1 history of flow analysis methods art poskanzer color by roberta weir exploring the secrets of the...
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History of Flow Analysis History of Flow Analysis MethodsMethods
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 Degree of Equilibration Constituents at Early Time
Partonic Matter Study the Little Bang in the Laboratory
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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
1998
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Bevalac at Berkeley
SuperHILACSuperHILAC
BevatronBevatronBevatronBevatron
Grunder 1974
Ghiorso 1972
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Central collisions of relativistic heavy ions
GSI-LBL, J. Gosset et al., PRC 16, 629 (1977)
FireballCoalescencept vs. y
Westfall 1976
Gosset 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 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
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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)
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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 CadN/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
Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991)
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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 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
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Peripheral Collision
x
yz
x
yz
(near) Central Collision
X
Y
X
Y
Centrality Dependence
Masashi Kaneta
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Elliptic Flow
Animation by Jeffery Mitchell (Brookhaven National Laboratory)
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
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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 anisotropymomentum 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 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
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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 BRAHMSPHOBOS
PHENIXSTAR
AGS
TANDEMS
Relativistic Heavy Ion Collider (RHIC) at Brookhaven
1 km
animation by Mike Lisa3 km
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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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Cumulants
Four-particle correlation subtracts nonflow to first order
nonflow
N. Borghini, P.M. Dinh, and J.-Y. Ollitrault, PRC 64, 054901 (2001)
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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:
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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
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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
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)
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Higher Harmonics
J. Adams et al., PRL 92, 062301 (2004)
more details of the event shapein momentum space
Kolb
vn v2
n/2
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scaling by numberof constituent quarks
plotted vs. trans. kinetic energySTAR, Yan Lu (2006)
Particle Identification
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Scaling
Roy Lacy, nucl-ex/0610029 (2006)
scaling by number of constituentquarks and integrated v2
plotted vs. trans. kinetic energy
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RHIC Achievements
Hydrodynamics good v2 self quenching -> early time Higher harmonic scaling as v2
n/2
Parton coalescence at intermediate pt
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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• Remove nonflow and fluctuations