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History of Flow Analysis MethodsHistory of Flow Analysis Methods
Art Poskanzer
Color by Roberta Weir
Exploring the secretsof the universe
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Collective Flow Motivation Collective Properties of Nuclei
Nuclear physics, bulk properties of matter Equation of State Constituents at Early Time
Partonic Matter Study the Little Bang in the Laboratory
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Shock Waves - 1959
Annals of Physics 6, 1 (1959)
First prediction of collective flow at high energy
Angle depends on the speed of soundwhich depends on the Eq. of State
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Shock Waves
W. Scheid, H. Muller, and W. Greiner,PRL 32, 741 (1974)
M.I. Sobel, P.J. Siemens, J.P. Bondorf, andH.A. Bethe, Nucl. Phys. A251, 502 (1975)
G.F. Chapline, M.H. Johnson, E. Teller, and M.S. Weiss, PRD 8, 4302 (1973)
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No Shock Waves
GSI-LBL, A.M. Poskanzer et al., PRL 35, 1701 (1975)reviewed in H.R. Schmidt, Int. J. Mod. Phys. A6, 3865 (1991)
H.G. Baumgardt et al., Z. Physik A 273, 359 (1973)Peaks in tracks in AgCl crystals
Poskanzer and Greiner 1984
d/d d/dΩ
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Shock Waves Again
D.H. Rischke, H. Stoecker, and W. Greiner. PRD 42, 2283 (1990)
Flow in conical shock waves Away side jet
J. Casalderrey-Solana, E.V. Shuryak,and D. Tracy, arXiv hep-ph/0411315 (2004)
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Kinds of Flow
participant-spectator picture
J.D. Bowman, W.J. Swiatecki, and C.F. Tsang, LBL-2908 (1973)
Swiatecki 1982
bounce-off
anisotropic
radial
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Central collisions of relativistic heavy ions
GSI-LBL, J. Gosset et al., PRC 16, 629 (1977)
FireballCoalescencept vs. y
Westfall 1976Gosset 1976
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Nature 1979
“Relativistic nuclear collisions”from A. M. Poskanzer, Nature 278, 17 (1979)
“At still higher densities it is possible that the nucleons might break up into their constituents to produce quark matter”
R. Stock and A.M. Poskanzer, Comments on Nuclear and Particle Physics 7, 41 (1977)
Stock 1976
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Inspiration from Hydrodynamics
H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980)
U
Ne
Stocker 1995
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Plastic Ball
First 4π detector for nuclear physics: 1980-90
Collective FlowSqueeze-out
Plastic Ball, A. Baden et al., Nucl. Instru. and Methods 203, 189 (1982)
1983Gutbrod 1985
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Sphericity
Best ellipsoid for each event by diagnalizingkinetic energy flow tensor:
pz
(Beam)
Reaction plane
x
y
z
s
py
px
P. Danielewicz and M. Gyulassy Phys. Lett. B 129, 283 (1983)M. Gyulassy, K.A. Frankel, and H. Stocker, Phys. Lett. 110B, 185 (1982)
Major axis and beam axisdetermine event plane
M. Lisa (1999)
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Polar Flow Angle
“The only true signature of collective flowis a clear maximum of dN/d cos away from = 0”
Directed Flow
M. Gyulassy, K.A. Frankel, and H. Stocker, Phys. Lett. 110B, 185 (1982)
Gyulassy 1995
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Discovery of Collective Flow
Plastic Ball, Gustafsson et al., PRL 52, 1590 (1984)
Non-zero flow angle distributionfor Nb, but not Ca dN/dcos
Bevalac 400 MeV/A
Ritter 1985
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Directed Flow
Plastic Ball, H.G. Ritter et al., Nucl. Phys. A447, 3c (1985)
Au + Au
Clear collective flow
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“Flow”
Plastic Ball, K.G.R. Doss et al., PRL 57, 302 (1986)
• F defined as the slopeof the line at mid-rapidity
px/A
y/yproj
• Collective transversemomentum transfer• Filter theory to comparewith data
Flow
Beam Energy (MeV/A)
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Squeeze-outbounce
squeeze squeeze
400 MeV/A Au+Au (MUL 3)
Plastic Ball, H.H. Gutbrod et al., Phys. Lett. B216, 267 (1989)Diogene, M. Demoulins et al., Phys. Lett. B241, 476 (1990)
