1. Lattice QCD at finite temperature Péter Petreczky
Nuclear Theory Group and RIKEN-BNL
Brookhaven National Laboratory
QCD Thermodynamics on the lattice
Bulk Thermodynamics:
Nature of transition to the “new state”,
transition temperature,
Equation of state
Chiral and quark number suscpetibilities
Spatial and temporal correlators:
Free energy of static quarks ( potential )
Heavy quarkonia correlators and spectral
functions
Light meson correlators (dilepton rate)
Quark and gluon propagators and
quasi-particle masses
40th Recontres De Moriond, La Thuile, March, 2005

2. QCD Phase diagram at T>0
At which temperature does the transition occur ? What is the nature of transition ?
Resonance Gas : Chapline et al, PRD 8 (73) 4302
global symmetries of QCD are violated in lattice formulation
staggered fermions :

3. The chiral transition at T>0
2+1F :
Petreczky, J. Phys. G30 (2004) S1259

4. The chiral susceptibility at T>0
Improved stagg., asqtad,
MILC, hep-lat/
Improved stagg. HYP: better flavor
symmetry at finite lattice spacing

5. Equation of state at T>0
Requirements: for lattice
Computational cost grow as :
Karsch et al, EPJC 29 (2003) 549, PLB 571 (2003) 67

6. 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: = - r

7. Separate singlet and octet contributions using projection operators
Nadkarni, PRD 34 (1986) 3904
Color singlet free energy:
Color octet free energy:
Color averaged free energy:

8. Free energies of static charges in absence dynamical quarks:
Kaczmarek, Karsch, Petreczky, Zantow, hep-lat/
confinement, sr
deconfinement => screening
Vacuum (T=0) physics at
short distances

9. Running coupling constant at finite temperature
Effective running coupling constant at short distances :
T=0 non-perturbative
physics
Perturbation theory:
Kaczmarek, Karsch, P.P., Zantow, Phys.Rev.D70 (2004)
T-dependence
3-loop running coupling
Necco, Sommer, NPB 622 (02)328

10. Free energies of static charges in full QCD
string breaking
Petreczky, Petrov, PRD (2004)
screening
Vacuum physics

11. Entropy and internal energies of static charges
resonace gas ?

12. Schroedinger equation : 1S charmonia states survive up to
Quenched QCD :
Kaczmarek, Karsch, Petreczky, Zantow, hep-lat/
Schroedinger equation :
1S charmonia states survive up to
Shuryak, Zahed, hep-ph/ , Wong, hep-ph/

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

14. Heavy quarkonia spectral functions
Isotropic Lattice
Anisotropic Lattice
time
space
space
Jakovác, P.P.,Petrov, Velytsky, in progress
Fermilab action,
also
Asakawa, Hatsuda, PRL 92 (04)
Umeda et al, hep-lat/
Datta, Karsch, Petreczky, Wetzorke,
PRD 69 (2004)
Non-perturbatively impr. Wilson action

15. Charmonia spectral functions at T=0
Jakovác, P.P.,Petrov,
Velytsky, work in progress,
calculation on 1st QCDOC
prototype
Lattice artifacts
by K. Jansen
FAQ: Could it be that also the
1st peak is a lattice artifact
Answer: NO

16. Charmonia spectral functions on isotropic lattice
Heavy quarkonia spectral functions from MEM :
Datta, Karsch, Petreczky, Wetzorke, PRD 69 (2004)
1S ( ) is dissolved at
1P ( ) is dissolved at
1S state was found to be bound till also in Umeda et al, hep-lat/
Asakawa, Hatsuda, PRL 92 (04)

17. Charmonia at finite temperature on anisotropic lattice
Jakovác, P.P.,Petrov, Velystksy, work in progress

18. Summary
In “real” QCD the transition seems to be crossover not a true phase
transition. Chiral aspect of the transition strongly depends on the effects
of finite lattice spacing ;
no evidence for chiral transition from the lattice yet !
Bulk thermodynamic quantities below and in the vicinity of
are well described by hadron resonance gas model
The interactions between quarks remains non-perturbative
above deconfinement transition but no evidence for “extraordinary” large
coupling
1S charmonia, can exist in the plasma as resonance up to
temperatures P charmonia dissolve at

19. Charmonia correlators at T>0 on isotropic lattice
If spectral function do not change
across :

20. spectral function at high energy is not described by the free theory,
What is the physics behind the 2nd and 3rd peaks ?
Lattice spectral functions in the free theory,
Karsch, Laerman, Petreczky, Stickan, PRD 68 (2003)
spectral function at high energy is not described by the free theory,
2nd and 3rd peaks are part of distorted continuum. Finite lattice
spacing effects are small in the correlator and their size is in accordance
with expectations from the free field theory limit.

21. 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:
-perturbation theory
- default model