Quasiparticle Perspective on CEP

B. KämpferResearch Center Rossendorf/Dresden Technical University Dresden

with M. Bluhm, R. Schulze, D. Seipt, supported by BMBF, GSI, EU

- Quasiparticle Model vs. Lattice QCD- Including the CEP- Somewhat Hydro

NJL Model(Schaefer-Wambach)

NJL Perspective

PNJL: Weise, Ratti,...

nothing(Fodor et al.)

Lattice QCD Results

1. Phase Boundary

2. EoS

= 0

Taylor expansion

reweighting, overlapping, complex mu

Imp

rove

d c

alc

uls

.

Quasiparticle Model

latticeeffective1-loop selfenergies

stat. + thermo.consist.:),( Tp

Biele fe ld 2001

E. Shuryak:

Bielefeld-Swansea data

c0

c2

c4

c6

phase transition

Important forCosmology: T(t)

Important forCosmology: n(t)

c2 QPM susceptibility

peak:crit. behavior

Isentropic Expansionchemical freeze-out: T, muB s/n

QPM thermodynamics looks fine

Nf=2

Including the CEP

1.

B )(T, (r,h)2.

h

r

Tkink in

div. of

PhenomenologicalConstruction

(holds only near CEP)

Gebhard, Krey

QPM

3. Singular Part of EoS: Parametric Form

QCD: 3D Ising Model

Guida+Zinn-Justin

(r,h) (R, )

h=const

r=const

R=const

0=const

Toy Model I: smooth reg. EoS

1.

2. critical curve

3. CEP:

additional information

Allton et al. 2002170 MeV

Fodor-Katz

pQCD

333

Finite Grid Effects

CEP:Attractor - Repulsor

no focusing effect

Wambach et al.

unphysical

CEP

Barz,Kämpfer,Csernai,LukacsPLB 1984

A Funnel Effect due to Phase Transition?

1D Hydro &relaxation time approx.

focusing effect

squeezing of chem. freeze-out pointsexp. not observed

Toy Model II: 2-Phase Ansatz

Nonaka, Asakawa (2004)

critical curve:given by

Toy Model III: QPM & CEP

change of effective carriersof baryon number fluctuations

lattice

Need of Modifying lQCD by CEP?

Conjecture: hydro evolution ofv2, pT at top-RHIC & LHC does not feel CEP

using P. Kolbs code + init.parametersKolb-Rapp off-equilibrium hadron EoS

with U. Heinz/Ohio

K. Paech et al.Hydro with CEP

Aoki

Karsch

Bernard 0.1

Bernard 0.2

2+1 EoS ready? RHICInit.conds.

A Family of EoS‘s

QPM

lin.interpol.

*fix

+

+

+

interpolation is betterthan extrapolation

sound waves

Strange Baryons

data disfavor phase transitionHuovinen 2005: opposite conclusion (inspection of small pT)

non-hydro behavior of open charm?

D Mesons Meson

or K?

Looking for Hydro Scaling

To Do List

1. shape fluctuations

K. Werner (core-corona)

2. shape & energy density fluctuations

T. Kodama et al.

Summary & Outlook

-- Lattice QCD vs. Quasiparticle Model:perfect description of either p(T,0) or p(T,mu)extrapolation to larger mu consistency of chem.freeze-out and isentropes

-- Toy models for including CEP:many free parameters, size of critical region = ?lattice QCD + CEP = small effects allowed

-- v2 hydro:RHIC: EoS at Tc does not matter too much

-- CERN-SPS – CBM-FAIR: very different

QPM

lQCD

QCD

EoS

hydro

Relativistic Hydro

Init. Conds.: b dependent profiles fromwounded nucleon & binary collisions

s < 110 fm-3, nB < 0.4 fm-3: RHIC200

Freeze-out: Cooper-Frye, T = 100 MeV Kolb-Rapp off-equilibrium

EoS: p(e,nB), T(e,nB), muB(e,nB)

P. Kolb et al.

with U. Heinz/Ohio

Interpolation is Better than Extrapolation

lQCD

lQCD/res.gas/KR

*

V2: weak dependence on EoS

w/o CEP

The 10% Problem

c0

c2 c0

Weak Dependence of v2 on EoS

High Density EoS

: bag model

x

Progress of lQCD:High-density part fixed

Progress of lQCD:Low-density part fixed

tiny baryon density effects

(=resonance gas: Redlich)

QPM(1.0)

QPM(2.0)

with CEP