Schmidt 1986
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Squeeze Angle
Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991)
around the major axis
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R
Projection of 2-dimensional sphericity eigenvectorsout-of-plane / in-plane
Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991)
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RN
Squeeze-out RatioAzimuthal distribution projected out-of-plane / in-plane
Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991)
around the major axis
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Transverse Plane
Transverse Plane y
x
Anisotropic Flow as a function of rapidity
H. Wieman (2005)
around the beam axis
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Transverse Momentum Analysis
P. Danielewicz and G. Odyniec, Phys. Lett. 157B, 146 (1985)
Second to use the transverse planeFirst to define 1st harmonic Q-vectorFirst to use weightingFirst to use sub-eventsFirst to remove auto-correlations
Mistake in event plane resolution
data mixed events
correlationof sub-eventplanes
negative in backwardhemisphere
Danielewicz
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Azimuthal Alignment
WA80, P. Beckmann et al., Modern Phys. Lett. A2, 163 (1987)
length distribution of Q1-vectornormalized by the multiplicity
Q1/M
randomized azimuths
Ca
Nb
Au
Siemiarczuk 1986
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Prediction of positive elliptic flowAt a meeting in Jan ‘93, Jean-Yves told me he was predicting in-plane elliptic flow at high beam energies. I responded that we had just discovered out-of-plane elliptic flow
Ollitrault
J.-Y. Ollitrault, PRD 46, 229 (1992), PRD 48, 1132 (1993)
space elliptic anisotropy momentum elliptic anisotropy
2-dimensional transverse sphericity analysis
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Fourier Harmonics
S. Voloshin and Y. Zhang, hep-ph/940782; Z. Phys. C 70, 665 (1996)
First to use Fourier harmonics:
Event plane resolution correction made for each harmonic
See also, J.-Y. Ollitrault, arXiv nucl-ex/9711003 (1997)
First to use the terms directed and elliptic flow for v1 and v2
Unfiltered theory can be compared to experiment!
First to use mixed harmonics
and J.-Y. Ollitrault, Nucl. Phys. A590, 561c (1995)
Voloshin
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Azimuthal Flow Angle
px
py
for n=1:
S. Voloshin and Y. Zhang, Z. Phys. C 70, 665 (1996)
wi negative in backwardhemisphere for odd harmonics
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First AGS Flow
E877, J. Barrette et al., PRL 73, 2532 (1994)centrality
vn
backward
mid
forward
Forward-Backward subevent ratio
centralityQ-dist methodv1 observedFirst v2 positive at high energy First v4 observed
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First SPS Elliptic Flow
NA49, T. Wienold et al., Nucl. Phys. A610, 76c (1996)
Forward-Backwardsubevent resolution
centralityWienold
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Directed and Elliptic Flow at the SPS
NA49, C. Alt et al., PRC 68, 034903 (2003)
pions protons
y
pt
First to use inverse of lab azimuthal distribution for flattening event plane
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No effect on directed flowif acceptance is symmetricabout ycm
Does not affect elliptic flowif 2nd harmonic event planeis used
Momentum Conservation
N. Borghini, P. Dinh, J.-Y. Ollitrault, A. Poskanzer, S. Voloshin, PRC 66, 014901 (2002)
v1
Other nonflow effects:HBT, resonance decays, final state interactions, 2-track resolution, etc.J.-Y. Ollitrault, Nucl. Phys. A590, 561c (1995)
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Standard Event Plane Method
A.M. Poskanzer and S.A. Voloshin, PRC 58, 1671 (1998)
Define 2 independent groups of particles Flatten event plane azimuthal distributions in lab Correlate subevent planes
Calculate subevent plane resolution
Calculate event plane resolution
Correlate particles with the event plane
Correct for the event plane resolution
Average over , pt, or both (with yield weighting)
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RHIC Day One Physics
