Transcript La Jolla 2006

Elliptic Flow and Constituent Quark Scaling
in High Energy Nuclear Collisions
Marcus Bleicher1 & Xianglei Zhu2
1Institut für Theoretische Physik
2Frankfurt Institute for Advanced Studies
Goethe Universität Frankfurt
Germany
Marcus Bleicher, La Jolla 2006
Thanks to
• Sascha Vogel (Talk on resonances)
• Stephane Haussler
• Hannah Petersen
• Diana Schumacher
• Qingfeng Li
• Horst Stoecker (Talk on mono-jets)
• Xianglei Zhu
• Paul Sorensen (Talk about STAR)
• Nu Xu
Marcus Bleicher, La Jolla 2006
Parton Number Scaling of v2
•in leading order of v2,
recombination predicts:
Is this the only explanation?
 pt 
v  pt   2v  
 2
B
p  pt 
v2  pt   3v2  
 3
M
2
P. Soerensen, UCLA & STAR @ SQM2003
p
2
 smoking gun for recombination
 measurement of partonic v2 !
Taken from: Bass, Nonaka, Mueller, Fries
Marcus Bleicher, La Jolla 2006
Content
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Introduction
Different methods for v2
Constituent quark scaling
Summary
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The tool: UrQMDv2.2
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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
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Model check: Multiplicities
• Rapidity distributions in line with data (Phobos)
• Centrality dependence in line with data
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Bratkovskaya, M.B. et al., Phys.Rev.C69:054907,2004
Model 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
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Q. Li, M.B., H. Stoecker, nucl-th/0602032; Data: STAR
Model check: Correlations
• Correlations are well described
except for most central reactions
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Anisotropic flow
Reaction Plane
Fourier expansion of the transverse
angular distribution of the emitted particles:
dN
1
dN 


1  2v icos(i(  R ))

pt dpt dyd 2 pt dpt dy 
i1

pt  p2x  p2y
vn  cos(n(   R )) 
v0 – radial flow
v1 – directed flow
v2 -- elliptic flow
Marcus Bleicher, La Jolla 2006

Elliptic flow
coordinate-space-anisotropy

momentum-space-anisotropy
y
x
 y2  x2
 2
 y  x2
•
•
py
v 2  cos2 ,   tan ( )
px
1
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
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V2 at RHIC
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Magnitude of v2 is large
Meson-baryon ordering
Constituent quark scaling
Decrease of v2 at high pT
Are these unique QGP signatures?
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Cumulant: Rapidity
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
• Differential flow
At large eta, the nonflow 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.
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Cumulants: Centrality
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
• 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.
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Elliptic flow: Magnitude
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
• Integral flow
• V2 from UrQMD is
about 50% smaller
than the data
• Space for parton
rescattering?
STAR data is from
nucl-ex/0409033
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Initial ‘string matter’
• String matter dominates
the early stages
lack of early pressure
H. Petersen, X. Zhu, M.B.
‘string matter‘ = QGP?
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Energy dependence
• Qualitative description OK
• Importance of potentials at
low energies
H. Petersen, X. Zhu, M.B.
• Lack of pressure shows up at
lower SPS energies
 Color glas initial state might
fix the initial pressure problem
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Back to the story line:
Multi-strange hadrons have less radial flow
 freeze-out early
 all v2 should be from QGP
Thus, if W, X and f have v2
Proof of parton coalescence (and QGP)
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Indications of early freeze-out
K. Schweda, STAR
• Two different groups:
(a) p,K,p
(b) f, W
• Multi-strange particle
freeze-out earlier than
bulk
 Sensitivity to early (partonic) stage
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Early freeze-out: models
• Omega does not
flow strong enough
 early freeze-out
UrQMD
A. Dumitru, S. Bass, M.B., H. Stoecker, Phys.Lett.B460:411-416,1999
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When is v2 created?
Y. Lu, M.B., et al., nucl-th/0602009
• 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
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Do multi-strange hadrons flow?
• Data indicates
approximate 3:2 scaling
with constituent quarks
P. Sorensen, QM 2005
• Baryons are generally
below mesons
•Decrease of v2 at high pT
Is this rough scaling a
signal for recombination?
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Compare apples to apples
• Differential flow
X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005
•v2{2} is heavily
affected by the nonflow 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
LYZ-method in UrQMD: nucl-th/0601049
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Y. Lu, M.B., et al., nucl-th/0602009
V2(pT) for various hadrons
min. bias
UrQMD
Open – Mesons
Full -- 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
lightLahadrons
Marcusto
Bleicher,
Jolla 2006
Y. Lu, M.B., et al., nucl-th/0602009
NCQ-scaling
UrQMD
• multi-strange baryons
follow the normal matter
 f does flow!
(maybe fonly flows because
of KK recombination)
NCQ-scaling of v2 is roughly reproduced in UrQMD!
Marcus Bleicher, La Jolla 2006
Summary
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
Constituent quark scaling (w/o ReCo!)
However, transport models w/o QGP produce to few pressure
in the early stage above 30 GeV
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