History of Flow Analysis Methods

1
History of Flow Analysis Methods
Exploring the secrets of the universe

• Art Poskanzer

Color by Roberta Weir
2
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
First prediction of collective flow at high
energy
Angle depends on the speed of sound which depends
on the Eq. of State
Annals of Physics 6, 1 (1959)
4
Shock Waves
G.F. Chapline, M.H. Johnson, E. Teller, and M.S.
Weiss, PRD 8, 4302 (1973)
W. Scheid, H. Muller, and W. Greiner, PRL 32, 741
(1974)
M.I. Sobel, P.J. Siemens, J.P. Bondorf, and H.A.
Bethe, Nucl. Phys. A251, 502 (1975)
5
No Shock Waves
Peaks in tracks in AgCl crystals
H.G. Baumgardt et al., Z. Physik A 273, 359 (1973)
GSI-LBL, A.M. Poskanzer et al., PRL 35, 1701
(1975)
reviewed in H.R. Schmidt, Int. J. Mod. Phys. A6,
3865 (1991)
6
Shock Waves Again
Flow in conical shock waves
Away side jet
D.H. Rischke, H. Stoecker, and W. Greiner. PRD
42, 2283 (1990)
J. Casalderrey-Solana, E.V. Shuryak, and D.
Tracy, arXiv hep-ph/0411315 (2004)
7
Kinds of Flow
participant-spectator picture
J.D. Bowman, W.J. Swiatecki, and C.F. Tsang,
LBL-2908 (1973)
8
Central collisions of relativistic heavy ions
Fireball Coalescence pt vs. y
GSI-LBL, J. Gosset et al., PRC 16, 629 (1977)
9
Nature 1979
At still higher densities it is possible that
the nucleons might break up into their
constituents to produce quark matter
Relativistic nuclear collisions from A. M.
Poskanzer, Nature 278, 17 (1979)
R. Stock and A.M. Poskanzer, Comments on Nuclear
and Particle Physics 7, 41 (1977)
10
Inspiration from Hydrodynamics
Ne
U
H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44,
725 (1980)
11
Plastic Ball
First 4p detector for nuclear physics 1980-90
Collective Flow Squeeze-out
1983
Gutbrod 1985
Plastic Ball, A. Baden et al., Nucl. Instru. and
Methods 203, 189 (1982)
12
Sphericity
Best ellipsoid for each event by
diagnalizing kinetic energy flow tensor
Major axis and beam axis determine event plane
M. Lisa (1999)
M. Gyulassy, K.A. Frankel, and H. Stocker, Phys.
Lett. 110B, 185 (1982)
P. Danielewicz and M. Gyulassy Phys. Lett. B 129,
283 (1983)
13
Polar Flow Angle
Directed Flow
The only true signature of collective flow is a
clear maximum of dN/d cos? away from ? 0
M. Gyulassy, K.A. Frankel, and H. Stocker, Phys.
Lett. 110B, 185 (1982)
14
Discovery of Collective Flow
Bevalac 400 MeV/A
Non-zero flow angle distribution for Nb, but not
Ca
dN/dcos?
Plastic Ball, Gustafsson et al., PRL 52, 1590
(1984)
15
Directed Flow
Au Au
Clear collective flow
Plastic Ball, H.G. Ritter et al., Nucl. Phys.
A447, 3c (1985)
16
Flow
px/A

