r. lacey, suny stony brook 1 arkadij taranenko helmholtz international summer school: “dense...
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R. Lacey, SUNY Stony Brook
Arkadij Taranenko
Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna , Russia, July 14-26, 2008
Nuclear Chemistry Group SUNY Stony Brook, USA
Elliptic Flow measurements at RHIC
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R. Lacey, SUNY Stony Brook
Phase diagram (QCD) and RHIC Phase diagram (QCD) and RHIC
How one can probe this new state of matter (QGP)?
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R. Lacey, SUNY Stony Brook
One want to see a probe (phenomena) which is
Exist only in Heavy-Ion Collisions (HIC) Provides reliable estimates of pressure & pressure gradients Can address questions related to thermalization Gives insides on the transverse dynamics of the medium Provides access to the properties of the medium – EOS, viscosity , etc Well calibrated : measured at Ganil (MSU), SIS, AGS, SPS energies
Elliptic Flow in Heavy-Ion Collisions
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R. Lacey, SUNY Stony Brook
Arkadij Taranenko
Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna , Russia, July 14-26, 2008
Nuclear Chemistry Group SUNY Stony Brook, USA
Elliptic Flow measurements from RHIC to SIS
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R. Lacey, SUNY Stony Brook
“Squeeze-Out” - First Elliptic flow signal in HIC
Reaction Plane
-180 -90 0 90 1800
0.1 [
co
rre
cte
d]
ddN
N1
[Deg]
+
-180 -90 0 90 1800
0.1 [
co
rre
cte
d]
ddN
N1
[Deg]
+
0.01± = 0.03 1v
0.01± = -0.13 2v+/- 90deg
v2 < 0mid-rapiditymid-rapidity
x
y
ψR
φ=Φ-ΨR
Diogene, M. Demoulins et al., Phys. Lett. B241, 476 (1990)
Plastic Ball, H.H. Gutbrod et al., Phys. Lett. B216, 267 (1989)
Reaction plane
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R. Lacey, SUNY Stony Brook
-180 -90 0 90 1800
0.1
[c
orr
ecte
d]
ddN
N1
[Deg]
+
-180 -90 0 90 1800
0.1
[c
orr
ecte
d]
ddN
N1
[Deg]
+
0.01± = 0.03 1v
0.01± = -0.13 2v+/- 90deg
v2 < 0mid-rapiditymid-rapidity
Cheuk-Yin WONG , Physics Letters, 88B, p 39 (1979)Sergei Voloshin, Y. Zhang, Z. Phys. C70,(1996), 665
-180 -90 0 90 180
0
0.2
[c
orre
cte
d]
ddN
N1
[Deg]
p < 0.15n 0.05 < y
-180 -90 0 90 180
0
0.2
[c
orre
cte
d]
ddN
N1
[Deg]
p < 0.15n 0.05 < y
0.01± = -0.27 1v
0.01± = -0.02 2v
v1 < 0
+/- 180deg
...)φ)(v)(φv(dydp
Nd
dφdydp
Nd
tt
2cos2cos212
121
23
Directed flow Elliptic flow
Fourier decomposition of single particle (semi) inclusive spectra:
x
y
ψR
φ=Φ-ΨR
KAOS
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R. Lacey, SUNY Stony Brook
Small Elliptic flow, Large Elliptic Flow?
-180 -90 0 90 1800
0.1
[c
orre
cte
d]
ddN
N1
[Deg]
+
-180 -90 0 90 1800
0.1
[c
orre
cte
d]
ddN
N1
[Deg]
+
0.01± = 0.03 1v
0.01± = -0.13 2v+/- 90deg
v2 < 0mid-rapiditymid-rapidity
ROUT/IN=N(900) + N(2700)N(00) + N(1800)
=1- 2 V2
1 + 2 V2
V2= -0.2 → ROUT/IN = 2 ( two times more particles emitted out-of-plane than in the plane )
SIS
RHIC
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R. Lacey, SUNY Stony Brook
Where to stop or If Elliptic Flow is very large
To balance the minimum a v4 > (10v2-1)/34 is required
v4 > 4.4% if v2=25%
222
4224
4 )(
6)4cos(
yx
yyxx
pp
ppppv
STAR, J. Phys. G34 (2007)
V4~V22 [ Vn~V2
n/2 ]
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R. Lacey, SUNY Stony Brook
Excitation function of elliptic flow – Do we understand it ?Excitation function of elliptic flow – Do we understand it ?
