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7/7/2006Correlations & Fluctuations Workshop in
Florence, Italy 1
Angular correlations at PHOBOS
Wei LiMassachusetts Institute of Technology
for the collaboration
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Correlations & Fluctuations Workshop in Florence, Italy 27/7/2006
collaboration (July 2006)
Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel,Wit Busza (Spokesperson), Zhengwei Chai, Vasundhara Chetluru, Edmundo García, Tomasz Gburek,
Kristjan Gulbrandsen, Clive Halliwell, Joshua Hamblen, Ian Harnarine, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Jay Kane,
Piotr Kulinich, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed,
Eric Richardson, Christof Roland, Gunther Roland, Joe Sagerer, Iouri Sedykh, Chadd Smith, Maciej Stankiewicz, Peter Steinberg, George Stephans, Andrei Sukhanov, Artur Szostak, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres,
Peter Walters, Edward Wenger, Donald Willhelm, Frank Wolfs, Barbara Wosiek, Krzysztof Woźniak, Shaun Wyngaardt, Bolek Wysłouch
ARGONNE NATIONAL LABORATORY BROOKHAVEN NATIONAL LABORATORYINSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY
NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGOUNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER
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Correlations & Fluctuations Workshop in Florence, Italy 37/7/2006
OverviewMotivation: Clusters from F&B multiplicity correlations at PHOBOS;
Two-particle angular correlation as another point of view to study in detail the multiplicity and shape of the clusters;
Definitions;MC studies;Cluster model and rapidity correlation function;Other studies in HI collision;
In this talk, mainly the analysis technique will be discussed since results of PHOBOS data are not ready for publication yet.
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Correlations & Fluctuations Workshop in Florence, Italy 47/7/2006
Clusters in F&B Multiplicity Correlations
P NCP N−
=+
σC2 ~ <K>
Cluster Multiplicity K
This topic will be discussed in more details in Constantin Loizides’ talkη∆
0.5 1 1.5 2
2 C
σ
1
1.5
2
2.5
3 Data
HIJING
AMPT
0-20% Central
η∆0.5 1 1.5 2
40-60% Peripheral
σC2 as a function of ∆η at fixed |η|=2
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Correlations & Fluctuations Workshop in Florence, Italy 57/7/2006
∆η
Two-particle angular correlations
PYTHIA 200Gev at -3<η<3 without weak decay
∆φ
RII (∆η,∆φ
)
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Correlations & Fluctuations Workshop in Florence, Italy 67/7/2006
Two-particle correlation function (C.F.)
( , )( , ) ( 1)( 1)( , )
II n
n
FR nB
η φη φη φ
∆ ∆∆ ∆ =< − − >
∆ ∆4
1 2 1 21 2 1 2
2 2
1 1 2 21 1 2 2
1( , ) ( , , , )( 1)
1 1( , ) ( , ) ( , )
II nn n
n
I I n nn n n
n n
dFn n d d d d
d dBn d d n d d
ση φ ρ η η φ φσ η η φ φ
σ ση φ ρ η φ ρ η φσ η φ σ η φ
∆ ∆ =−
∆ ∆ = ⋅
∼
∼
1 2 1 2 1 2 1 2( , , , ) 1
( , ) 1
IIn
In
d d d d
d d
ρ η η φ φ η η φ φ
ρ η φ η φ
=
=
∫∫
Inclusive two-particle correlation function:
( , ) 1
( , ) 1
n
n
F d d
B d d
η φ η φ
η φ η φ
∆ ∆ ∆ ∆ =
∆ ∆ ∆ ∆ =
∫∫
Foreground:
Background:
Normalization relation:
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Correlations & Fluctuations Workshop in Florence, Italy 77/7/2006
A product of two single particle densities;Constructed by event-mixing which randomly selects particles from different but similar events. (vertex position, centrality etc.)Integral is normalized to be 1.
Two-particle correlation function
( , )nB η φ∆ ∆
( , )nF η φ∆ ∆ Represents two particle density distribution;Obtained by taking particle pairs from the same events;Integral is normalized to be 1.
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Correlations & Fluctuations Workshop in Florence, Italy 87/7/2006
In :
is weighed by (n-1) event-by-event and then averaged over all the events to avoid dilution of the correlations trivially due to high multiplicity;A division of background distribution will help cancel the inefficiency of the detector in the foreground distribution such as acceptance.
