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Hydrodynamical Evolution near the QCD Critical End Point. Duke University Chiho NONAKA. in Collaboration with. Masayuki Asakawa ( Kyoto University ). November, 2003@Collective Flow and QGP properties, BNL. RHIC. T. Critical end point. CFL. 2SC. m. GSI. Critical End Point in QCD ?.

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hydrodynamical evolution near the qcd critical end point

Hydrodynamical Evolution near the QCD Critical End Point

Duke University

Chiho NONAKA

in Collaboration with

Masayuki Asakawa (Kyoto University)

November, 2003@Collective Flow and QGP properties, BNL

critical end point in qcd

RHIC

T

Critical end point

CFL

2SC

m

GSI

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
phenomenological consequence

Still we need to study

  • EOS
  • Focusing
  • Dynamics (Time Evolution)
  • Hadronic Observables : NOT directly reflect properties at E
    • Fluctuation, Collective Flow
Phenomenological Consequence ?

M. Stephanov, K. Rajagopal, and E.Shuryak,

PRL81 (1998) 4816

critical end point

Divergence of Fluctuation

Correlation Length

If expansion is adiabatic.

eos with cep

T

QGP

Hadronic

h

r

m

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

eos of 3 d ising model

h : external magnetic field

QCD

Mapping

T

h

r

m

EOS of 3-d Ising Model
  • Parametric Representation of EOS

Guida and Zinn-Justin NPB486(97)626

thermodynamical quantities

T

QGP

Hadronic

h

r

m

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

equation of state
Equation of State

CEP

Baryon number density

Entropy Density

comparison with bag excluded volume eos
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

sound velocity

Sound velocity along n /s

B

/L

/L

TOTAL

TOTAL

  • Clear difference between

n /s=0.01 and 0.03

B

Sound Velocity
  • Effect on Time Evolution
  • Collective flow

EOS

slowing out of equilibrium

r

h

faster (shorter)

expansion

Focusing

Slowing out of Equilibrium
  • Berdnikov and Rajagopal’s 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 : Bjorken’s solution along nB/s

t0 = 1 fm, T0 = 200 MeV

correlation length i

x

  • Max.

depends on n /s.

eq

B

h

  • Trajectories pass through the region where
  • x is large. (focusing)

r

eq

Correlation Length (I)
  • x

eq

Widom’s scaling low

correlation length ii

t

  • x is larger than x at Tf.
  • Differences among xs on n /s are small.
  • In 3-d, the difference between x and x becomes
  • large due to transverse expansion.

eq

B

eq

Correlation Length (II)
  • x : time evolution (1-d)

Model C (Halperin RMP49(77)435)

consequences in experiment i
Consequences in Experiment (I)

CERES:Nucl.Phys.A727(2003)97

  • Fluctuations
  • CERES
  • 40,80,158 AGeV Pb+Au
  • collisions

Mean PT Fluctuation

No unusually large

fluctuation

CEP exists in near RHIC energy

region ?

consequences in experiment ii

?

EOS with CEP

EOS with CEP gives

the natural explanation

to the behavior of T .

Entropy density

f

J. Cleymans and K. Redlich,

PRC, 1999

Consequences in Experiment (II)
  • Kinetic Freeze-out Temperature

Low T comes from

large flow.

?

f

Xu and Kaneta,

nucl-ex/0104021(QM2001)

cep and its consequences

Its Consequences

  • Slowing out of equilibrium
  • Large fluctuation
  • Freeze out temperature at RHIC
  • Fluctuation

Focusing

CEP and Its Consequences

Future task

  • Realistic hydro calculation with CEP