At Santa Fe APS meeting in Oct. 1998 I predicted day one physics would be elliptic flow
At the same meeting one RHIC spokesperson predictedthat the “effects of elliptic flow will be small at RHIC”
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StFlowMakers
STAR, A.M. Poskanzer and R.J. Snellings (1999)
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First RHIC Elliptic Flow
130 GeV/A Au+Au
22 k events
STAR, K.H. Ackermann et al., PRL 86, 402 (2001)
First paper from STAR
Data approach hydrofor central collisions
Snellings Voloshin Poskanzer
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Other Methods
• Particle pair-wise correlations
PHENIX, K. Adcox et al., PRL 89, 21301 (2002)Streamer Chamber, S. Wang et al., PRC 44, 1091 (1991)
no event plane
• Scalar Product
STAR, C. Adler et al., PRC 66, 034904 (2002)
similar to standard method
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q-dist Method
STAR, C. Alt et al., PRC 68, 034903 (2003)
nonflow effects
flow vector
multiplicity
modified Bessel function
no event plane
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Multi-particle Methods
• Lee-Yang Zeros
R.S. Bhalerao, N. Borghini, and J.-Y. Ollitrault, Nucl. Phys. A 727, 373 (2003)FOPI, N. Bastid et al., arXiv nucl-ex/0504002 (2005)
All-particle correlation subtracts nonflow to all orders
Streamer Chamber, J. Jiang et al., PRL 68, 2739 (1992)
• Explicitly shows flow is a multi-particle correlation
• Cumulants
N. Borghini, P.M. Dinh, and J.-Y. Ollitrault, PRC 64, 054901 (2001)
Four-particle correlation subtracts nonflow to first ordernonflow
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High pt
STAR, J. Adams et al., PRC, submitted (2005)
Modified Event Plane Method:Exclude from the event plane particleswith |∆| < 0.5 around highest pt particle:Removes intra-jet correlations at high pt
Filimonov 2005
only momentum anisotropy
only space anisotropy
uncorrelated jets
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Methods Comparison
STAR, J. Adams et al., PRC, submitted (2005)
2-part. methods
multi-part. methods
Ratio to the Standard Method:
Because of nonflow and fluctuations the truth lies between the lower band and the mean of the two bands
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all v2
six decades
Elliptic Flow vs. Beam Energy25% most centralmid-rapidity
Wetzler 2004
In-planeelliptic flow
squeeze-out
bounce-off
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Mixed Harmonics2nd har. event plane N-particle cumulants v1EP1,EP2
v13
N. Borghini, P.M. Dinh, and J.-Y. Ollitrault, PRC, 66, 014905 (2002)
CERES, S.A. Voloshin, German PhysicalSociety meeting (1998)
Removes nonflowUses best determined event plane
STAR, J. Adams et al., PRC submitted (2005)
Oldenburg 2005
Tang
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Resolution for Higher Harmonics
square-root of subevent correlation
signal to fluctuation noise
Same harmonicV4 vs. 2nd
V6 vs. 2nd
STAR, J. Adams et al., PRC, submitted (2005)
Application ofmixed harmonics
Removes nonflow
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Higher Harmonics
J. Adams et al., PRL 92, 062301 (2004)
more details of the event shapein momentum space
Kolb
vn v2n/2
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Particle Identification
pt/n
v2/n
STAR preliminary
v2
pt
Ω
scaling by numberof constituent quarks
Sorensen
STAR, J. Adams et al., PRC, submitted (2005)
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RHIC Achievements Physics
Hydrodynamics good v2 self quenching -> early time Higher harmonic scaling as v2
n/2
Parton coalescence at intermediate pt
Analysis Differential results: pt, y, and centrality PID
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Conclusions 25 years of flow analysis development
Extract parameters independent of acceptance
Standard Method was the most efficient of statistics
With RHIC run 4, systematics are more important than statistics• Separation in of particles and plane• Mixed harmonics• Check <sin(n)> for resonance decays
• Multi-particle correlations -> Lee-Yang ZerosN. Borghini and J.-Y. Ollitrault, PRC 70, 064905 (2004)