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Anisotropic Flow. Raimond Snellings. What have we learned from elliptic flow so far? According to:. U. Heinz : Resulting in a well-developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c (arXiv:hep-ph/0109006). - PowerPoint PPT Presentation
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Anisotropic Flow
Raimond Snellings
Raimond Snellings; Trento 2004 2
What have we learned from elliptic flow so far? According to:
– U. Heinz: Resulting in a well-developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c (arXiv:hep-ph/0109006).
– E. Shuryak: Probably the most direct signature of QGP plasma formation, observed at RHIC (arXiv:nucl-th/0112042).
– L. McLerran: one needs very strong interactions amongst the quark and gluons at very early times in the collision (arXiv:hep-ph/0202025).
– M. Gyulassy: The most powerful probe of the QGP equation of state: the mass dependence of v2; One of the three lines of evidence for the QGP at RHIC (arXiv:nucl-th/0403032).
Raimond Snellings; Trento 2004 3
Outline
• Elliptic flow:– v2 at low pt, the dependence on particle mass
and its relation to freeze-out parameters in a hydro motivated picture
– Some uncertainties related to the measurement – What are the changes from SPS to RHIC
energies?
Raimond Snellings; Trento 2004 4
Elliptic flow of the bulk
• 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
coordinate space
py
px
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
Raimond Snellings; Trento 2004 5
Time evolution
• Elliptic Flow reduces spatial anisotropy -> self quenching
SCIENCE Vol: 298 2179 (2002)
Hydro calculation: P. Kolb, J. Sollfrank and U.Heinz
Raimond Snellings; Trento 2004 6
Main contribution to elliptic flow develops early in the collision
Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45
Raimond Snellings; Trento 2004 7
Non-central heavy-ion collisions: coordinate system
1
2 ,
tan ( )
cos 2( )
y
x
rv
p
p
2 2
2 2
` `
` `
y x
y x
Raimond Snellings; Trento 2004 8
Hydrodynamic limit
STAR
PHOBOS
Hydrodynamic limit
STAR
PHOBOS
Compilation and Figure from M. Kaneta
Integrated Elliptic Flow
First time in Heavy-Ion Collisions a system created which at low pt is in quantitative agreement with ideal hydrodynamic model predictions for v2 up to mid-central collisions
2 cos 2( )rv
PHOBOS: Phys. Rev. Lett. 89, 222301 (2002) STAR: Phys. Rev. Lett. 86, 402 (2001)
PHENIX: Phys. Rev. Lett. 89, 212301 (2002)
RQMD
Raimond Snellings; Trento 2004 9
Identified particle v2 • Typical pt dependence
for different masses• 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
Hydro: P. Huovinen, P. Kolb, U. Heinz
STAR
Raimond Snellings; Trento 2004 10
Hadron Cascade
UrQMD: Marcus Bleicher and Horst Stocker,arXiv:hep-ph/0006147
Magnitude off in v2 and different scale in pt
Raimond Snellings; Trento 2004 11
v2(pt,mass)
• All particles reasonably described at low-pt with common set of parameters
• PHENIX (squares) and STAR agree well
STAR, PHENIX preliminary
Raimond Snellings; Trento 2004 12
Everything flows?
pT [GeV/c]
M. Kaneta (PHENIX) QM2004
J. Castillo (STAR) QM2004
What about charm?
Raimond Snellings; Trento 2004 13
Reaction plane determination
• Anisotropic flow ≡ azimuthal correlation with the reaction plane
• Experimentally the reaction plane r is unknown
• Can introduce “non-flow” contributions
Raimond Snellings; Trento 2004 14
Determining the reaction plane
iii
iii
1B,A2 2cosw
2sinwTan
2
1
Raimond Snellings; Trento 2004 15
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
Raimond Snellings; Trento 2004 16
Elliptic flow as a function of centrality
STAR Nucl. Phys. A698 (2002) 193
Non-flow considerable for central and peripheral events
Raimond Snellings; Trento 2004 17
Calculating flow using multi particle correlations
r( ψ )cos ( ) inn rv n e
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
Raimond Snellings; Trento 2004 18
Higher moments
<v2n> ≠ <v2>n
1/ 636 4 2 21
2
1/ 4
2 2 2
22 42 2 2
22
2
2
4
{4}
{2}
{6} 12
2
9
v
v
v v v v v
v
v v
v
2 2
2 2
y x
y x
Raimond Snellings; Trento 2004 19
Integrated v2 from cumulants
A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020
About 20% reduction from v2{2} to v2{4}
v2{4} ≈ v2{6}
Raimond Snellings; Trento 2004 20
The possible fluctuation contribution
“standard” v2{2} overestimates v2 by 10%, higher order cumulant underestimate v2 by 10% at intermediate centralities
M. Miller and RS, arXiv:nucl-ex/0312008
Raimond Snellings; Trento 2004 21
Integrated v2 from cumulants
A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020
About 20% reduction from v2{2} to v2{4}
v2{4} ≈ v2{6}
Raimond Snellings; Trento 2004 22
How does it compare to data?
M. Miller and RS, arXiv:nucl-ex/0312008
Raimond Snellings; Trento 2004 23
Non-flow or fluctuations?