RHIC
SPS
SIS
GANIL/MSU
AGS
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R. Lacey, SUNY Stony Brook
At E/A < 100 MeV: attractive nuclear mean field potential : rotating system of projectile and target
b – impact parameter
Low energy heavy-ion collisions: E/A=25 MeV
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R. Lacey, SUNY Stony Brook
Excitation function of elliptic flow – 0.4-10 GeV(SIS/AGS) energiesExcitation function of elliptic flow – 0.4-10 GeV(SIS/AGS) energies
SPS
SIS
AGS
Passage time: 2R/(βcmγcm)Expansion time: R/cs cs=c√dp/dε - speed of sound ( time for the development of expansion perpendicular to the reaction plane)
Delicate balance between:
1) Ability of pressure developed early in the reaction zone to affect a rapid transverse expansion of nuclear matter
2) Passage time for removal of the shadowing of participant hadrons by projectile and target spectators
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R. Lacey, SUNY Stony Brook
If the passage time is long compared to the expansion time (spectator blocking) → squeeze-out
x
y
Azimuthal anisotropy in momentum space (elliptic flow)
px
py
dN/d
-/2 0 /2
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R. Lacey, SUNY Stony Brook
In-plane elliptic flow (due to pressure gradient) at high beam energies.
x
y
Azimuthal anisotropy in momentum space (elliptic flow)
px
py
dN/d
-/2 0 /2
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R. Lacey, SUNY Stony Brook
Interplay of passage/expansion times
Passage time: 2R/(βcmγcm)Expansion time: R/cs cs=c√dp/dε - speed of sound
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R. Lacey, SUNY Stony Brook
Squeeze-out Mechanism
Particle emitted in the center-of-mass of the system and moving in a transverse direction with velocity vT will be shadowed by spectators during the passage time: tpass=2R/(βcmγcm) simple
geometry estimate→ vTtpass/2 > R-b/2 or
vT > (1-b/2R) (βcmγcm)
V2 will increase with vT and impact parameter b
(KAOS – Z. Phys. A355 (1996); (E895) - PRL 83 (1999) 1295
Squeeze-out contribution
reflects the ratio : cs/(βcm γcm)
cs=c√dp/dε - speed of sound
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R. Lacey, SUNY Stony Brook
Elliptic Flow@ SIS/AGS
Low Energy:Low Energy:Squeeze-out
High EnergyHigh Energy In-plane
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R. Lacey, SUNY Stony Brook
elliptic flow
P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592
Determination of the Equation of State of dense matterfrom collective flow of particles
dN/d1 + 2v1cos + 2v2 cos2
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R. Lacey, SUNY Stony Brook
Prologue:Prologue: Constraints for the Hadronic EOSPrologue:Prologue: Constraints for the Hadronic EOS
0.15 ,0.219sN
Kc c cm
Soft and hard EOS
Good Constraints for the EOS Good Constraints for the EOS achieved achieved
Danielewicz, Lacey, Lynch
3410 Pa
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R. Lacey, SUNY Stony Brook
Elliptic flow at RHIC
b – impact parameter
“spectators”
“spectators”
Longitudinal and transverse expansion => no influence of spectator matter at midrapidity
Passage time: ~ 0.15 fm/c
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R. Lacey, SUNY Stony Brook
ε drives pressure gradients which result in flow.
time to thermalize the system (0 ~ 0.2 - 1 fm/c)
Bjorken~ 5 - 15 GeV/fm3
dy
dE
RT
Bj0
2
11
s/
P ²
Thermalization2 2
2 2
y x
y x
eccentricity
PRL87, 052301 (2001)
Significant Energy Density is produced in Au+Au collisions at RHICSignificant Energy Density is produced in Au+Au collisions at RHICSignificant Energy Density is produced in Au+Au collisions at RHICSignificant Energy Density is produced in Au+Au collisions at RHIC
Substantial elliptic flow signals should be Substantial elliptic flow signals should be present for a variety of particle species !present for a variety of particle species !
