Duke University

1
Hydrodynamical Evolution near the QCD Critical
End Point

• Duke University
• Chiho NONAKA

in Collaboration with
Masayuki Asakawa (Kyoto University)
November, 2003_at_Collective Flow and QGP
properties, BNL
2
Critical End Point in QCD ?
Suggestions

• NJL model (Nf 2)

K. Yazaki and M.Asakawa., NPA 1989

• Lattice QCD

• Reweighting
• Z. Fodor and S. D. Katz
• (JHEP 0203 (2002)
  014)

• Imaginary chemical potential
• Forcrand and Philipsen hep-lat/0307020

3
Phenomenological Consequence ?
M. Stephanov, K. Rajagopal, and E.Shuryak, PRL81
(1998) 4816
critical end point
Divergence of Fluctuation
Correlation Length
If expansion is adiabatic.
4
EOS with CEP

• How to Construct EOS with CEP?
• Assumption
• Critical behavior dominates in a large region
  near end point
• Near QCD end point singular part of EOS
• Mapping
• Matching with known QGP and
• Hadronic entropy density
• Thermodynamical quantities

3d Ising Model
QCD
Same Universality Class
5
EOS of 3-d Ising Model

• Parametric Representation of EOS

Guida and Zinn-Justin NPB486(97)626
6
Thermodynamical Quantities

• Singular Part of EOS near Critical Point
• Gibbs free energy
• Entropy density
• Matching
• Entropy density
• Thermodynamical quantities
• Baryon number density, pressure, energy
  density

7
Equation of State
CEP
Baryon number density
Entropy Density
8
Focusing and CEP
9
Comparison with Bag Excluded Volume EOS

• n /s trajectories in T- m plane

B
Bag Model Excluded Volume Approximation (No
End Point)
With End Point
Usual Hydro Calculation
Not Focused
Focused
10
Sound Velocity

• Effect on Time Evolution
• Collective flow

EOS
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Slowing out of Equilibrium

• Berdnikov and Rajagopals Schematic Argument

B. Berdnikov and K. Rajagopal, Phys. Rev. D61
(2000) 105017
slower (longer) expansion
Correlation length longer than xeq
xeq
x
along r const. line

• Effect of Focusing on x?

E
h
Time evolution Bjorkens solution along nB/s
t0 1 fm, T0 200 MeV
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Correlation Length (I)

• x

eq
Widoms scaling low
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Correlation Length (II)

• x time evolution (1-d)

Model C (Halperin RMP49(77)435)
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Consequences in Experiment (I)
CERESNucl.Phys.A727(2003)97

• Fluctuations
• CERES
• 40,80,158 AGeV PbAu
• collisions

Mean PT Fluctuation
No unusually large fluctuation
CEP exists in near RHIC energy region ?
15
Consequences in Experiment (II)

• Kinetic Freeze-out Temperature

Low T comes from large flow.
?
f
Xu and Kaneta, nucl-ex/0104021(QM2001)
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CEP and Its Consequences
Future task

• Realistic hydro calculation with CEP