M. Miller and RS, arXiv:nucl-ex/0312008
NA49: Phys.Rev. C68 (2003) 034903
N
gvv 22
222 42
N. Borghini, P.M. Dinh, J-Y Ollitrault: Phys. Rev. C 63 (2001) 054906
Raimond Snellings; Trento 2004 24
Uncertainties
• Non-flow and fluctuations expected in general to both contribute
• At mid-central collisions (20-60%) the estimated effect is about 10%. IMO best estimate of the true flow are in between (v2{2}+v2{4})/2 and v2{4}
Raimond Snellings; Trento 2004 25
Elliptic flow at lower energies
P. Kolb, J. Sollfrank, and U. Heinz, Phys. Rev. C. C62 054909 (2000).
• Increase of about 50% in v2 from top SPS to top RHIC energy
Raimond Snellings; Trento 2004 26
Hydrodynamics + RQMD
D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).
Raimond Snellings; Trento 2004 27
Energy dependence
NA49Phys.Rev. C68
(2003) 034903
At low energies pions, at RHIC charged hadrons. This makes a difference, this figure approximates the excitation plot of h-
Raimond Snellings; Trento 2004 28
v2(pt) SPS-RHIC
• Integrated v2 depends on slope and <pt>
• <pt> pions 17 GeV ≈ 400 MeV/c, 130 GeV charged particles <pt> ≈ 500 MeV/c
NA49: Phys. Rev. C68 (2003) 034903;
CERES: Phys. Rev. Lett. 92 (2004) 032301
Raimond Snellings; Trento 2004 29
Similar or very different?
arXiv:nucl-ex/0305001
Raimond Snellings; Trento 2004 30
Similar or very different??
• Note: only statistical errors plotted
Raimond Snellings; Trento 2004 31
Similar or very different?
Raimond Snellings; Trento 2004 32
Summary• Consistent measurements of elliptic flow at RHIC from PHENIX, PHOBOS
and STAR• Elliptic flow for all measured particles at low-pt well described by boosted
thermal particle distributions• Smooth increase in elliptic flow from SPS to RHIC. Detailed measurements
of identified particle v2(pt) by the RHIC experiments (or perhaps SPS data not presented yet) will provide a clearer picture
• At intermediate centralities (20-60%) I estimate not more than 10% uncertainty in the integrated elliptic flow values
• At RHIC the large elliptic flow is not described by hadronic models; strong (partonic) interactions at early stage of the collision are needed
• From comparisons with ideal hydro calculations early thermalization deduced (is this the only possibility? what is the freedom in EOS? What about HBT?)
D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).
Raimond Snellings; Trento 2004 33
Backup
Raimond Snellings; Trento 2004 34
Elliptic flow; excitation function
NA49Phys.Rev. C68
(2003) 034903 NA49
STAR
Raimond Snellings; Trento 2004 35
Hydro + Jet Quenching?
X.-N. Wang: nucl-th/0305010
T. Hirano and Y. Nara: nucl-th/0307015
Coupling of hydro and parton energy loss gives a reasonable description of the data and also has a mass dependence at higher-pt
Raimond Snellings; Trento 2004 36
Flow (radial, directed and elliptic)
x
y
x
y
z
x
• Only type of transverse flow in central collision (b=0) is transverse flow.
• Integrates pressure history over complete expansion phase
• Elliptic flow, caused by anisotropic initial overlap region (b > 0).
• More weight towards early stage of expansion.
• Directed flow, sensitive to earliest collision stage (pre-equilibrium, b > 0)
Raimond Snellings; Trento 2004 37
v1 predictions (QGP invoked)
J. Brachmann et al., Phys. Rev. C. 61 024909 (2000)
L.P. Csernai, D. Rohrich: Phys. Lett. B 458 (1999) 454
Raimond Snellings; Trento 2004 38
v1 predictions (more general, QGP interpretation not necessary)
R.S., H. Sorge, S.A. Voloshin, F.Q. Wang, N. Xu: Phys. Rev. Lett 84 2803 (2000)
M. Bleicher, H. Stocker: Phys. Lett. B 526 (2002) 309 (UrQMD)
Raimond Snellings; Trento 2004 39
Directed flow at the SPS (NA49)
NA49: Phys.Rev. C68 (2003) 034903
Raimond Snellings; Trento 2004 40
First measurement of v1 at RHIC
A. Tang, M. Oldenburg, A. Poskanzer, J. Putschke, RS, S. Voloshin
• Confirms v2 is in-plane at RHIC
• Suggestive of limiting fragmentation picture
• Consistent with theory predictions
• The data with current statistics shows no sign of a wiggle (also does not exclude the magnitude of the wiggle as predicted
Raimond Snellings; Trento 2004 41
Is there boost invariance?PHOBOS v2()
Preliminary v2200
Final v2130
200
130
average over
all centrality
(Npart ~200)
PHOBOS: Phys. Rev. Lett. 89, 222301 (2002)
Raimond Snellings; Trento 2004 42
Elliptic flow at higher pt, extracted using multi-particle correlations
Significant v2 up to ~7 GeV/c in pt as expected from jet quenching. However at intermediate pt the magnitude is unexpectedly large
STAR Preliminary
v2{2}
v2{RP}
v2{4}
A. Tang (STAR) QM 2004
Raimond Snellings; Trento 2004 43
Early freeze-out in a blast wave approach
• Low-pt measurements and comparison to full dynamical calculations important for drawing a conclusion !!!!
STAR, PHENIX preliminary