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Marcus Bleicher, Strange Quark Matter 2006
Elliptic Flow and Constituent Quark ScalingElliptic Flow and Constituent Quark Scaling
Marcus Bleicher1 & Xianglei Zhu2
1Institut für Theoretische Physik2Frankfurt Institute for Advanced Studies
Goethe Universität Frankfurt
Germany
Marcus Bleicher, Strange Quark Matter 2006
Thanks to the UrQMD group@ Frankfurt
Thanks to the UrQMD group@ Frankfurt
• Sascha Vogel (Resonances)
• Stephane Haussler (Event-by-Event Fluctuations)
• Hannah Petersen (Flow at FAIR)
• Diana Schumacher (Di-Leptons)
• Qingfeng Li (HBT)
• Xianglei Zhu (Elliptic Flow and Charm)
• and Horst Stoecker, Yan Lu, Paul Sorensen, Nu Xu
Marcus Bleicher, Strange Quark Matter 2006
Parton Number Scaling of v2Parton Number Scaling of v2
P. Soerensen, UCLA & STAR @ SQM2003
•in leading order of v2, recombination predicts:
Bass, Nonaka, Mueller, Fries, 2003
Is this the only explanation?
Marcus Bleicher, Strange Quark Matter 2006
ContentsContents
• Introduction
• Different methods for v2
• Constituent quark scaling
• Summary
Marcus Bleicher, Strange Quark Matter 2006
The tool: UrQMDv2.2The tool: UrQMDv2.2
• Non-equilibrium transport model• Hadrons and resonances• String excitation and fragmentation• Cross sections are parameterized
via AQM or calculated by detailed balance• pQCD hard scattering at high energies
• Generates full space-time dynamics of hadrons and strings
Marcus Bleicher, Strange Quark Matter 2006
Model check: Multiplicities Model check: Multiplicities
• Rapidity distributions in line with data (Phobos)
• Centrality dependence in line with data
Marcus Bleicher, Strange Quark Matter 2006
Model check: -correlationsModel check: -correlationsQ
. Li
, M
.B.,
H.
Sto
ecke
r, n
ucl-
th/0
602
032;
D
ata:
ST
AR
• Correlations are well described except for most central reactions
Marcus Bleicher, Strange Quark Matter 2006
Anisotropic flowAnisotropic flow
ϕϕ =
⎡ ⎤= + −Φ⎢ ⎥⎣ ⎦
= +
∑ i Ri 1t t t t
2 2t x y
dN 1 dN1 2v cos(i( ))
p dp dyd 2 p dp dy
p p p
Fourier expansion of the transverseangular distribution of the emitted particles:
v1 – directed flowv2 -- elliptic flow
Reaction PlaneReaction Plane
cos( ( ))n Rv n ϕ=< −Ψ >
Marcus Bleicher, Strange Quark Matter 2006
Elliptic flowElliptic flow
coordinate-space-anisotropy momentum-space-anisotropy
€
ε =⟨y 2 − x 2⟩⟨y 2 + x 2⟩
v2 = cos2ϕ , ϕ = tan−1(pypx)
• Elliptic flow is a self-quenching effect shuts itself off after the early stage of the reaction
• Radial flow (<pT>) is an integral quantity developed over the whole reaction time
Marcus Bleicher, Strange Quark Matter 2006
V2 at RHICV2 at RHIC
• Magnitude of v2 is large
• Meson-baryon ordering • Constituent quark scaling
• Decrease of v2 at high pT
Are these unique QGP signatures?
Marcus Bleicher, Strange Quark Matter 2006
Cumulant: RapidityCumulant: Rapidity
• Differential flowAt large eta, the non-flow effects are less obvious. If the v2
fluctuations are also negligible to the cumulant method, the v2{2}, v2{4} and v2{6} should all agree with the exact v2.
At large eta, the non-flow effects are less obvious. If the v2
fluctuations are also negligible to the cumulant method, the v2{2}, v2{4} and v2{6} should all agree with the exact v2.
X.
Zhu
, M
.B.,
H.
Sto
ecke
r, P
hys.
Rev
.C7
2:0
6491
1,20
05
Marcus Bleicher, Strange Quark Matter 2006
Cumulants: CentralityCumulants: Centrality
• Integral flow In the most central bin:The fluctuations give larger v2{6} but smaller v2{4}
In the very peripheral bins:The fluctuations give larger v2{6} and v2{4}
Agree with the prediction of MCG model
BUT:In the semi-central bins:the v2 fluctuations can be neglected.
In the most central bin:The fluctuations give larger v2{6} but smaller v2{4}
In the very peripheral bins:The fluctuations give larger v2{6} and v2{4}
Agree with the prediction of MCG model
BUT:In the semi-central bins:the v2 fluctuations can be neglected.
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
Marcus Bleicher, Strange Quark Matter 2006
Compare apples to applesCompare apples to apples
• Differential flow
•v2{2} is heavily affected by the non-flow effects especially at large pT.
•The non-flow effects have been eliminated in v2{4} and v2{6}.
•But v2{4} is still a little larger than the exact v2.
Use Lee-Yang zero method
•v2{2} is heavily affected by the non-flow effects especially at large pT.
