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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

3

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)

5

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

6

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

9

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

40A. Wetzler (2005)

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)