QCD Thermodynamics on Lattice

1
QCD Thermodynamics on Lattice
Peter Petreczky Brookhaven National
Laboratory
1. Bulk QCD thermodynamics

• Transition and EOS at Tgt0
• QCD at Tgt0, mugt0
• Deconfinement vs. chiral transition in QCD
  comparison with resonance gas model

2. Testing hot QCD with pair
(screening, mesons etc.)

• Free energy of static quark anti-quark pair
• Meson spectral function from lattice QCD
• Quarkonia spectral functions above
  deconfinement
• Light meson spectral function above
  deconfinement

2
Bulk Thermodynamics in SU(3) gauge theory
What is the order of the transition ? What is the
transition temperature What is the EOS ?
Boyd et al., Nucl. Phys. B496 (1996) 167
Necco, Nucl. Phys. B683 (2004) 167
The problem has been solved !
3
QCD phase diagram at Tgt0
Lattice calculations of QCD for physical value of
the quark (pion) masses is extremely difficult
Bielefeld, Coulombia, CP-PACS, MILC
Physical point (HPQCD, MILC, UKQCD
) hep-lat/0405022
Chiral extrapolation of With impr. KS
fermions Bielefeld, 2000,
p4 action, NPB 605(2001) 579 MILC, 2004,
Asqtad action,
hep-lat/0405029
MILC, impr. KS
Impr. Wilson fermions CP-PACS PRD 63 (2001)
034502 Nakamura, Latttice 2004
Transition in real QCD is most likely a rapid
crossover
Fodor and Katz, std. KS, JHEP 0404 (2004) 050

Staggered and Wilson fermions violate flavor
symmetries of QCD !!
4
Finite temperature transition with asqtad action
(I)
MILC Coll., hep-lat/0405029, hep-lat/0309118,
hep-lat/0209079,
hep-lat/0110067
Chiral condensate and susceptibility
5
Finite temperature transition with asqtad action
(II)
Quark number susceptibilities
fluctuations of conserved charges

SB limit is almost reached at 2Tc
Cut-off effects are smaller than in the free
theory Nt6 is already very close to the continuum
6
Is there a 1st order transition in Nf2 QCD ?
Carmona et al., hep-lat/0309035, Di Giacomo,
Lattice 04, Pica, Lattice 04 Standard
staggered action
However, 1st transition is also observed for Nf4
standard staggered action, but for HYP
staggered action there is a only a
crossover Hasenfratz, Knechtli, hep-lat/0105022
7
Transition in the continuum limit
MILC Coll.
Transition gets smoother on finer
lattices, imrovement of flavor symmetry ?
HYP staggered fermions at Nt4 -gt
Hasenfratz, Knechtli, hep-lat/0202019
8
QCD thermodynamics in the presence of finite
chemical potential

• Technical problem
• Finite complex action
  reweighting sign problem, overlap problem
• Multi-parameter reweghting, Fodor, Katz
• Taylor expansion around mu0, Bielefeld-Swansea
  Coll.
• Analytic continuation from imaginary mu, de
  Focrand, Philipsen DElia, Lombardo
• See pleanry talk by S. Katz on Lattice 2003,
  hep-lat/0310051

Physics problem
Interesting phase diagram in
the plane
If there is a crossover at
a chiral
Critical end-point
exist at some value of
the chemical
potential,
Stephanov, Rajagopal, Shuryak,
PRL 81 (98) 4816


Where is the Endpoint ??
9
Locating the critical end-point

• Multiparameter rewigting

• Lee-Yang zeroes

See talk by Ejiri, Lattice 2004
Crossover
Phase transition
2001 Fodor, Katz, JHEP 0203 (2002) 014
Lattices

10
Fodor, Katz, JHEP 0404 (2004) 050
2004
crossover
1st order

de Forcrand, Philipsen
Fodor, Katz
Comparison with analytic continuation
11
Taylor expansion around zero chemical potential
and EOS
Multiparameter reweighting
Allton et al., Phys. Rev. D68 (2003) 014507
including n3, see talk by Ejiri
Csikor et al., JHEP 0405 (2004) 046
Continuum SB
12
New developments calculations with fixed baryon
number
Kratochvila, de Forcrand, Lattice 2004 Alexandru,
Lattice 2004
The sign problem is less severe but are this
study are feasible For larger volumes ?
(currently 44)
13
Comparison with resonance gas at low T
1000 Exp. Know resonances
Karsch, Redlich, Tawfik, PLB 571 (2003) 67
Consequences
Compare with LGT results (Bielefeld-Swansea
Coll)
For fixed the ratio of These
observable is T-independent
The ratios of the expansion coeffiecients are

14
Ratios of different quantities
Karsch, Redlich, Tawfik, EPJC 29 (2003) 549, PLB
571 (2003) 67
Bielefeld Swansea Coll.
See talk by Ejirii on Lattice 2004
15
To predict the temperature dependence of the
pressure, susceptibilities we need the quark
mass dependence of hadron masses !
?
Reasonable description of lattice data
Karsch, Redlich, Tawfik, EPJC 29 (2003) 549
16
Quark number susceptibilities
See talk by Ejiri
17
What drives the transition in QCD ?
Deconfinement vs. chiral transition
Karsch, Redlich, Tawfik, EPJC 29 (2003) 549
Role of hadron resonances ?
for all
Though depends on
The deconfinement transition is driven
resonances (energy density) !
18
Testing hot QCD matter with quark anti-quark pair
All started with McLerran and Svetitsky, PRD 24
(1981) 450 Matsui and Satz, PLB 178 (1986) 416
What is the range of interaction and what is g(T)
?

