# Presentation: 144695

## History of Flow Analysis Methods

**Art Poskanzer**

- Color by Roberta Weir

- Exploring the secrets
- of the universe

## 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**

## Kinds of Flow

- participant-spectator picture

- J.D. Bowman, W.J. Swiatecki, and C.F. Tsang, LBL-2908 (1973)

## Bevalac at Berkeley

## Central collisions of relativistic heavy ions

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

- Fireball
- Coalescence
- pt vs. y

## 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)

## Inspiration from Hydrodynamics

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

**U**

**Ne**

## Plastic Ball at the Bevalac

- First 4π detector for nuclear physics: 1980-90

- Collective Flow
- Squeeze-out

- Plastic Ball, A. Baden et al., Nucl. Instru. and Methods **203**, 189 (1982)

- 1983

- Gutbrod 1985

## Sphericity

- Best ellipsoid for each event by diagonalizing
- kinetic energy flow tensor:

- 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 axis
- determine event plane

- M. Lisa (1999)

## Polar Flow Angle

- “The only true signature of collective flow
- is 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)

## Discovery of Collective Flow

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

- Non-zero flow angle distribution
- for Nb, but not Ca

- dN/dcos

- Bevalac 400 MeV/A

## Directed Flow

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

- Au + Au

- Clear collective flow

## “Flow”

- Plastic Ball, K.G.R. Doss et al., PRL **57**, 302 (1986)

-  F defined as the slope
- of the line at mid-rapidity

- px/A

- y/yproj

-  Collective transverse
- momentum transfer

-  Filter theory to compare
- with data

## Squeeze-out

- 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)

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

## R

- Projection of 2-dimensional sphericity eigenvectors
- out-of-plane / in-plane

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

## RN

- Squeeze-out Ratio
- Azimuthal distribution projected out-of-plane / in-plane

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

- around the major axis

## Transverse Plane

- Anisotropic Flow as a function of rapidity

- H. Wieman (2005)

- around the beam axis

**self quenching expansion**

- S = π x y

## Centrality Dependence

- (near) Central Collision

**Centrality Dependence**

- Masashi Kaneta

## Elliptic Flow

- Animation by Jeffery Mitchell (Brookhaven National Laboratory)

## Transverse Momentum Analysis

- P. Danielewicz and G. Odyniec, Phys. Lett. **157B**, 146 (1985)

- Second to use the transverse plane
- First to define 1st harmonic Q-vector
- First to use weighting
- First to use sub-events
- First to remove auto-correlations

- Mistake in event plane resolution

- Danielewicz

## Azimuthal Alignment

- WA80, P. Beckmann et al., Modern Phys. Lett. **A2**, 163 (1987)

- length distribution of Q1-vector
- normalized by the multiplicity

- Siemiarczuk 1986

## Prediction of positive elliptic flow

- At 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

## 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)

## Azimuthal Flow Angle

**Azimuthal Flow Angle**

- for n=1:

- S. Voloshin and Y. Zhang, Z. Phys. C **70**, 665 (1996)

- wi negative in backward
- hemisphere for odd harmonics

## First Flow at Brookhaven AGS 

- E877, J. Barrette et al., PRL **73**, 2532 (1994)

- Q-dist method
- v1 observed
- First v2 positive at high energy
- First v4 observed

## Move to CERN SPS in Geneva

**Move to CERN SPS in Geneva**

## First SPS Elliptic Flow

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

## Directed and Elliptic Flow at the SPS

- NA49, C. Alt et al., PRC **68**, 034903 (2003)

- First to use inverse of lab azimuthal distribution for flattening event plane

## Momentum Conservation

- if acceptance is symmetric
- about y**cm**
- Does not affect elliptic flow
- if 2nd harmonic event plane
- is 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)

## 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 ********, p****t****, or both (with yield weighting)**

## Relativistic Heavy Ion Collider (RHIC) at Brookhaven

**Relativistic Heavy Ion Collider (RHIC) at Brookhaven**

**1 km**

- animation by Mike Lisa

- 3 km

## STAR (Solenoidal Tracker at RHIC)

## 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 hydro
- for central collisions

## 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

## q-dist Method

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

- no event plane

## Cumulants

- Four-particle correlation subtracts nonflow to first order

- nonflow

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

## 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:**

## Lee and Yang

**prediction of non-conservation of parity in weak interactions**
**1952**
**Statistical Theory of Phase Transitions**

**Lee and Yang**

- Chen Ning Yang

- Tsung-Dao Lee

## Methods Comparison

- STAR, J. Adams et al., PRC, submitted (2005)

- Ratio to the Standard Method:

- Because of nonflow and fluctuations the truth lies
- between the lower band and the mean of the two bands

## q-Dist with Nonflow and Fluctuations

**STAR preliminary**

## Elliptic Flow vs. Beam Energy

- A. Wetzler (2005)

- all v2

- six decades

**Elliptic Flow vs. Beam Energy**

- 25% most central
- mid-rapidity

- In-plane
- elliptic flow

- squeeze-out

- bounce-off

## v2 /

**v****2 ****/******

## Higher Harmonics

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

- more details of the event shape
- in momentum space

- vn  v2n/2

## Particle Identification

- STAR, Yan Lu (2006)

**Particle Identification**

## Scaling

**Scaling**

- Roy Lacy, nucl-ex/0610029 (2006)

## RHIC Achievements

**Hydrodynamics good**
**v****2**** self quenching -> early time**
**Higher harmonic scaling as v****2****n/2**
**Parton coalescence at intermediate p****t**

## Large Hadron Collider at CERN

- 27 km

## 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**