FLOW, FREEZE-OUT AND EOS IN RELATIVISTIC

HEAVY-ION COLLISIONS AT NICA

L. Bravina for

UiO heavy-ion theory group

Physics at NICA (Dubna, Sept. 9-12, 2009)

Content

• Flow: how to quantify this phenomenon

• Connection to Equation of State• Transverse flow at AGS and SPS

energies• Freeze-out of hadrons in microscopic

models• Flow and freeze-out• Thermalization, Equilibration and

EoS at NICA• Summary of signals to study at NICA

Flow: How to quantify it

W. Scheid, H. Muller, and W. Greiner,PRL 32, 741 (1974)

M.I. Sobel, P.J. Siemens, J.P. Bondorf, an H.A. Bethe, Nucl. Phys. A251, 502 (1975)

G.F. Chapline, M.H. Johnson, E. Teller, and M.S. Weiss, PRD 8, 4302 (1973)E. Glass Gold et al. Annals of Physics 6, 1 (1959)

H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980)

Ne

The idea to use collective flow to Probe the properties of nuclear matter is long-standing

They are predicted to provide unprecedented access to the properties of Nuclear matter

R. Lacey, QM’05 talk

DEFINITIONS. NON-CENTRAL COLLISIONS (B>0 )

DISTRIBUTIONSRapidity dependence

Transverse momentum dependence

Centrality dependence

n=1,2,…

Motivation:connection to

Equation of State

DISAPPEARANCE OF DIRECTED FLOW

Hung and Shuryak, PRL 75 (1995) 4003

Braun-Munzinger, NPA 661 (1999) 261c

In case of first order phase transition

DISAPPEARANCE OF DIRECTED FLOW

Transition to Quark-Gluon Plasma leads to decrease in pressure and, therefore, to softening of the directed flow

DIRECTED FLOW OF NUCLEONS AND FRAGMENTS

W. Reisdorf, H.G. Ritter Annu.Rev.Nucl.Part.Sci. 47 (1997) 663

Plastic Ball Collaboration introduced a slope parameter

Directed flow of nucleons and fragments has linear slope in normal direction => normal flow

Transverse flow (between AGS and SPS)

Directed flow

DIRECTED FLOW OF NUCLEONS. 3-FLUID HYDRO

The model predicts a local minimum in the excitation function of directed flow at energies between 10 and 20 AGeV (so far not been observed)

J. Brachmann et al., PRC 61 (2000) 024909

DIRECTED FLOW OF PIONS AND PROTONS AT 40 AGEV

C. Alt et al. (NA49), PRC 68 (2003) 034903 Soft

enin

g of

dir

ecte

d flo

w o

f pr

oton

s at m

idra

pidi

ty

DIRECTED FLOW OF PIONS AND PROTONS AT 158 AGEV

C. Alt et al. (NA49), PRC 68 (2003) 034903 Ant

iflow

of p

roto

ns in

pe

riph

eral

eve

nts

SOFTENING OF DIRECTED FLOW

COMPARISON WITH EXPERIMENTAL DATA

E. Zabrodin et al. , PRC 63 (2003) 034902; L. Bravina et al., PRC 61 (2000) 064802

SOFTENING OF DIRECTED FLOW

Although the normal flowcomponent is always larger than the antiflow one, in central rapidity window the antiflow can overshadow its normal counterpart

L.Bravina et al., NPA 715 (2003) 665c

DIRECTED FLOW IN DIFFERENT P_T - INTERVALS

The directed flow of high-pT pions (and other mesons) seems to have a normal slope

L.Bravina et al., PRC 63 (2001) 034902

CONCLUSIONS (DIRECTED FLOW )

Elliptic flow

ELLIPTIC FLOW OF PIONS AND PROTONS AT 40 AGEV

C. Alt et al. (NA49), PRC 68 (2003) 034903 Sign

ifica

nt d

ip a

t mid

rapi

dity

fo

r pr

oton

flow

in c

entr

al e

vent

s

ELLIPTIC FLOW OF PIONS AND PROTONS AT 40 AGEV

C. Alt et al. (NA49), PRC 68 (2003) 034903

However, the dip at midrapidity disappears if one uses the {2} or {4} cumulant method

Open question:

Flow and freeze-out

TIME EVOLUTION OF ELLIPTIC FLOW (RHIC)

Au+Au @ 130 and 200 AGeV

Analysis should be repeated at NICA enrgies

ELLIPTIC FLOW AND FREEZE-OUT

ELLIPTIC FLOW AND FREEZE-OUT

Pions and nucleons are coming from different areas

L. B. et al., PLB 631 (2005) 109

FREEZE-OUT OF HADRONSL. B. et al., PRC 60 (1999) 044905

SEQUENTIAL FREEZE-OUTSPS

AGSL. B. et al., PRC 60 (1999) 044905 ; PLB 354 (1995) 196

ABSENCE OF SHARP FREEZE-OUT

CONCLUSIONS (FREEZE-OUT)

FREEZE-OUT AT RHIC: URQMD

FREEZE-OUT AT RHIC: QGSM

5. FREEZE-OUT AT RHIC: URQMD

M.S. Nilsson, ”LHC and beyond” (Lund, Feb. 2009)

FREEZE-OUT AT RHIC: QGSM

M.S. Nilsson , ”LHC and beyond” (Lund, Feb. 2009)

Summary and perspectives

• Collective phenomena, such as directed and elliptic flow, should be studied together with the freeze-out conditions (i.e., femtoscopic correlations)

