Elliptic flow at RHIC
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Elliptic flow at RHIC
Raimond Snellings
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Why is elliptic flow interesting?• Coordinate space configuration anisotropic (almond
shape) however, initial momentum distribution isotropic (spherically symmetric)
• Only interactions among constituents generate a pressure gradient, which transforms the initial coordinate space anisotropy into a momentum space anisotropy (no analogy in pp)
• Multiple interactions lead to thermalization -> limiting behavior ideal hydrodynamic flow
y
x
py
px
coordinate space
Momentum space
12 , tan ( )cos 2( ) y
xrv
p
p
3 2
31
11 2 cos
2 n rnt t
d N d NE v nd p p dp dy
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Time evolution in a ideal hydrodynamic model calculation
• Elliptic Flow reduces spatial anisotropy -> shuts itself off
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Main contribution to elliptic flow early in the collision
Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45
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v2 versus centrality
STAR PRL 86, (2001) 402
|| < 1.3
0.1 < pt < 2.0
First time in Heavy-Ion Collisions a system created which at low pt is in quantitative agreement with hydrodynamic model predictions for v2 up to mid-central collisions
PHOBOS
PHENIX
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Identified particle v2 • Typical pt dependence• Heavy particles more
sensitive to velocity distribution (less effected by thermal smearing) therefore put better constrained on EOS
Fluid cells expand with collective velocity v, different mass particles get different p
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Identified particle v2 (130 GeV)
dashed solid
T (MeV) 135 20 100 24
0(c) 0.52 0.02 0.54 0.03
a (c) 0.09 0.02 0.04 0.01
S2 0.0 0.04 0.01
The STAR Collaboration, Phys. Rev. Lett. 87 (2001) 182301
Source not spherical in coordinate space at freeze-out!
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v2(pt,mass) 130 vs. 200 GeV
• Identified particle v2 at 130 and 200 GeV very close
Preliminary
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PHENIX and STAR
PHENIX
STAR
Preliminary
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PHOBOS v2()
Preliminary v2200
Final v2130
200
130
Only a little increase
average over
all centrality
(Npart ~200)
Centrality dependence study is limited by statistics
Inkyu Park Talk
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v2(pt) for high pt particlesM. Gyulassy, I. Vitev and X.N. Wang
http://www.lbl.gov/nsd/annual/rbf/nsd1998/rnc/RNC.htmR17. Event Anisotropy as a Probe of Jet QuenchingR.S and X.-N. Wang R.S, A.M. Poskanzer, S.A. Voloshin, STAR note, nucl-ex/9904003
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Charged particle v2 at high-pt
STAR preliminary
STAR preliminary
Above 6 GeV we do not have a reliable answer (yet) what the real flow contribution is
PHENIX preliminary
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What have we learned from elliptic flow at RHIC
– L. McLerran: one needs very strong interactions amongst the quark and gluons at very early times in the collision (hep-ph/0202025).
– U. Heinz: resulting in a well-developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c (hep-ph/0109006).
– E. Shuryak: probably the most direct signature of QGP plasma formation, observed at RHIC (nucl-th/0112042).
– QGP conclusions are model dependent and in my opinion these models are not sufficiently constrained yet. (RS)
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Excitation FunctionsT
th [G
eV
]<
r>
[c]
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Elliptic flow; excitation function
NA49nucl-ex/0303001
preliminary
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v2(pt) SPS-RHIC
• Surprisingly close!
• <pt> pions 158 A GeV ≈ 300 MeV
• <pt> charged particles 200 GeV ≈ 500 MeV
• Integrated v2 mainly driven by <pt>
Preliminary
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Why does hydro describe v2 at RHIC and not at the SPS?
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The “Reaction Plane”
• Anisotropic flow ≡ azimuthal correlation with the reaction plane
• Experimentally the reaction plane r is unknown
• Can introduce “non-flow” contributions
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Event plane resolution• Event plane resolution
N * v22
• Most non flow contributions v2 1/N
• Kovchegov and Tuchin: N = Nwounded
• Non flow contribution will be constant in this variable. Dashed red line estimate of non-flow in first STAR flow paper
iii
iii
1B,A2 2cosw
2sinwTan
2
1
STAR, PRL 86, (2001) 402, Nucl. Phys. A698 (2002) 193
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Elliptic flow as a function of centrality
STAR Nucl. Phys. A698 (2002) 193
Non-flow considerable for central and peripheral events
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Calculating flow using multi particle correlations
)ψ( r)(cos inrn env
2 1 2 1 21 ( ) ( ) (( ) 2) ( ) ( {2})r r r rinn
in in in ine e e ee v Assumption all correlations between particles due to flow
Non flow correlation contribute order (1/N), problem if vn≈1/√N
1 2 3 4 3 4 3 21 2 1 4( ) ( ) ( )( ) ( ) 4( {4})in in inin in
n ve e e e e
Non flow correlation contribute order (1/N3), problem if vn≈1/N¾
N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001) 054906
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Integrated v2 from cumulants
STAR, PRC 66,(2002) 034904
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Non-flow estimate from pp
See Aihong’s talk
At low-pt non-flow estimate from pp 5-10% of observed v2 in AA
STAR preliminary
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Yet another view on non-flow2 2
2 2
y x
y x
v Fluctuation probably too large; estimate of maximum effect on v2
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Comparing optical to MC Glauber
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Eccentricity Fluctuations
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Fluctuation and their effect on cumulant calculations
1/ 422 4{4} 2v v v v
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Fluctuation contribution to extracted v2
v2{2} at mid-central collisions 10% higher than real v2
v2{4} at mid-central collisions 10% lower than real v2
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Conclusion
• Comparable measurements of elliptic flow from PHENIX, PHOBOS and STAR
• Elliptic flow well described by boosted thermal particle distributions
• Flow is large; indicative of strong parton interactions at early stage of the collision
• Up to pt = 6 GeV/c sizable elliptic flow• Elliptic flow measurement at low to intermediate pt is real
correlation with the reaction plane• Fluctuation could be main contribution to non-flow; At
mid-central collisions the maximum effect is 10%
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Identified particle v2 at high-pt
• See Huan’s talk
• Double splitting of v2(pt) for the different particles
• parton coalescence at intermediate pt? Voloshin QM2002
Preliminary