ph/