• We propose to make model predictions (UrQMD, QGSM, HSD, AMPT, etc) of distributions presented it this talk for NICA energy range

OR LITTLE BIG BANG

Strange Quark Matter’2008, Beijing, 09.10.2008

EOS at NICA energies and role of resonances L.Bravina (University of Oslo) in collaboration with I.Arsene, J.Bleibel, M.Bleicher, G.Burau, A.Faessler, C.Fuchs, M.Nilsson, H.Stocker, K.Tywoniuk, E.Zabrodin

MOTIVATION: EQUATION OF STATE

Tricritical point is located around 10-40 GeV (LQCD)

We have to explore this energy range to study the possible phase transition

QGP can be formed already at low energies

H. Stoecker, J. Phys. Conf. Ser. 50 (2006) 300 L. Bravina et al., PRC 60 (1999) 024904; 63 (2001) 064902

Central cell:Relaxation to equilibrium

EQUILIBRATION IN THE CENTRAL CELL

Kinetic equilibrium: Isotropy of velocity distributions Isotropy of pressure

Thermal equilibrium: Energy spectra of particles are described by Boltzmann distribution

Chemical equlibrium: Particle yields are reproduced by SM with the same values of

STATISTICAL MODEL OF IDEAL HADRON GASinput values output values

Multiplicity

Energy

Pressure

Entropy density

PRE-EQUILIBRIUM STAGE

Homogeneity of baryon matter Absence of flow

The local equilibrium in the central zone is quite possible

Models employed:UrQMDQGSM

KINETIC EQUILIBRIUM

Isotropy of velocity distributions

Isotropy of pressure

Velocity distributions and pressure become isotropic for all energies

L.B

ravi

na e

t al.,

PR

C 7

8 (2

008)

014

907

KINETIC EQUILIBRIUM

Isotropy of velocity distributions

Isotropy of pressure

Velocity distributions and pressure become isotropic for all energies

L.B

ravi

na e

t al.,

PR

C 7

8 (2

008)

014

907

THERMAL AND CHEMICAL EQUILIBRIUM

Boltzmann fit to the energy spectra Particle yields

Thermal and chemical equilibrium seems to be reached

L.B

ravi

na e

t al.,

PR

C 7

8 (2

008)

014

907

HOW DENSE CAN BE THE MEDIUM?

”B

ig”

cell

(V =

5x5

x5 fm

^3)

Dramatic differences at the non-equilibrium stage; after beginning of kinetic equilibrium the energy densities and the baryon densities are the same for ”small” and ”big” cell

“Sm

all”

cel

l (V

=>

0)

Equation of StateT vs. energy,

etc

ISENTROPIC EXPANSION

Expansion proceeds isentropically (with constant entropy per baryon). This result supports application of hydrodynamics

EQUATION OF STATE IN THE CELL

pressure vs. energy

sound velocity

EQUATION OF STATE: SOUND VELOCITY VS. T

comparison with Hagedorn model

and chemical potential

Heavy resonances

Big difference between models with and w/o heavy resonances

The difference increases with bombarding energy

L.B

ravi

na e

t al.,

PR

C 7

8 (2

008)

014

907

Still sonic velocity drops faster than in Hagedorn model . Non-zero chemical potential ?

M. C

hoin

acki

et a

l., P

RC

71

(200

5) 0

4490

2

EQUATION OF STATE:

energy and entropy densities vs. T

No difference between the models

Zero chem. potential

Non-zero chem. potential

(1)

(2)

If then (2) is transformed to (1)

Modification of analysis

(small cells)

EOS IN THE CELL: OBSERVATION OF KNEE

temperature vs. chemical potentials

Although the “knee” is similar to that in 2-flavor lattice QCD, it is related to inelastic (chemical) freeze-out in the system

S. Ejiri et al., PRD 73 (2006) 054506

L.Bravina et al., PRC 78 (2008) 014907

Conclusions• Both models favor formation of equilibrated matter for a

period of 10-15 fm/c• During this period the expansion of matter in the central

cell proceeds isentropically with constant S/B • The EOS has a simple form: P/e = const , where the

speed of sound squared varies from 0.12 (AGS) to 0.14 (40 AGeV), and to 0.15 (SPS & RHIC) => onset of saturation

• Heavy resonances: are seeing in or , but not in energy(entropy) vs. T - distributions

• T vs. mu: the knee structure which appears at the onset of equilibrium is related to chemical freeze-out

2 ( )sc T 2 ( )s bc

Back-up Slides

MODELS AT OUR DISPOSAL: HYDJET++, QGSM, URQMD

Current projects: Bulk particle production in soft and hard processes; anisotropic flow; equation of state; particle freeze-out; role of resonances; HBT correlations; jet quenching;

shadowing, heavy quarkonia production ...

DIRECTED FLOW OF NUCLEONS. 3-FLUID HYDRO

The antiflow component is a source of the reduction of directed flow at midrapidity

NB! This is a very rare case when the antiflow behavior is reproduced in hydrodynamic model

J. Brachmann et al., PRC 61 (2000) 024909

DIRECTED FLOW OF PIONS AND PROTONS AT 158 AGEV

C. Alt et al. (NA49), PRC 68 (2003) 034903

What is this?

Red, green,blue

points

QUARK-GLUON STRING MODEL (QGSM) AND ULTRA-RELATIVISTIC QUANTUM MOLECULAR DYNAMICS (URQMD)

Excitation of color neutral strings