qcd thermodynamics at low and high temperatures
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QCD thermodynamics at low and high temperatures
high-T ( T>>Λ), perturbation theory should work, however:
expansion in g shows poor convergence
( reorganization of the perturbative series )
g^6 -order contribution is not calculable in the loop expansion
non-perturbative (lattice) method is desirable
low-T : hadrons are “good” degrees of freedom and weakly interacting for T<<Λ
(use chPT, Gerber, Leutwyler, NPB 321 (89) 387 )
The simplest approach : consider gas of non-interacting hadrons
too naïve ? Not necessarily many hadronic interactions dominated by
resonance exchange in the s-channel , e.g.
interacting hardon gas non-interacting resonance gasHagedorn, Nouvo Cim. 35 (65) 395
Chapline et al, PRD 8 (73) 4302
Karsch et al, Eur.Phys.J.C29 (03)549
ρππ →
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Deconfinement transition : rapid increase of the pressure, energy denisty, entropy
density (liberation of many new degrees of freedom ?) Cabbibo, Parisi, PLB 59 (75) 67
Is it a phase transition ? What is the order parameter ?
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Lattice Monte-Carlo simulations :Kuti et al, PLB 98 (81) 199
McLerran, Svetitsky, PRD 24 (81) 450
Engels et al, PLB 101 (81) 89
free energy of static quarks
rapid rise in the energy density
Lattice set-up:
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• Use different volumes and Ferrenberg-Swedsen re-weighting to combine
information collected at different gauge couplings
Finite volume behavior can tell the order of the phase transition, e.g. for 1st
order transition the peak height scales as spatial volume !
Boyd et al., Nucl. Phys. B496 (1996) 167
How to determine the transition temperature ?
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Necco, Nucl. Phys. B683 (2004) 167
Necco, Sommer, NPB 623 (02) 271
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Continuum limit for L ?
needs renormalization !
Dumitru et al, hep-th/0311223
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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
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The renormalized Polyakov loop
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12
T/Tc
Nτ=4
Nτ=8
Nτ=16
Kaczmarek et al, PLB 543 (02) 41, PRD 70 (04) 074505, hep-lat/0309121
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Kaczmarek, Phys.Rev.D62 (00) 034021
Correlation length near the transition
small inverse correlation length => weak 1st order phase transition
QCD is far from the large N-limit !
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Deconfinement transition in QCD
Dynamical quarks break Z(3) symmetry => no phase transition
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RBC-Bielefeld Collaboration:
M. Cheng, N.H. Christ, S. Eijiri, K. Hübner, C. Jung, F., O. Kaczmarek, F. Karsch,
E. Laermann, J. Liddle, R. Mawhinney, C. Miao, P. Petreczky, K. Petrov, C. Schmidt,
W. Söldner, J. Van der Heide
Static quark anti-quark free energy in 2+1f QCD
preliminary
preliminary
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Static quark anti-quark free energy in 2+1f QCD
preliminary
preliminary
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Renormalized Polyakov loop in 2+1F QCD
see talk by Karsch at Lattice 2007,
data for temporal extent=8 are from HotQCD Collaboration
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How different is full QCD from SU(3) gauge theory ?
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0
1
2
3
4
5
1 1.5 2 2.5 3 3.5 4
T/Tc
mD/T Nf=0Nf=2
Nf=2+1meff
Screening mass in 2+1F QCD
quarks modify the perturbative
pre-factors, non-perturbative
effects are in the soft gluon
sector
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Homework: