1
QM2009 summary: Soft physics:
Flow and hydrodynamics
A. Marin (GSI)
2
OUTLINE
• HBT• Flow• Hydrodynamics
3
HBT PUZZLE (S. Pratt)
RHIC HBT PUZZLE: flow & spectra OK HBT radii NOT OK ideal hydro (no viscosity)1st order phase transition 0 =1.0 fm/c
4
HBT PUZZLE (S. Pratt)
Solution:Early acceleration (t < 1 fm/c)Shear viscosityEoS (crossover)Initial energy profile
Fixing HBT requires increasing explosivityBulk viscosity decreases radial flowEarly flow increases elliptic flowviscosity decreases elliptic flow
S. Pratt, arXiv:0812.4714v1
5
Effect of Eccentricity Effect of Eccentricity FluctuationsFluctuationsand Nonflowand Nonflow
on Elliptic Flow Methods on Elliptic Flow MethodsJean-Yves Ollitrault, Art Poskanzer, and Sergei Voloshin
QM09
6
Reaction, Participant, and Event Planes
participant plane
coordinate space
momentum space
7
Methods“Two-particle”:• v2{2}: each particle with every other particle• v2{subEP}: each particle with the EP of the other subevent• v2{EP} “standard”: each particle with the EP of all the others• v2{SP}: same, weighted with the length of the Q vectorMany-particle:• v2{4}: 4-particle - 2 * (2-particle)2
• v2{q}: distribution of the length of the Q vector• v2{LYZ}: Lee-Yang Zeros multi-particle correlation
review of azimuthal anisotropy:arXiv: 0809.2949
STAR, J. Adams et al., PRC 72, 014904 (2005)
2-part. methods
multi-part. methods
"Because of nonflow and fluctuations the true v2 lies between the lower band and the mean of the two bands.”
8
Differences of Measured v2 Values
All differences proportional to
Without additional assumptionscan not separate nonflow and fluctuations
nonflowfluctuations
9
Data Corrected to <v2>
published
agreement for mean v2 in participant plane
corrected to PP
10
corrected to RP
v2 in the Reaction Plane
in Gaussian fluctuation approximation:
Voloshin, Poskanzer, Tang, and Wang, Phys. Lett. B 659, 537 (2008)
a v2 for theorists
11QM2009, Knoxville, March 30 - April 4 Patricia Fachini 11
Patricia Fachini
for the STAR collaboration
Motivation
Measurements
Results
Conclusions
ρ0 Production in Cu+Cu Collisions at √sNN = 200 and 62.4 GeV in STAR
12
• Significant ρ0 v2 measured pT > 1.2 GeV/c v2 ~ 13 ± 4%.
Elliptic Flow
12QM2009, Knoxville, March 30 - April 4 Patricia Fachini
13QM2009, Knoxville, March 30 - April 4 Patricia Fachini 13
Elliptic Flow
• Resonance v2 ρ0(770) production mechanism scale NCQ v2/nππ ρ0 n = 4 or qq ρ0 n = 2
a, b, c, and d constants extracted using KS0 and Λ v2 ρ0 v2 n= 4.7 ± 2.9
pT range covered not sufficient for conclusive statement on the ρ0 production mechanism.
v2(pT,n) = - dn1 + exp[-(pT/n – b)/c]
anX. Dong et al., Phys.Lett. B597 (2004) 328
n=2 n=4
14
Differential Measurements of Differential Measurements of Hexadecapole (VHexadecapole (V44) and Elliptic ) and Elliptic
( V( V22) Flow as a Probe for ) Flow as a Probe for
Thermalization at RHIC-Thermalization at RHIC-PHENIXPHENIX
Arkadij TaranenkoArkadij TaranenkoNuclear Chemistry Group Nuclear Chemistry Group
Stony Brook UniversityStony Brook University
for the PHENIX Collaboration
15
23/4/2123/4/21 Arkadij Taranenko, QM2009Arkadij Taranenko, QM20091515
KEKETT and CQN Scaling for v and CQN Scaling for v44KEKETT and CQN Scaling for v and CQN Scaling for v44
V4/(nq)2 vs KET /nq scaling observed for V4
1616
VV44 = k(V = k(V22))2 2 where k is the same for different particle species where k is the same for different particle species
vv44/(v/(v22))22 ratio for different particle species ratio for different particle speciesvv44/(v/(v22))22 ratio for different particle species ratio for different particle species
17
23/4/2123/4/21 Arkadij Taranenko, QM2009Arkadij Taranenko, QM20091717
Baryon and meson V2 & V4 scale to a universal curve
as a function of (KET)/nq
PHENIXPreliminary
Flow is universal?Flow is universal?Flow is universal?Flow is universal?
1818
PHENIX Preliminary
Good fits to the vGood fits to the v2 2 & v& v4 4 of charged hadrons of charged hadrons Good fits to the vGood fits to the v2 2 & v& v4 4 of charged hadrons of charged hadrons
Model ansatz extended from v2 to v4. Good fits obtained both for scaled v2 and v4 . What about fits for PID?
2
4 42 2
0
1hd
nv v K
K
npart
KN
1
0
2 1
K
Kvv nhd
2
Two fit parameters: v2
hd and ( is fixed)
24 2v v →
ε – participant eccentricity from Glauber Model
19
Event Anisotropy v2 at STARParticle type, Beam energy and Centrality dependence
ShuSu Shi for the STAR collaboration
Nuclear Science Division, Lawrence Berkeley National LaboratoryInstitute of Particle Physics, Central China Normal University
20
Test Hydro in Small System
Ideal hydro: P. Huovinen, private communication
pT < 2 GeV/c Smaller v2 for heavier
hadrons as expected from hydrodynamics.
Sizable v2(Ξ) even in small system
Ideal hydro fails to reproduce the data
Fluctuation of v2? Viscosity ? Incomplete thermalization ?
STAR preliminary
21
v2 in Cu + Cu (Au +Au) at 200 and 62.4 GeV are comparable within statistical errors
v2 at Cu + Cu 62.4 GeV ~ 12.5 M events- Same procedure used for 200 GeV. - Event plane resolution is 0.088 0.004 in 0 - 60 %, about factor 2 smaller than that in 200 GeV due to lower multiplicity.
STAR Au + Au 200 GeV : PRC77, 054901 (2008) Au + Au 62.4 GeV : PRC75, 054906 (2007)
Energy Dependence
STAR preliminary
22
STAR preliminary
Au + Au at 200 GeV
Au + Au : PRC77, 054901 (2008)
System Size Dependence
Does v2 in most central reach ideal hydrodynamic limit ?
v2 scaled by eccentricity Remove the initial
geometry effect
v2 seems solely depending on initial geometry and number of participant in 200 GeV collisions
v2 ∝ v2(ε, Npart)
23
STAR preliminary
v2/ε scaling: S. Voloshin (for STAR Collaboration), J.Phys.G34(2007)S883PHENIX π, K and p: nucl-ex/0604011v1CGC eccentricity: H.J. Drescher and Y. Nara, PRC 76 041903 (2007), H.J. Drescher and Y.Nara, PRC 75 034905 (2007)
Ideal Hydro Limit
STAR preliminary
Hydro limit
ΞΛ p K h
STAR preliminary
Ideal Hydro Limit Even in central Au + Au collisions, fitting results indicate
that the system is still away from hydro limit
24
Effectiveη/s Extracted from Model
Caveats:Transport model motivated~ best for dilute system of massless particles no phase transition
STAR preliminary
Data shows particle type dependence, not a built-in feature in the modelCan viscous hydrodynamics explain the particle type dependence ?