Phase Transition:
3/1
170
fmGeV
MeVT
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R. Lacey, SUNY Stony Brook
Substantial elliptic flowSubstantial elliptic flow signals are observed for a variety of particle signals are observed for a variety of particle species at RHIC. Indication of species at RHIC. Indication of rapid thermalizationrapid thermalization? ?
Fine Structure of Elliptic Flow at RHIC
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R. Lacey, SUNY Stony Brook
Mass ordering of v2 and ideal fluid hydrodynamics Mass ordering of v2 and ideal fluid hydrodynamics Mass ordering of v2 and ideal fluid hydrodynamics Mass ordering of v2 and ideal fluid hydrodynamics
Flavor dependence of v2(pT) enters mainly through mass of the particles → in hydro all particles flow with a common velocity !!! v2 results are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small η/s ) → small viscosity Large cross sectionsLarge cross sections strong couplings
PHENIX : PRL 91, 182301 (2003) STAR : PRC 72, 014904 (2005)
pT<1.8 GeV (~ 99% of all particles)
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R. Lacey, SUNY Stony Brook
Elliptic Flow: ultra-cold Fermi-GasElliptic Flow: ultra-cold Fermi-Gas
• Li-atoms released from an optical (laser) trap exhibit elliptic flow analogous to what is observed in ultra-relativistic heavy-ion collisions
• Interaction strength among the atoms can be tuned with an exteranl magnetic field (Feshbach res)
Elliptic flow is a general feature of strongly interacting systems?
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R. Lacey, SUNY Stony Brook
Hadron Gas ?
0 100 200 300N part
0.0
0.1
0.2
0.3
<v 2>
STAR
HSD CalculationpT>2 GeV/c
Hydrodynamic
STAR
PHOBOS
Hydrodynamic
STAR
PHOBOS
RQMD
Hadronic transport models (e.g. RQMD, HSD, ...) with hadron formation times ~1 fm/c, fail to describe data.
Clearly the system is not a hadron gas.
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R. Lacey, SUNY Stony Brook
Elliptic flow at SPS and ideal hydrodynamics
CERES
Different picture than at RHIC!?
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R. Lacey, SUNY Stony Brook
Intermediate pIntermediate pTT range : Meson vs Baryon range : Meson vs Baryon Intermediate pIntermediate pTT range : Meson vs Baryon range : Meson vs Baryon
Intermediate pT : (2< pT<5 GeV/c):
• elliptic flow v2(pT): saturates and tends to depends on the particle species-type ( meson vs baryon)
•Suppression pattern (RCP or RAA) is different – meson/baryon effect
•p/π ratio – more (anti-)protons than
pions at intermediate pT ( 2-5 GeV)
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R. Lacey, SUNY Stony Brook
Scaling breaks
Elliptic flow scales with KET up to KET ~1 GeV Indicates hydrodynamic behavior? Possible hint of quark degrees of freedom become more apparent at higher KET
Baryons scale together
Mesons scale together
= mT – m
Transverse kinetic energy scalingTransverse kinetic energy scaling
( WHY ? )( WHY ? ) 21
2Therm colKE KE KE m u
PP
PHENIX: Phys. Rev. Lett. 98, 162301 (2007)
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R. Lacey, SUNY Stony Brook
v2 /nq vs KET/nq scaling works for the full measured range with deviation less than 10% from the universal scaling curve!
