1. Recent developments in lattice QCD Péter Petreczky
Physics Department and RIKEN-BNL
Thermodynamics of 2+1 flavor QCD for nearly physical quark masses
Equation of State
Quark number and strangeness fluctuations
Color screening at high temperatures
Quarkonium correlators
Quarkonium properties at T>0
Transport contribution to quarkonium correlators
Conclusions
Zimányi 75 Memorial Workshop, RMKI, Budapest, July 2-4, 2007

2. Doering, Van der Heide, Kaczmarek, Laermann, Miao (Bielefeld)
Lattice calculations with p4fat3 action
fat3 link improvement
of flavor symmetry
next-to-nearest neighbors
(p4) rotational symmetry to
RHMC algorithm :
x 20 speedup at small m
RBC-Bielefeld collaboration :
Ejiri, Karsch, Jung, P.P, Schmidt, Umeda (BNL)
Cheng, Christ, Mawhiney (Columbia), Datta (Mumbai), Petrov (NBI)
Doering, Van der Heide, Kaczmarek, Laermann, Miao (Bielefeld)

3. Equation of State Calculations : , and lattices,
and along the line of constant physics ( LCP ) :
are varied in the way physical quantities, e.g and

4. Equation of State (cont’d)
rise in the entropy and energy density
happens in the same temperature
interval where the rapid change of the chiral condensate and Polyakov loop takes place
no large cutoff dependence in
the pressure and entropy denisty
deviation from ideal gas limit is about
10% at high T

5. Equation of State (cont’d)
(2+1) flavor QCD
qualitative agreement
with resonance gas at low T
Resummed perturbative calculations from :
Blaizot, Iancu, Rebhan, hep-ph/
Lattice data on pressure and entropy density
at high temperatures can be described
by re-summed perturbation theory

6. Quark number and strangeness fluctuations

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

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

9. Lattice results on charmonium spectral functions
1S charmonium survives deconfinement :
This seemingly contradicts to large
color screening of static charges !
Umeda et al, EPJ C39S1 (05) 9
Asakawa, Hatsuda, PRL 92 (04)
Datta et al, PRD 69 (04)
No problem lattice results
can be reproduced using
potential models:
Shuryak, Zahed, PRD 70 (04)
Wong, PRC 72 (05) 03496
Alberico et al, PRD 72 (05)
Rapp, Cabrera, hep-ph/
Wong, Crater, PRD 75 (07)
Alberico et al, PRD 75 (07)
Are potential model applicable at
T>0 ?
Mócsy, P.P., PRD 73 (06)
more recently confirmed by :
Iida et al, PRD74 (06)
Aarts et al, arXiv:  [hep-lat]
New high statistics with careful analysis of systematic errors:
Jakovác, P.P., Petrov, Velytsky, PRD 75 (07)

10. Charmonia spectral functions at T=0
Jakovác, P.P., Petrov, Velytsky, PRD 75 (07)
For the spectral function is sensitive to lattice cut-off ;
Strong default model dependence in the continuum region

11. Charmonia correlators at T>0
temperature dependene of
If there is no T-dependence in the spectral
function, PS SC
in agreement with previous calculations:
Datta et al, PRD 69 (04)

12. Charmonia spectral functions in PS channel at T>0
ground state peak is shifted, excited
states are not resolved when
become small
no temperature dependence in the
PS spectral functions within errors
Jakovác, P.P., Petrov, Velytsky, PRD 75 (07)

13. Vector correlator and heavy quark diffusion
1S charmonium states
survies
P.P., Petrov, Velytsky, Teaney, hep-lat/
Interactions
Free streaming :
Collision less
Boltzmann equation
Effective Langevin theory

14. P.P., Teaney PRD73 (06)

15. Summary
Pressure, energy density and entropy density have be calculated at two lattice
spacing show a rapid rise at temperature in agreement with
deviation from the ideal gas limit is about 10% for temperatures and
no significant cutoff dependence has been seen
Cheng et al, PRD 75 (07)
Fluctuations of quark number and strangeness at high temperatures are
close to the ideal gas limit, at finite baryon density these fluctuations are
enhanced in the vicinity of the transition
Interactions between static quarks are strongly screened in the quark gluon plasma,
the onset of screening is seen at distances comparable to the 1S quarkonium size
S-wave charmonium correlators are temperature independent and there is
no T-dependence in the reconstructed spectral functions, however, details are not
resolved
Can 1S charmonia exist in the plasma ? What about color screening ?
see talk by Ágnes Mócsy
Transport contribution to charmonium correlators have been isolated :
small thermal velocity for heavy quarks, no constraint on the diffusion constant

16. Aoki et at, JHEP 0601 (2006) 089 (impr. flavor symmetry only)