•The non-flow effects have been eliminated in v2{4} and v2{6}.
•But v2{4} is still a little larger than the exact v2.
Use Lee-Yang zero methodX
. Z
hu,
M.B
., H
. S
toec
ker,
Phy
s.R
ev.C
72:
064
911,
200
5
LYZ-method in UrQMD: nucl-th/0601049
Marcus Bleicher, Strange Quark Matter 2006
Elliptic flow: MagnitudeElliptic flow: Magnitude
• Integral flow
• V2 from UrQMD is about 50% smaller than the data
• Space for parton rescattering?
STAR data is from nucl-ex/0409033
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
Marcus Bleicher, Strange Quark Matter 2006
Energy dependenceEnergy dependenceH
. Pet
erse
n, X
. Zhu
, M.B
.
• Qualitative description OK
• Importance of potentials at low energies
• Lack of pressure shows up at lower SPS energies
Marcus Bleicher, Strange Quark Matter 2006
When is v2 created?When is v2 created?
• The earlier a particle is emitted the larger is the elliptic flow
• The higher the pT of a particle the larger is the elliptic flow
• High pT particles are more sensitive to the initial v2
Y.
Lu,
M.B
., e
t al
., n
ucl-t
h/06
020
09
Marcus Bleicher, Strange Quark Matter 2006
Initial ‘string matter’Initial ‘string matter’
• String matter dominates the early stages
lack of early pressure
‘string matter‘ = QGP?
H. P
eter
sen,
X. Z
hu, M
.B.
Strong color field or color glas or a hydrodynamical initial state fix the initial pressure problem
Marcus Bleicher, Strange Quark Matter 2006
Back to the story line:Back to the story line:
Messengers from the mixed phase: Multi-strange hadrons
freeze-out early all v2 should be from QGP
Thus, if , and ϕ have sufficient v2
Proof of partonic collectivity (maybe QGP)
Marcus Bleicher, Strange Quark Matter 2006
Indications of early freeze-outIndications of early freeze-out
• Two different groups: (a) ,K,p (b) ϕ,
• Multi-strange particle freeze-out earlier than bulk
Sensitivity to early (partonic) stage
K.
Sch
we
da,
ST
AR
Where will be the charm?
Marcus Bleicher, Strange Quark Matter 2006
Early freeze-out: modelsEarly freeze-out: models
• Flow ordering
different hadronic cross sections
A. Dumitru, S. Bass, M.B., H. Stoecker, Phys.Lett.B460:411-416,1999
UrQMD, RHIC
Marcus Bleicher, Strange Quark Matter 2006
Do multi-strange hadrons flow?Do multi-strange hadrons flow?P
. Sor
ense
n, S
QM
200
6
• Data indicates approximate 3:2 scaling with constituent quarks
• Baryons are generally below mesons
•Decrease of v2 at high pT
Is this rough scaling a signal for recombination?
Marcus Bleicher, Strange Quark Matter 2006
V2(pT) for various hadronsV2(pT) for various hadrons
Open – MesonsFull -- Baryons
1) Clear separation of meson and baryon v2
2) Low pT, v2(meson)>v2(baryon)3) High pT, v2(m)<v2(b)4) v2’s of multi-strange hadrons comparable to light hadrons
1) Clear separation of meson and baryon v2
2) Low pT, v2(meson)>v2(baryon)3) High pT, v2(m)<v2(b)4) v2’s of multi-strange hadrons comparable to light hadrons
min. bias
Y.
Lu,
M.B
., e
t al
., n
ucl-t
h/06
020
09
UrQMD
Maybe its just the additive Quark
model?
Marcus Bleicher, Strange Quark Matter 2006
NCQ-scalingNCQ-scaling
NCQ-scaling of v2 is roughly reproduced in UrQMD!NCQ-scaling of v2 is roughly reproduced in UrQMD!
•there might be an ordering of v2/n:<<<N
Y.
Lu,
M.B
., e
t al
., n
ucl-t
h/06
020
09
UrQMD
AQM cross sections:
N: 26 mb: 23 mb: 20 mb: 16 mb
: 18 mbK: 14 mb
Marcus Bleicher, Strange Quark Matter 2006
B-M AsymmetryB-M Asymmetry
Inclusion of gluons in recombination was predicted to lead to a larger meson v2/n than baryon v2/n:B.Müller, et al. nucl-th/0503003
Marcus Bleicher, Strange Quark Matter 2006
SummarySummary
At RHIC (transport models w/ strings and hadrons):
Part of v2 might also come from hadronic stage
non-flow correlations are correct
Mass ordering is correct
(B-M) Asymmetry has correct shape
Constituent quark scaling (w/o ReCo! but AQM)
However, transport models w/o QGP produce too few pressure in the early stage above 30 GeV
Marcus Bleicher, Strange Quark Matter 2006
Model check: ExpansionModel check: Expansion
Transverse Expansion of the bulk is described
Model uncertainties on level of 30-50%
Uncertainties depend on:PYTHIA implementation and properties of high mass resonances
Bra
tkov
ska
ya,
M.B
. et
al.,
Phy
s.R
ev.C
69:0
549
07,2
004