KEKETT + Quark number Scaling + Quark number Scaling KEKETT + Quark number Scaling + Quark number Scaling PHENIX: Phys. Rev. Lett. 98, 162301 (2007)
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R. Lacey, SUNY Stony Brook
KET + Number of constituent Quarks (NCQ) scaling
Scaling seems to hold well for different centralities up to 60% centrality
Centrality dependence
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R. Lacey, SUNY Stony Brook
KEKETT/n scaling and beam energy dependence /n scaling and beam energy dependence
Au+Au (62.4-200 GeV)Au+Au (62.4-200 GeV)
STAR Collaboration: Phys. Rev. C 75(2007) 054906
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R. Lacey, SUNY Stony Brook
KEKETT/n scaling and system size (AuAu/CuCu)/n scaling and system size (AuAu/CuCu)
KET/n scaling observed across different colliding systems
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R. Lacey, SUNY Stony Brook
v4 Scaling
• The similar scaling for v4 is found recently at PHENIX.• Compatible with partonic flow picture.
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R. Lacey, SUNY Stony Brook
KET/n Scaling tests at SPS
V2 vs KET/n scaling breaks at SPS? – the statistical errors are too large : one need to measure v2 of φ meson at SPS
C. Blume (NA49) QM2006 talk
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R. Lacey, SUNY Stony Brook
Elliptic flow of φ meson and partonic collectivity at RHIC.
φ meson has a very small σ for interactions with non-strange particles φ meson has a relatively long lifetime (~41 fm/c) -> decays outside the fireball Previous measurements (STAR) have ruled out the K+K- coalescence as φ meson production mechanism -> information should not be changed by hadronic phase φ is a meson but as heavy as baryons (p, Λ ) : m(φ)~1.019 GeV/c2 ; (m(p)~0.938 GeV/c2: m(Λ)~1.116 GeV/c2) -> very important test for v2 at intermediate pt ( mass or
meson/baryon effect?)
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R. Lacey, SUNY Stony Brook
v2 of φ meson and partonic collectivity at RHIC
v2 vs KET – is a good way to see if v2 for the φ follows that for mesons or baryons
v2 /n vs KET/n scaling clearly works for φ mesons as well
nucl-ex/0703024
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R. Lacey, SUNY Stony Brook
Elliptic flow of multistrange hadrons (φ, Ξ and ) with their large masses and small hadronic behave like other particles → consistent with the creation of elliptic flow at partonic level before hadron
formation
Multi-strange baryon elliptic flow at RHIC (STAR)
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R. Lacey, SUNY Stony Brook
Elliptic flow of D meson
All non-photonic electron v2 (pT < 2.0 GeV/c) were assumed to come from D decay D-> e, Pt spectrum constrained by the data Different assumptions for the shape of D meson v2(pt): pion,kaon and proton v2(pt) shapes
Measurements and simulations: Shingo Sakai (PHENIX)(See J. Phys G 32, S 551 and his SQM06,HQ06,QM06 talks for details )
Measurements of elliptic flow of non-photonic electrons (PHENIX)
Simulations for D meson v2(pt):
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R. Lacey, SUNY Stony Brook
Elliptic flow of D meson: Scaling test
The D meson not only flows, it scales over the measured rangeThe D meson not only flows, it scales over the measured range
Heavy-quark relaxation time τR>> τL : τR ~ (Mhq /T)τL ~8 τL for Mhq ~1.4 GeV and T=165 MeV
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R. Lacey, SUNY Stony Brook
Elliptic Flow at RHIC energies
For a broad range of reaction centralities (impact parameters) elliptic flow at RHIC energies (62.4-200 GeV) depends only (?) on transverse kinetic energy of the particle KET and number of valence quarks nq ?
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R. Lacey, SUNY Stony Brook
KET/n Scaling tests for Ideal Hydro
Why Ideal hydro works so bad after close look?
- In ideal hydro ( η = 0 !!! )
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R. Lacey, SUNY Stony Brook
proton pion From PHENIX White Paper
Nucl. Phys. A757 (2005) 184
Elliptic flow at RHIC and ideal fluid hydrodynamics Elliptic flow at RHIC and ideal fluid hydrodynamics Elliptic flow at RHIC and ideal fluid hydrodynamics Elliptic flow at RHIC and ideal fluid hydrodynamics
For pT <1.5 GeV/c V2(pT) and pT spectra of identified hadrons are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small η/s ) → small viscosity Large cross sectionsLarge cross sections strong couplings
Rapid Rapid Thermalization Thermalization
??