Inferred η/s depends strongly on the eccentricity model
T: π spectra slope 200 MeVR: Glauber or CGC calculation
H. J. Drescher et al, PRC 76 024905 (2007)
25
The World Collection of η/s STAR preliminary
See M. Sharma ’s talk for pT correlation
26
27
28
29
30
31
Viscous hydrodynamics
Quark Matter 2009
Huichao Song and Ulrich Heinz
The Ohio State University
Supported by DOE
04/02/2009
March 30-April 4, Knoxville, TN
with shear and bulk viscosity
32
Luzum & Romatschke, PRC 2008 Glauber CGC
-Glauber vs.CGC ~100% effect on the extracted value of
-A detailed extraction of shear viscosity entropy ratio also requires:
)41(/ s
s/
-viscous late hadronic stage -non-equilibrium chemistry in HG has been studied in ideal hydro
-bulk viscosity ? -Present conservative upper limit:
5
33
shear viscosity bulk viscosity
Viscous hydro with shear & bulk viscosity
(2nd order shear-bulk -mixing term (Muronga, Rischke) not included.)
0)( xT
Conservation laws:
gpuupeT )()(
u
T
T
2
12
Evolution equations for shear pressure tensor and bulk presurre:
u
T
Tu
2
1)(
34
Shear viscosity vs. bulk viscosity (I)
-Shear viscosity: decelerate cooling process in early stage accelerate cooling process in middle and late stages
-Bulk viscosity: decelerate cooling process
Same initial & final conditionsideal hydro viscous hydro-shear only viscous hydro-bulk only
Local temperature
35
Shear viscosity vs. bulk viscosity (II)
-shear viscosity: increases radial flow, results in flatter spectra
-bulk viscosity: decreases radial flow, results in steeper spectra
radial flow spectra
Same Initial & final conditionsideal hydro viscous hydro-shear only viscous hydro-bulk only
0,4/1 c1,0 c
0,0 css //
36
Viscous v2 suppression: shear and bulk viscosity ideal hydro visc. hydro:
-at RHIC, 2 x min. bulk viscosity could result in ~50% additional v2 suppression
-when extracting the from RHIC data, bulk viscous effects cannot be neglected s/
20%30%
ss //
1,4/1 c0,4/1 c
2,4/1 c
37
Viscous v2 suppression: shear and bulk viscosity ideal hydro visc. hydro:
-at RHIC, 2 x min. bulk viscosity could result in ~50% additional v2 suppression
-when extracting the from RHIC data, bulk viscous effects cannot be neglected s/
20%30%
ss //
1,4/1 c0,4/1 c
2,4/1 c
0
)0( bulk viscosity effects:
(a) Change the flow profile during hydro evolution (b) Additional spectra correction along freeze-out surfacef
Song & Heinz: v2 will decrease, flow corrections only (a), , at freeze-out Monnai & Hirano: v2 will increase, spectra corrections only(b), ideal hydro for evolution
38
Effects from initialization of (III)
-viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure
Smaller vs. larger relaxation time
39
A Short Summary
-When extracting QGP viscosity from experimental data, bulk viscosity effects should not be neglected
-first attempts to constrain from RHIC data indicate )41(5/ s
a realistic EOS, initialization, bulk viscosity, highly viscous hadronic stage
s/
-More theoretical inputs are needed for bulk viscosity:
No consistent simultaneous treatment yet of:
- relaxation time- initialization for bulk pressure - bulk viscosity of hadronic phase, etc
40
Effects of Bulk Viscosity on pT-Spectra and Elliptic Flow Parameter
Akihiko MonnaiDepartment of Physics, The University of Tokyo, JapanCollaborator: Tetsufumi Hirano
Quark Matter 2009March 30th- April 4th, 2009, Knoxville, TN, U.S.A. arXiv:0903.4436 [nucl-th]
41
Introduction (II)
Hydrodynamic analyses needs the Cooper-Frye formula at freezeout
(i) for comparison with experimental data,
(ii) as an interface to a cascade model.
Viscous corrections come in two ways:
(3+1)-D viscous hydro required. We estimate this for a multi-component gas.