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

• Collective transverse
• momentum transfer

• Filter theory to compare
• with data

y/yproj
Plastic Ball, K.G.R. Doss et al., PRL 57, 302
(1986)
17
Squeeze-out
400 MeV/A AuAu (MUL 3)
Diogene, M. Demoulins et al., Phys. Lett. B241,
476 (1990)
Plastic Ball, H.H. Gutbrod et al., Phys. Lett.
B216, 267 (1989)
18
Squeeze Angle
Plastic Ball, H.H. Gutbrod et al., PRC 42, 640
(1991)
19
R?
Projection of 2-dimensional sphericity
eigenvectors out-of-plane / in-plane
Plastic Ball, H.H. Gutbrod et al., PRC 42, 640
(1991)
20
RN
Squeeze-out Ratio Azimuthal distribution
projected out-of-plane / in-plane
around the major axis
Plastic Ball, H.H. Gutbrod et al., PRC 42, 640
(1991)
21
Transverse Plane
Anisotropic Flow as a function of rapidity
H. Wieman (2005)
around the beam axis
22
Transverse Momentum Analysis
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
Danielewicz
Mistake in event plane resolution
P. Danielewicz and G. Odyniec, Phys. Lett. 157B,
146 (1985)
23
Azimuthal Alignment
length distribution of Q1-vector normalized by
the multiplicity
Siemiarczuk 1986
WA80, P. Beckmann et al., Modern Phys. Lett. A2,
163 (1987)
24
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
25
Fourier Harmonics
First to use Fourier harmonics
Event plane resolution correction made for each
harmonic
Unfiltered theory can be compared to experiment!
First to use mixed harmonics
First to use the terms directed and elliptic flow
for v1 and v2
S. Voloshin and Y. Zhang, hep-ph/940782 Z. Phys.
C 70, 665 (1996)
See also, J.-Y. Ollitrault, arXiv nucl-ex/9711003
(1997)
and J.-Y. Ollitrault, Nucl. Phys. A590, 561c
(1995)
26
Azimuthal Flow Angle
wi negative in backward hemisphere for odd
harmonics
for n1
S. Voloshin and Y. Zhang, Z. Phys. C 70, 665
(1996)
27
First AGS Flow
Q-dist method v1 observed First v2 positive at
high energy First v4 observed
E877, J. Barrette et al., PRL 73, 2532 (1994)
28
First SPS Elliptic Flow
NA49, T. Wienold et al., Nucl. Phys. A610, 76c
(1996)
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Directed and Elliptic Flow at the SPS
First to use inverse of lab azimuthal
distribution for flattening event plane
NA49, C. Alt et al., PRC 68, 034903 (2003)
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Momentum Conservation
v1
No effect on directed flow if acceptance is
symmetric about ycm Does not affect elliptic
flow if 2nd harmonic event plane is used
Other nonflow effects
HBT, resonance decays, final state interactions,
2-track resolution, etc.
J.-Y. Ollitrault, Nucl. Phys. A590, 561c (1995)
N. Borghini, P. Dinh, J.-Y. Ollitrault, A.
Poskanzer, S. Voloshin, PRC 66, 014901 (2002)
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Standard Event Plane Method

• 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)

A.M. Poskanzer and S.A. Voloshin, PRC 58, 1671
(1998)
32
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
predicted that the effects of elliptic flow will
be small at RHIC
33
StFlowMakers
STAR, A.M. Poskanzer and R.J. Snellings (1999)
34
First RHIC Elliptic Flow
First paper from STAR
130 GeV/A AuAu
22 k events
Data approach hydro for central collisions
STAR, K.H. Ackermann et al., PRL 86, 402 (2001)
35
Other Methods

• Particle pair-wise correlations

no event plane
Streamer Chamber, S. Wang et al., PRC 44, 1091
(1991)
PHENIX, K. Adcox et al., PRL 89, 21301 (2002)
36
q-dist Method
no event plane
STAR, C. Alt et al., PRC 68, 034903 (2003)
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Multi-particle Methods
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High pt
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Methods Comparison
Ratio to the Standard Method
Because of nonflow and fluctuations the truth
lies between the lower band and the mean of the
two bands
STAR, J. Adams et al., PRC, submitted (2005)
40
Elliptic Flow vs. Beam Energy
25 most central mid-rapidity
all v2
bounce-off
In-plane elliptic flow
squeeze-out
six decades
A. Wetzler (2005)
41
Mixed Harmonics
STAR, J. Adams et al., PRC submitted (2005)
CERES, S.A. Voloshin, German Physical Society
meeting (1998)
Removes nonflow Uses best determined event plane
N. Borghini, P.M. Dinh, and J.-Y. Ollitrault,
PRC, 66, 014905 (2002)
42
Resolution for Higher Harmonics
Application of mixed harmonics
Removes nonflow
STAR, J. Adams et al., PRC, submitted (2005)
43
Higher Harmonics
vn ? v2n/2
more details of the event shape in momentum space
J. Adams et al., PRL 92, 062301 (2004)
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Particle Identification
scaling by number of constituent quarks
STAR, J. Adams et al., PRC, submitted (2005)
45
RHIC Achievements

• Physics
• Hydrodynamics good
• v2 self quenching -gt early time
• Higher harmonic scaling as v2n/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 ltsin(n?)gt for resonance decays
• Multi-particle correlations -gt Lee-Yang Zeros

N. Borghini and J.-Y. Ollitrault, PRC 70, 064905
(2004)