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QCD Equation of State - Impact on elliptic flow and transverse
momentum spectra
Marcus BluhmForschungszentrum Dresden-Rossendorf
• Comparison with lattice QCD• Chiral extrapolation• RHIC & LHC – v2, transverse momentum spectra
with B. Kämpfer, R. Schulze, D. Seipt & U. Heinzsupported by BMBF, GSI
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T
µB
Motivation
early universe: µB <<< T
WIMP‘s: Tf.o. ~ MX / 25
RHICLHC-ALICE
µB < T
quark starsµB >> Tp(e,nB)
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Quasi-Particle Model
MB et al., Eur. Phys. J. C 2007MB et al., Eur. Phys. J. C 2007
Σ 2-part. irred. diagr.
CJT
2-loop QCDthermodynamics
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k/mg
finite widths Im ΠT ≠ 0
k
asymptotic dispersion relations:
chiral expansion in mq/T:
replace g G
gluons
2+1
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Equation of State
Nf=2+1
2000 … 2007
sensible chiral extrapolation
not testable: dependence on Nσ, Nτ, action, …
Tc is external information
cs2
mq
Tc = 170 MeV
Πq = mq2 + 2mf
2 h(mq/T)
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T/Tc
Isospin susceptibility
diagonal and non-diagonal susceptibilities
c2I
c4I
Sensible µB - extrapolation
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EoS for RHIC + LHC – Family of EoS‘s
QPM
lin.interpol.
*fix
+
+
+
high energy density region fixed
baryon density effectstiny
low density region fixed
µB = 0
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RHIC top energy
strange baryons
P.Kolb
directly emitted hadrons
S0 = 110 fm-3
n0 = 0.4 fm-3
τ0 = 0.6 fm/c
e0 = 29.8 GeV fm-3
p0 = 9.4 GeV fm-3
T0 = 357 MeV
EoS favored with soft region around Tc and rapid increase above Tc
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LHC estimates
conservative guess: s0 = 330 fm-3 , τ0 = 0.6 fm/ce0 = 127 GeV fm-3
p0 = 42 GeV fm-3
T0 = 515 MeV
pT spectra flatterv2 at fixed pT smaller
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Summary & Outlook
• Quasi-particle model based on 2-loop QCD Φ • Comparison with lattice QCD• Family of EoS‘s for RHIC & LHC – chiral extrapolation• Application: v2, p┴-spectra
• soft EoS near Tc with rapid rise in cs2 above Tc favored
• LHC: pT-spectra flatter, v2(pT) smaller
• variation of EoS, initial & final conditions• event-by-event fluctuations, viscous effects
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Light hadrons
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Bielefeld-Swansea data
c0
c2
c4
c6
„phase transition“
D=1.15
neglect strong interaction
QPM
lQCD
MB et al., PLB 2005