Cooper & Frye (‘74)
Quark Matter 2009, Knoxville, Tennessee, April 2Quark Matter 2009, Knoxville, Tennessee, April 2ndnd 2009 2009Effects of Bulk Viscosity on Effects of Bulk Viscosity on ppTT-spectra and Elliptic Flow Parameter-spectra and Elliptic Flow Parameter
Introduction (II)Introduction (II)Introduction (I)Introduction (I) Relativistic Kinetic Theory Relativistic Kinetic Theory
variation of the flow modification of the distribution
* :normal vector to the freezeout hypersurface element,
:distribution of the ith particle, :degeneracy.
particles
hadronresonancegas
QGP
freezeout hypersurface Σ
42
pT-Spectra
Au+Au, , b = 7.2(fm), pT -spectra of
Model of the bulk pressure:
: free parameter
The bulk viscosity lowers <pT> of the particle spectra.
Elliptic Flow Coefficient Elliptic Flow Coefficient vv22((ppTT))ppTT-Spectra-Spectra
Quark Matter 2009, Knoxville, Tennessee, April 2Quark Matter 2009, Knoxville, Tennessee, April 2ndnd 2009 2009Effects of Bulk Viscosity on Effects of Bulk Viscosity on ppTT-spectra and Elliptic Flow Parameter-spectra and Elliptic Flow Parameter
EoS, Transport Coefficients and FlowEoS, Transport Coefficients and Flow
43
Elliptic Flow Coefficient v2(pT)
Au+Au, , b = 7.2(fm), v2(pT) of
The bulk viscosity enhances v2(pT).
*Viscous effects might be overestimated for:
(1) No relaxation for is from the Navier-Stokes limit.
(2) Derivatives of are larger than those of real viscous flow
Results with Quadratic AnsatzResults with Quadratic Ansatz
Quark Matter 2009, Knoxville, Tennessee, April 2Quark Matter 2009, Knoxville, Tennessee, April 2ndnd 2009 2009Effects of Bulk Viscosity on Effects of Bulk Viscosity on ppTT-spectra and Elliptic Flow Parameter-spectra and Elliptic Flow Parameter
ppTT-Spectra-Spectra Elliptic Flow Coefficient Elliptic Flow Coefficient vv22((ppTT))
44
A Transport Calculation with an Embedded (3+1)d Hydrodynamic Evolution:
Elliptic Flow Results from Elab=2-160 AGeVQuark Matter 2009,
31.03.09, Knoxville, Tennessee
Hannah Petersen, Universität FrankfurtThanks to: Jan Steinheimer, Michael Mitrovski, Gerhard Burau, Qingfeng Li, Gunnar Gräf, Marcus Bleicher, Horst Stöcker, Dirk Rischke
(H.P. et al., PRC 78:044901, 2008, arXiv: 0806.1695)(H.P. et al., arXiv: 0901.3821, PRC in print)
45
Initial State• Contracted nuclei have passed
through each other
– Energy is deposited– Baryon currents have
separated • Energy-, momentum- and baryon
number densities are mapped onto the hydro grid
• Event-by-event fluctuations are taken into account
• Spectators are propagated separately in the cascade
(J.Steinheimer et al., PRC 77,034901,2008)
(nucl-th
/0607018
, nucl-th
/05110
21)
Elab=40 AGeV b=0 fm
46
(3+1)d Hydrodynamic EvolutionIdeal relativistic one fluid dynamics employing:
– HG: Hadron gas including the same degrees of freedom as in UrQMD (all hadrons with masses up to 2.2 GeV)
– CH: Chiral EoS from SU(3) hadronic Lagrangian with first order transition and critical endpoint
– BM: Bag Model EoS with a strong first order phase transition between QGP and hadronic phase
D. Rischke et al., NPA 595, 346, 1995,
D. Rischke et al., NPA 595, 383, 1995
Papazoglou et al., PRC 59, 411, 1999
47
Freeze-out 1) Transition from hydro to
transport when < 730 MeV/fm³ (≈ 5 *
0) in all cells of one transverse slice (Gradual freeze-out, GF) iso-eigentime criterion
2) Transition when < 5* 0 in all cells(Isochronuous freeze-out, IF)
• Particle distributions are generated according to the Cooper-Frye formula
with boosted Fermi or Bose distributions f(x,p) including mB and mS
• Rescatterings and final decays calculated via hadronic cascade (UrQMD)
Chemical FO by Cleymans et al.
