FLOW, FREEZE-OUT and EoS in relativistic heavy-ion collisions at NICA
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Transcript of FLOW, FREEZE-OUT and EoS in relativistic heavy-ion collisions at NICA
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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)
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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
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Flow: How to quantify it
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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
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DEFINITIONS. NON-CENTRAL COLLISIONS (B>0 )
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DISTRIBUTIONSRapidity dependence
Transverse momentum dependence
Centrality dependence
n=1,2,…
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Motivation:connection to
Equation of State
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DISAPPEARANCE OF DIRECTED FLOW
Hung and Shuryak, PRL 75 (1995) 4003
Braun-Munzinger, NPA 661 (1999) 261c
In case of first order phase transition
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DISAPPEARANCE OF DIRECTED FLOW
Transition to Quark-Gluon Plasma leads to decrease in pressure and, therefore, to softening of the directed flow
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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
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Transverse flow (between AGS and SPS)
Directed flow
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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
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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
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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
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SOFTENING OF DIRECTED FLOW
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COMPARISON WITH EXPERIMENTAL DATA
E. Zabrodin et al. , PRC 63 (2003) 034902; L. Bravina et al., PRC 61 (2000) 064802
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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
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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
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CONCLUSIONS (DIRECTED FLOW )
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Elliptic flow
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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
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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
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Open question:
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Flow and freeze-out
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TIME EVOLUTION OF ELLIPTIC FLOW (RHIC)
Au+Au @ 130 and 200 AGeV
Analysis should be repeated at NICA enrgies
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ELLIPTIC FLOW AND FREEZE-OUT
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ELLIPTIC FLOW AND FREEZE-OUT
Pions and nucleons are coming from different areas
L. B. et al., PLB 631 (2005) 109
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FREEZE-OUT OF HADRONSL. B. et al., PRC 60 (1999) 044905
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SEQUENTIAL FREEZE-OUTSPS
AGSL. B. et al., PRC 60 (1999) 044905 ; PLB 354 (1995) 196
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ABSENCE OF SHARP FREEZE-OUT
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CONCLUSIONS (FREEZE-OUT)
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FREEZE-OUT AT RHIC: URQMD
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FREEZE-OUT AT RHIC: QGSM
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5. FREEZE-OUT AT RHIC: URQMD
M.S. Nilsson, ”LHC and beyond” (Lund, Feb. 2009)
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FREEZE-OUT AT RHIC: QGSM
M.S. Nilsson , ”LHC and beyond” (Lund, Feb. 2009)
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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
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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
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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
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Central cell:Relaxation to equilibrium
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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
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STATISTICAL MODEL OF IDEAL HADRON GASinput values output values
Multiplicity
Energy
Pressure
Entropy density
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PRE-EQUILIBRIUM STAGE
Homogeneity of baryon matter Absence of flow
The local equilibrium in the central zone is quite possible
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Models employed:UrQMDQGSM
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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
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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
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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
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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)
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Equation of StateT vs. energy,
etc
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ISENTROPIC EXPANSION
Expansion proceeds isentropically (with constant entropy per baryon). This result supports application of hydrodynamics
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EQUATION OF STATE IN THE CELL
pressure vs. energy
sound velocity
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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
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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)
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Modification of analysis
(small cells)
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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
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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
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Back-up Slides
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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 ...
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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
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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
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QUARK-GLUON STRING MODEL (QGSM) AND ULTRA-RELATIVISTIC QUANTUM MOLECULAR DYNAMICS (URQMD)
Excitation of color neutral strings