Rapid Rapid Thermalization Thermalization
??
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R. Lacey, SUNY Stony Brook
T. Hirano: Highlights from a QGP Hydro + Hadronic Cascade Model
hadronic -“ late viscosity”
b=7.2fm 0-50%Adapted from S.J.Sanders (BRAHMS) @ QM2006
AuAu200Hadronic dissipative effects on elliptic flow and spectra
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R. Lacey, SUNY Stony Brook
What is the lowest viscosity at RHIC?
Shear viscosity ( η ) – how strongly particles interact and move collectively in a body system. In general, strongly interacting systems have smaller (η) than weakly interacting.
But, (η/s) has a lower bound: in standard kinetic theory η=(n<p>λ)/3 , where n - proper density , <p>- average total momentum, λ – momentum degradation transport mean free path. The uncertainty principle implies : λ>1/<p> , for relativistic system, the entropy density (s~4n) and (η/s) > 1/12
(η/s) > 1/12 [from “Dissipative Phenomena in Quark-Gluon Plasmas “
P. Danielewicz, M. Gyulassy Phys.Rev. D31, 53,1985. ]
KSS bound (η/s) > 1/4π
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R. Lacey, SUNY Stony Brook
Constraining /s with PHENIX datafor RAA & v2 of non-photonic electrons
• Rapp and van Hees Phys.Rev.C71:034907,2005 – Simultaneously describe PHENIX
RAA(E) and v2(e) with diffusion coefficient in range DHQ (2T) ~4-6
• Moore and Teaney Phys.Rev.C71:064904,2005 – Find DHQ/(/(+p)) ~ 6 for Nf=3
• Combining– Recall +p = T s at B=0
– This then gives /s ~(1.5-2)/4– That is, within factor of 2-3 of
conjectured lower bound
Phys. Rev. Lett. 98, 172301 (2007)
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R. Lacey, SUNY Stony Brook
Estimation of /s from RHIC data
• Damping (flow, fluctuations, heavy quark motion) ~ /s
– FLOW:Has the QCD Critical Point Been Signaled by Observations at RHIC?, R. Lacey et al., Phys.Rev.Lett.98:092301,2007 (nucl-ex/0609025)
– The Centrality dependence of Elliptic flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD, H.-J. Drescher et al., (arXiv:0704.3553)
– FLUCTUATIONS: Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions, S. Gavin and M. Abdel-Aziz, Phys.Rev.Lett.97:162302,2006 (nucl-th/0606061)
– DRAG, FLOW: Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at √sNN = 200 GeV (PHENIX Collaboration), A. Adare et al., to appear in Phys. Rev. Lett. (nucl-ex/0611018)
4π
1)0.2(1.1
s
η 1.21.1
4
1)8.30.1(
s
4
1)0.23.1(
s
4
1)5.29.1(
s
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R. Lacey, SUNY Stony Brook
Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?, P. Romatschke and U.
Romatschke, Phys. Rev. Lett. 99:172301, 2007
• Calculation:2nd order causal viscous hydro:
(Glauber IC’s
4
1)0.20(
s
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R. Lacey, SUNY Stony Brook
T. Hirano: Hydro + Cascade
QGP viscosity or hadronic viscosity – both ?
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R. Lacey, SUNY Stony Brook
Small deviations from scaling will yield insights on novel hadronization process.
Key Future Test
Detector Upgrades + RHIC I AuAu 2 nb-1
baryon (sss) is a stringent test due to the large mass and OZI suppressed hadronic interactions.