48
Initial State for Non-Central CollisionsPb+Pb at Elab=40 AGeV with b= 7fm at tstart=2.83 fm
Energy density profile Weighted velocity profile
Event-by-event fluctuations are taken into account (H.P. et.al., arXiv:0901.3821, PRC in print)
GeV/fm3
GeV/fm3
49
Elliptic Flow
• Smaller mean free path in the hot and dense phase leads to higher elliptic flow
• At lower energies: hybrid approach reproduces the pure UrQMD result
• Gradual freeze-out leads to a better description of the data (H.P. et.al., arXiv:0901.3821, PRC in
print)Data from E895, E877, NA49, Ceres, Phenix, Phobos, Star
50
v2/ Scaling
• More realistic initial conditions and freeze-out
Qualitative behaviour nicely reproduced
• Uncertainty due to eccentricity calculation
• Uniqueness of the hydro limit is questioned
(H.P. et.al., arXiv:0901.3821, PRC in print)
Data and hydro limits from NA49 collaboration, PRC 68, 034903, 2003
51
Eccentricity fluctuation of initial conditions in hydrodynamics
Tetsufumi HiranoDepartment of Physics
Graduate School of ScienceThe University of Tokyo
Quark Matter 2009Quark Matter 2009
Collaborator: Yasushi Nara (Akita Intl. Univ.)Collaborator: Yasushi Nara (Akita Intl. Univ.)
52
Eccentricity Fluctuation
Interaction points of participants vary event by Interaction points of participants vary event by event.event. Apparent reaction plane also varies.Apparent reaction plane also varies. The effect is significant for smaller system such The effect is significant for smaller system such as Cu+Cu collisionsas Cu+Cu collisions
Adopted from D.Hofman(PHOBOS),Adopted from D.Hofman(PHOBOS),talk at QM2006talk at QM2006
A sample eventA sample eventfrom Monte Carlofrom Monte CarloGlauber modelGlauber model
i
0
53
Initial Condition with an Effect of Eccentricity Fluctuation
Rotate eachRotate each ii
to to truetrue
Throw a diceThrow a diceto choose to choose bb::bbminmin<<bb<<bbmaxmax
averageaverageover eventsover events
averageaverageover eventsover events
E.g.)E.g.)bbminmin= 0.0fm= 0.0fmbbmaxmax= 3.3fm= 3.3fmin Au+Au collisionsin Au+Au collisionsat 0-5% centralityat 0-5% centrality
With fluctuation effectsWith fluctuation effects
Without fluctuation effectsWithout fluctuation effects
54
Inputs in Model Calculations
Parameters are fixed in Au+Au collisionsParameters are fixed in Au+Au collisions
Glauber: Glauber:
KLN: standard parametersKLN: standard parameters
KLN: Kharzeev-Levin-Nardi model
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Eccentricity with Fluctuation Effects
Au+AuAu+Au Cu+CuCu+Cu
Large fluctuation in small system such as Large fluctuation in small system such as Cu+Cu and peripheral Au+AuCu+Cu and peripheral Au+Au
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Centrality Dependence (Glauber)
Au+AuAu+Au Cu+CuCu+Cu
Large fluctuation effects in Cu+Cu collisionsLarge fluctuation effects in Cu+Cu collisionsCu+Cu data also constrain the modelsCu+Cu data also constrain the models
Glauber initialization undershoots data!?Glauber initialization undershoots data!?
57
Centrality Dependence (KLN)
Large fluctuation effects again in Cu+Cu collisionsLarge fluctuation effects again in Cu+Cu collisionsReasonable agreement btw. data and MC-KLN!?Reasonable agreement btw. data and MC-KLN!?
Au+AuAu+Au Cu+CuCu+Cu
58
Backup slides
59
HBT nomenclature
x
Actual q distributionBackground q distribution==
The source S can be directly recovered with imaging
Make assumptions about the source
adapted from Annu. Rev. Nucl. Part. Sci. 2005. 55:357-402
DetectorDetector
Simplified foridentical particles
oror
Bose-EinsteinEnhancement atLow q
60
Include Fluctuations
in absence of fluctuations
for full events, it is more complicated
61
PHOBOS+ Equation for Subevents
Eq.
