Lattice QCD at finite temperature

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 Tgt0
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 Tgt0
21F
Petreczky, J. Phys. G30 (2004) S1259
4
The chiral susceptibility at Tgt0
Improved stagg., asqtad, MILC, hep-lat/0405029
Improved stagg. HYP better flavor symmetry at
finite lattice spacing
5
Equation of state at Tgt0
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 Tgt0 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/0309121
confinement, sr
deconfinement gt screening
Vacuum (T0) physics at short distances
9
Running coupling constant at finite temperature
Effective running coupling constant at short
distances
T0 non-perturbative physics
Perturbation theory
Kaczmarek, Karsch, P.P., Zantow, Phys.Rev.D70
(2004) 074505
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) 054503
screening
Vacuum physics
11
Entropy and internal energies of static charges
resonace gas ?
12
Quenched QCD

Kaczmarek, Karsch, Petreczky, Zantow,
hep-lat/0309121
Schroedinger
equation 1S charmonia states survive up
to Shuryak, Zahed, hep-ph/0403127, Wong,
hep-ph/0408020
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) 012001 Umeda
et al, hep-lat/0211003
Datta, Karsch, Petreczky, Wetzorke, PRD 69
(2004) 094507 Non-perturbatively impr. Wilson
action
15
Charmonia spectral functions at T0
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)
094507
1S ( ) is dissolved at


1P ( ) is dissolved at
1S state was found to be bound till
also in Umeda et al, hep-lat/0211003 Asakawa,
Hatsuda, PRL 92 (04) 012001
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 1P charmonia
  dissolve at

19
Charmonia correlators at Tgt0 on isotropic lattice
If spectral function do not change across
20
What is the physics behind the 2nd and 3rd peaks ?
Lattice spectral functions in the free theory,
Karsch, Laerman, Petreczky, Stickan, PRD 68
(2003) 034008
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) 091503,
Prog. Part. Nucl. Phys. 46 (01) 459
Likelyhood function
Shannon-Janes entropy
-perturbation theory
- default model