• Static quark anti-quark pair ? heavy quark
  potentials

Time scales 1/T lt t lt
Heavy quarkonia and open charm physics at Tgt0

• Heavy quark anti-quark pair ? heavy quarkonia
  spectral functions

Time scales 1/m lt tlt 1/mv
Heavy quarkonia physics at Tgt0

• Light quark anti-quark pair ? light meson
  spectral functions

Time scales t1/T
Thermal dilepton and photons,
mesons
19
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
Separate singlet and octet contributions using
projection operators
Nadkarni, PRD 34 (1986) 3904
20
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 T0 equivalent to definition through Wilson
loop, Philipsen, PLB 535 (2002) 138
21
Color averaged free energy
Kaczmarek, Karsch, P.P., Zantow, hep-lat/0309121
Singlet contribution is dominant for rTltlt1
Linear rise Screening long distances
rTgtgt1
T ln 9
Vacuum (T0) physics, short distances rTltlt1
22
Short vs. long distance physics in singlet free
energy
Effective running coupling constant at short
distances
T0 non-perturbative physics
Perturbation theory
Kaczmarek, Karsch, P.P., Zantow, hep-lat/0406036
T-dependence
3-loop running coupling Necco, Sommer, NPB 622
(02)328
23
Screening at large distances
High temperature perturbation theory
Kaczmarek, Karsch, P.P., Zantow, hep-lat/0406036
The only non-perturbative information
24
The entropy contribution and the internal energy
Numerically

Negative entropy contribution
Kaczmarek, Karsch, P.P., Zantow, hep-lat/0309121
25
Static free energy in full QCD
3 flavor QCD, asqtad action,
Petrov, Lattice 2004, Petrov, P.P, hep-lat/0405009
Effective screening radius
String breaking
screening
Vacuum physics
2 flavor QCD, p4 action
Kaczmarek et al., hep-lat/0312015
study extended to finite denisty
21 flavor QCD std. KS
decreases with increasing
Toth, Katz, Fodor Lattice 2004
26
Large decrease in
large increase in
Large increase in the entropy and internal energy
due to inclusion of a static meson !
Similar increase also observed if an extra baryon
is include in the system Kratochvila, Lattice
2004
27
Meson correlators and spectral functions
Experiment, dilepton rate
LGT
Imaginary time Real time
Quasi-particle masses and width
KMS condition
MEM
28
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
Other methods S. Gupta, hep-lat/0301006 G.P.
Lepage et al., hep-lat/0110175 Constrained curve
fitting
- default model
-perturbation theory
29
Cutoff effects in the spectral function
Does the integral represenation of the imaginary
time correlator holds on the
lattice ? How the cutoff effects in
manifest themselves in ?
Asymptotic freedom analyze cutoff
effects in in the free theory
Karsch, Laermann, P.P, Stickan, PRD 68 (2003)
014504
For Wilson action on anisotropic lattice
Cutoff effects are
entirely contained in
30
Wilson action Large cutoff effects
Move away as
Truncated FP action Bietenholz, NPB PS 53 (97)
921 Large reduction of the cutoff effects
31
Meson spectral functions at T0
CP-PACS, Yamazaki et al, PRD 65 (2002) 014501
No continuum only peaks, 2nd and 3rd peak scale
like 1/a !
This happens not only for Wilson action, see
poster by Blum, P.P, Latttice 04
32
Heavy quarkonia spectral functions (I)
Asakawa, Hatsuda, PRL 92 (2004) 012001 Wilson
action, anisotropic
lattices,
Datta, Karsch, P.P, Wetzorke, PRD 69 (2004)
094507 Non-perturbativel impr. Wilson action,
isotropic lattices,

Umeda, Nomura, Matsufuru, hep-lat/0211003 Fermilab
action, anisotropic lattices,
, extended operators
33
Heavy quarkonia spectral functions (II)
What do we get at low temperature from lattice
calculations ? Calculations performed on
isotropic lattices for 1/a4.04GeV, 4.86GeV,
9.72GeV
Datta, Karsch, P.P, Wetzorke, PRD 69 (2004) 094507
1/a4.86GeV
1/a9.72GeV
1/a4.04GeV
Lattice artifacts !!!


2nd and 3rd peaks are lattice artfifacts, no 2S
state
34
Heavy quarkonia spectral functions (III)
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)
094507
35
Heavy quarkonia spectral functions (IV)
Heavy quarkonia spectral functions from MEM
is dissolved at


Is dissolved at
Datta, Karsch, P.P., Wetzorke, PRD 69 (2004)
094507
Gradual dissolution of screening
cannot lead to suppression what is
the thermal width ???
36
Results from anisotropic lattices
Asakawa, Hatsuda, PRL 92 (2004) 012001 Point
operators
Umeda, Nomura, Matsufuru, Lattice 2004, Smeared
operators
37
Light meson spectral functions (I)
No light mesons are expected to exist above
deconfinement temperatures !
Asakawa, Hatsuda, Nakahara, Nucl.Phys. A715
(2003) 863
Anisotropic lattices Std. Wilson fermions
Meson resonance above deconfinement ! Approximate
degeneracy of PS, SC, V, AV channels !
38
Light meson spectral functions (II)
Karsch, Laermann, P.P.,Stickan,
Wetzorke, Nucl.Phys. A715 (2003) 701 work in
progress
Large deviation from 1
Isotropic lattices fixed by
NP clover fermions,
Scaling with T
Lattice artifacts !

39
Light meson spectral functions (III)
Vector spectral functions and thermal dilepton
rate
Karsch, Laermann, P.P.,Stickan, Wetzorke, PLB 530
(2002) 147, work in progress
Mesons below
Strong correlations above ??
Suppression of low mass dileptons above