Fluctuations!
I0,1 are modified Bessel functions
resolution parameter
only function of
62
Analytic Correction for Fluctuations
method similar to momentum conservation correction:N. Borghini, P.M. Dinh, J.-Y. Ollitrault, A.M. Poskanzer, and S.A. Voloshin,PRC 66, 014901 (2002)
63
Analytic Correction for Nonflow
nonflow
64
v2 Fluctuations from part Fluctuations
Assume width with same percent width as part:
2D Gaussian fluctuations in reaction plane lead toBessel-Gaussianfluctuations along theparticipant plane axis
is from standard deviation of nucleon MC Glauber of part
Bessel-Gaussian:
Voloshin et al., Phys. Lett. B659, 537 (2008)
65
• Assumptions
Application to Data
MC Glauber participant
less nonflow
66
Nonflow and Fluctuationswith my assumptions and parameters:
67
K0 =0.7 (from transport calculation)cs = speed of sound [fixed] = eccentricityS = transverse nuclear overlap areadN/dy – total multiplicity per unit rapidity
C.Gombeaud and J-Y.Ollitrault; Phys. Rev. C 77, 054904 (2008)
• Hydro description: – Ideal hydro: scale invariance leads to eccentricity scaling v2/ε ~ const– Real (viscous) hydro: Eccentricity scaling is broken and v2/ε !=const
• Transport description (Ollitrault):– Operational Ansatz: The Boltzmann equation reduces to
hydrodynamics when the mean free path is small– v2/ε is a function of the Knudsen number Kn = λ / R : [ R – transverse size of the system and λ is the mean free path ]
1
0
2 1
K
Kvv nhd
2
c
c
dy
dN
SK s
n
1
Kn→0 (ideal hydro limit) : v2/ε ~ constant
Kn>>1 (low density limit) : v2/ε~ v2hd/ (ε Kn / K0 )
6767
C. Marle, Annales Poincare Phys.Theor. 10,67 (1969).
2 free parameters in the fit = effective partonic cross section (4~6mb) v2
hd = hydrodynamic limit
Extraction of transport coefficients
PHOBOS data, s=200 GeVH-J.Drescher, A.Dumitru, C.Gombeaud, J-Y.Ollitrault; Phys. Rev. C 76, 024905 (2007)
6868
H. Song , U. W. Heinz Phys.Rev.C78:024902,2008
Operational test of hydro calculation
npart
KN
1
0
2 1
K
Kvv nhd
2
69
Results with Quadratic Ansatz
pT -spectra and v2(pT) of with
and the same EoS
Results with Quadratic AnsatzResults with Quadratic Ansatz SummarySummary
Quark Matter 2009, Knoxville, Tennessee, April 2Quark Matter 2009, Knoxville, Tennessee, April 2ndnd 2009 2009Effects of Bulk Viscosity on Effects of Bulk Viscosity on ppTT-spectra and Elliptic Flow Parameter-spectra and Elliptic Flow Parameter
Effects of the bulk viscosity is underestimated in quadratic ansatz.
Elliptic Flow Coefficient Elliptic Flow Coefficient vv22((ppTT))
70
Summary & Outlook
Consistent determination of for a multi-particle system
A non-zero trace tensor term is needed for the hadron resonance gas up to the mass of
Visible effects of on particle spectra
Bulk viscosity should be considered to constrain the transport coefficients with better accuracy from experimental data.
A (3+1)-dimensional viscous hydrodynamic flow is necessary to see more realistic behavior of the particle spectra.
SummarySummaryResults with Quadratic AnsatzResults with Quadratic Ansatz
Quark Matter 2009, Knoxville, Tennessee, April 2Quark Matter 2009, Knoxville, Tennessee, April 2ndnd 2009 2009Effects of Bulk Viscosity on Effects of Bulk Viscosity on ppTT-spectra and Elliptic Flow Parameter-spectra and Elliptic Flow Parameter
pT-spectra : suppressed
v2(pT) : enhancedwhen estimated with an ideal hydrodynamic flow.