Example: STAR Time of Flight + DAQ1000
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R. Lacey, SUNY Stony Brook
Viscosity-to-entropy ratio
minimum bias Au+Au, √s=200 GeV
Lower bound of η/s=1/4π in the strong coupling limit (P.Kovtun et al. PRL 94 (2005) 111601)
L.P.Csernai et al. PRL 97 (2006) 152303; R.Lacey at al. PRL 98 (2007) 092301
η/s for several substances
Strong indication for a minimum in the vicinity of Tc
Partonic fluid
Hydrodynamic scaling
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R. Lacey, SUNY Stony Brook
Eccentricity Calculation
V2,M(KET)=
Coalescence/recombination and KET
J.Jia and C. Zhang, Phys. Rev. C 75 (2007) 031901(R)
If one modify the momentum conservation relation into kinetic energy conservation relation in the coalescence formula – one will get :
2v2,q
1+2v22,q KET/2
≈ 2 v2,q ( KET/2 )
V2,B(KT)=3v2,q+3v3
2,q
1+6v22,q KET/3
≈ 3 v2,q(KET/3)
mesons
baryons
Problem with conventional quark coalescence models is energy violation ( 2→ 1, 3→ 1 channels ). What to do with it?
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R. Lacey, SUNY Stony Brook
Quark Coalescence based on a Transport EquationQuark Coalescence based on a Transport Equation
Resonance formation in quark-(anti)quark scattering as the dominant channel for meson production at RHIC – Energy ( 4-momentum ) conservation satisfied via a finite Γ.Is it a way to solve the problem?
L. Ravagli and R. Rapp: http://arxiv.org/abs/0705.0021
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R. Lacey, SUNY Stony Brook
Constituent Quark Number Scaling (QNS) of v2Simple models of hadronization by coalescence/recombination of constituent quarks, which only considers the momentum distribution of quarks and allows quarks with the same pT to coalesce into hadrons → relate quark and hadron v2:
v2p = v2
h(pT/n)/n,
n is the number of quarks in the hadron
Models imply
v2 is developed before hadrons form ( at partonic level )
2 2 2 2an22 3
d 3p pM tt
B tt
pv p vv
pv p
Coalescence/recombination of constituent quarks can explain both meson/baryon nature of suppression factors and v2 at intermediate pt
Greco, Ko, Levai; Muller, Nonaka, Bass;Hwa,Yang; Molnar, Voloshin
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R. Lacey, SUNY Stony Brook
v2(pT/n)/n QNS scaling: close look
With higher statistics v2 measurements, fine structurein QNS is observed: • pT>2GeV/c: QNS scaling only works at 20% level•pT<2GeV/c: QNS scaling breakes badly with systematic dependence on the hadron mass: it undershoots the v2 values of light mesons and overshoots the v2 values of heavy baryons
Imperfections of coalescence/recombination approach?
Wrong scaling variable?
Can one get a unified description of hadron production and elliptic flow at low and intermediate pT ?
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R. Lacey, SUNY Stony Brook
The idea to use collective flow to Probe the The idea to use collective flow to Probe the properties of nuclear matter is long-standingproperties of nuclear matter is long-standing
W. Scheid, H. Muller, and W. Greiner,PRL 32, 741 (1974)
H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980)
Ne
M.I. Sobel, P.J. Siemens, J.P. Bondorf, an H.A. Bethe, Nucl. Phys. A251, 502 (1975)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)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)E. Glass Gold et al. Annals of Physics 6, 1 (1959)
U
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R. Lacey, SUNY Stony Brook
Summary
• Universal scaling of the flow of both mesons and baryons (over a broad transverse kinetic energy range) via quark number scaling observed.
• Development of elliptic flow in the pre-hadronization phase demonstrated
• Outlook: mechanism of hadronisation at RHIC, what is the range of (η/s) at RHIC?
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R. Lacey, SUNY Stony Brook
Jet Quenching at RHICJet Quenching at RHIC
Strong quenching of jets, observed in
central Au+Au collisions →
Evidence of the extreme energy loss of partons traversing matter containing a large density of color charges
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R. Lacey, SUNY Stony Brook
Elliptic flow at RHIC
• The probe for early time– The dense nuclear overlap is
ellipsoid at the beginning of heavy ion collisions
– Pressure gradient is largest in the shortest direction of the ellipsoid
– The initial spatial anisotropy evolves (via interactions
and density gradients ) Momentum-space anisotropy
– Signal is self-quenching with time
...])φ[2(2φcos211
2122
3
3
RRT
vvdydp
Nd
pd
NdE
React
ion
plan
e
X
Z
Y
Px
Py Pz
])φ[2cos(2 Rv