1

History of Flow Analysis History of Flow Analysis MethodsMethods

Art Poskanzer

Color by Roberta Weir

Exploring the secretsof the universe

2

Collective Flow Motivation

Collective Properties of Nuclei Nuclear physics, bulk properties of matter

Equation of State Degree of Equilibration Constituents at Early Time

Partonic Matter Study the Little Bang in the Laboratory

3

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

1998

4

Bevalac at Berkeley

SuperHILACSuperHILAC

BevatronBevatronBevatronBevatron

Grunder 1974

Ghiorso 1972

5

Central collisions of relativistic heavy ions

GSI-LBL, J. Gosset et al., PRC 16, 629 (1977)

FireballCoalescencept vs. y

Westfall 1976

Gosset 1976

6

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

7

Inspiration from Hydrodynamics

H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980)

U

Ne

Stocker 1995

8

Plastic Ball at the Bevalac

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

9

Sphericity

Best ellipsoid for each event by diagonalizingkinetic 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)

10

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

11

Discovery of Collective Flow

Plastic Ball, Gustafsson et al., PRL 52, 1590 (1984)

Non-zero flow angle distributionfor Nb, but not CadN/dcos

Bevalac 400 MeV/A

Ritter 1985

12

Directed Flow

Plastic Ball, H.G. Ritter et al., Nucl. Phys. A447, 3c (1985)

Au + Au

Clear collective flow

13

“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)

14

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

Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991)

15

R

Projection of 2-dimensional sphericity eigenvectorsout-of-plane / in-plane

Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991)

16

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

17

Transverse Plane

Transverse Planey

x

Anisotropic Flow as a function of rapidity

H. Wieman (2005)

around the beam axis

self quenching expansionself quenching expansionε =

<y2> + <x2>

<y2> - <x2>S = π x y

18

Peripheral Collision

x

yz

x

yz

(near) Central Collision

X

Y

X

Y

Centrality Dependence

Masashi Kaneta

19

Elliptic Flow

Animation by Jeffery Mitchell (Brookhaven National Laboratory)

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

20

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

21

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

22

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 anisotropymomentum elliptic anisotropy

2-dimensional transverse sphericity analysis

23

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

24

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

25

First Flow at Brookhaven AGS

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

266 km

Move to CERN SPS in Geneva

27

First SPS Elliptic Flow

NA49, T. Wienold et al., Nucl. Phys. A610, 76c (1996)

Forward-Backwardsubevent resolution

centralityWienold

28

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

29

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)

30

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)

31

RHIC BRAHMSPHOBOS

PHENIXSTAR

AGS

TANDEMS

Relativistic Heavy Ion Collider (RHIC) at Brookhaven

1 km

animation by Mike Lisa3 km

32

STAR (Solenoidal Tracker at RHIC)

33

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

34

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

35

q-dist Method

STAR, C. Alt et al., PRC 68, 034903 (2003)

nonflow effects

flow vector

multiplicity

modified Bessel function

no event plane

36

Cumulants

Four-particle correlation subtracts nonflow to first order

nonflow

N. Borghini, P.M. Dinh, and J.-Y. Ollitrault, PRC 64, 054901 (2001)

37

Lee-Yang Zeros Method

All-particle correlation subtracts nonflow to all orders

R.S. Bhalerao, N. Borghini, and J.-Y. Ollitrault,Nucl. Phys. A 727, 373 (2003)

Flow vector projection on arbitrary lab angle,

Generating function for one

First minimum of |G|2 determines r0

Sum Generating Function:

38

1957 Nobel Prizeprediction of non-conservation of parity in weak interactions

1952Statistical Theory of Phase Transitions

Lee and Yang

Chen Ning YangTsung-Dao Lee

Photos by Deena Greer Gagliardi

Three RiversVillage

39

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

40

q-Dist with Nonflow and Fluctuations

Sorensen

STAR preliminarySTAR preliminary

41A. Wetzler (2005)

all v2

six decades

Elliptic Flow vs. Beam Energy

25% most centralmid-rapidity

Wetzler 2004

In-planeelliptic flow

squeeze-out

bounce-off

42S.A. Voloshin and A.M. Poskanzer, Phys. Letters B 474, 27 (2000)NA49, C. Alt et al., Phys. Rev. C 68 034903 (2003)

v2 /

HYDRO: Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909

S. Voloshin (2006)

43

Higher Harmonics

J. Adams et al., PRL 92, 062301 (2004)

more details of the event shapein momentum space

Kolb

vn v2

n/2

44

scaling by numberof constituent quarks

plotted vs. trans. kinetic energySTAR, Yan Lu (2006)

Particle Identification

45

Scaling

Roy Lacy, nucl-ex/0610029 (2006)

scaling by number of constituentquarks and integrated v2

plotted vs. trans. kinetic energy

46

RHIC Achievements

Hydrodynamics good v2 self quenching -> early time Higher harmonic scaling as v2

n/2

Parton coalescence at intermediate pt

47

Large Hadron Collider at CERN

27 km

48

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• Remove nonflow and fluctuations