71
Hybrid Approaches• Hadronic freezeout following a first order hadronization phase transition in
ultrarelativistic heavy ion collisions.S.A. Bass, A. Dumitru, M. Bleicher, L. Bravina, E. Zabrodin, H. Stoecker, W. Greiner, Phys.Rev.C60:021902,1999
• Dynamics of hot bulk QCD matter: From the quark gluon plasma to hadronic freezeout. S.A. Bass, A. Dumitru, Phys.Rev.C61:064909,2000
• Flow at the SPS and RHIC as a quark gluon plasma signature.D. Teaney, J. Lauret, Edward V. Shuryak, Phys.Rev.Lett.86:4783-4786,2001
• A Hydrodynamic description of heavy ion collisions at the SPS and RHIC.D. Teaney, J. Lauret, E.V. Shuryak, e-Print: nucl-th/0110037
• Hadronic dissipative effects on elliptic flow in ultrarelativistic heavy-ion collisions.T. Hirano, U. Heinz, D. Kharzeev, R. Lacey, Y. Nara, Phys.Lett.B636:299-304,2006
• 3-D hydro + cascade model at RHIC.C. Nonaka, S.A. Bass, Nucl.Phys.A774:873-876,2006
• Results On Transverse Mass Spectra Obtained With NexspherioF. Grassi, T. Kodama, Y. Hama, J.Phys.G31:S1041-S1044,2005
• See also recent work of K. Werner
72
Introduction
• Fix the initial state and freeze-out
learn something about the EoS and the effect of viscous dynamics
1) Non-equilibrium
initial conditions
via UrQMD
2) Hydrodynamic evolution or Transport calculation
3) Freeze-out via
hadronic cascade
(UrQMD) UrQMD-2.3 is available at www.th.physik.uni-frankfurt.de/~urqmd
73
Transverse Momentum Dependence
Hydro phase leads to higher flow values, but weak EoS dependence
NA49
(NA
49,
PR
C 6
8,
034903,
200
3)
Protons Pions
74
Conclusions• Integrated approach with the same initial conditions and
freeze-out for different EoS• Particle multiplicities and spectra are reasonably reproduced,
strangeness enhanced• Transverse momentum spectra indicate importance of non-
equilibrium effects• Phase transition is visible in HBT radii, but long fireball
lifetime so far not supported by the existing data• Flow results depend crucially on initial conditions and
freeze-outSee also • Poster 927 by Jan Steinheimer about new chiral EoS including
deconfinement phase transition • Poster 403 by Björn Bäuchle about direct photons
75
Comment on Monte Carlo Approach
How do we consider this?How do we consider this?
Naïve Glauber calculation: Naïve Glauber calculation:
MC-Glauber calculation: MC-Glauber calculation:
Finite Finite nucleonnucleonprofileprofile
76
Comment on Monte Carlo Approach (contd.)
Reduction of eccentricity by ~5-10%Reduction of eccentricity by ~5-10% Necessity of re-tuning parametersNecessity of re-tuning parameters
in Woods-Saxon densityin Woods-Saxon density We have retuned parameters.We have retuned parameters.
77
Comment on v2/ vs. (1/S)dN/dy
Hydro limitHydro limit= (no viscosity) = (no viscosity)
+ (small freezeout T)+ (small freezeout T) Ideal hydro of QGP Ideal hydro of QGP does NOT give a hydrodoes NOT give a hydro
limit curve due to limit curve due to hadronizationhadronization
and finite life time.and finite life time.
““hydro limit”hydro limit”
Exp. data would reflect life time of the QGP Exp. data would reflect life time of the QGP rather than its viscosity.rather than its viscosity.
78
Summary & Outlook
• Implement of eccentricity fluctuation in hydro initial conditions
• Large fluctuation effects seen in small system• MC-Glauber case
– Undershooting the data!? No room for viscosity?• MC-KLN case
– Reasonable results? Viscosity could play a role?• Realistic EOS, viscosity,…