A product of two single particle densities;Constructed by event-mixing which randomly selects particles from different but similar events. (vertex position, centrality etc.)Integral is normalized to be 1.
Two-particle correlation function
( , )nB η φ∆ ∆
( , )nF η φ∆ ∆
( , )( , ) ( 1)( 1)( , )
II n
n
FR nB
η φη φη φ
∆ ∆∆ ∆ =< − − >
∆ ∆
Represents two particle density distribution;Obtained by taking particle pairs from the same events;Integral is normalized to be 1.
( , )nF η φ∆ ∆
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Correlations & Fluctuations Workshop in Florence, Italy 97/7/2006
Background construction
Have to appropriately build mixed-event background to correct the acceptance:Particles from different events;Event vertices within 0.5cm (vertex resolution) are mixed.;Events within same centrality bin are mixed (not necessary for pp);In practice, a pool of 30000 events is used for event-mixing and many pools are combinedin the end.
η-φ distribution of hits on the Octagon detector
-1cm<vz<1cmη
φ
Octagon detector: η from -3 to 3 and almost full azimuthal angle
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Correlations & Fluctuations Workshop in Florence, Italy 107/7/2006
Turning on the detectorThings don’t seem to be very encouraging for a first look…
After incorporating the PHOBOS detector simulation to the raw generator:
Foreground: Background:
( , )B η φ∆ ∆( 1) ( , )nn F η φ< − ∆ ∆ >
∆η∆φ∆η
∆φ
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Correlations & Fluctuations Workshop in Florence, Italy 117/7/2006
∆η
Turning on the detector
Peak at (0,0) suffering from secondary effects:∆-electron(50%), γ conversion(40%) etc.
Since we have little information of the particles (only one hit), the secondary effects have to be corrected by MC simulation
200Gev PYTHIA+GEANT
Things don’t seem to be very encouraging for a first look…
After incorporating the PHOBOS detector simulation to the raw generator:
Foreground: Background:
( , )B η φ∆ ∆( 1) ( , )nn F η φ< − ∆ ∆ >
∆η∆φ∆η
∆φ
∆φ
RII (∆η,∆φ
)
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Correlations & Fluctuations Workshop in Florence, Italy 127/7/2006
Turning on the detector
Fortunately, the overall structure except the high spike doesn’t get distorted very much.Secondary effects sitting on top of the actual correlations at (0,0) need to be corrected.
200Gev PYTHIA+GEANT,cutting off the peak
200Gev Raw PYTHIA
However, things are not actually too bad…
∆φ∆φ
∆η∆ηR
II (∆η,∆φ
)
RII (∆η,∆φ
)
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Correlations & Fluctuations Workshop in Florence, Italy 137/7/2006
How to handle the high peak
The physics we are going to study has a range of about 1 unit in ∆η.Cutting off a small region won’t cause too much loss of information.
First of all, we reject a small region of |∆φ|<5.625,|∆η|<0.3 from both foregroundand background which cause the biggest uncertainties based on MC simulation.
∆φ∆φ
∆η∆η
RII (∆η,∆φ
)
RII (∆η,∆φ
)
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Correlations & Fluctuations Workshop in Florence, Italy 147/7/2006
Correcting the secondary effects
— =
HIJING+GEANT Correction functionRAW HIJING
Then, we build correction function from HIJING
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Correlations & Fluctuations Workshop in Florence, Italy 157/7/2006
Correcting the secondary effects
— =
HIJING+GEANT
PYTHIA+GEANT
Correction functionRAW HIJING
Then, we build correction function from HIJING
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Correlations & Fluctuations Workshop in Florence, Italy 167/7/2006
Correcting the secondary effects
— =
≈
HIJING+GEANT
Raw PYTHIA Corrected PYTHIAPYTHIA+GEANT
Correction functionRAW HIJING
Correction almost recovers the original correlations!
Then, we build correction function from HIJING
More quantitative comparison will be discussed later
subtracted
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Correlations & Fluctuations Workshop in Florence, Italy 177/7/2006
What can we learn?Phenomenological model: Clusters;To quantitatively compare with the models by looking at 1D pseudo- rapidity correlation function:
( )( ) ( 1)( 1)( )
II n
n
FR nB
ηηη
∆∆ =< − − >
∆
( ) ( , )
( ) ( , )
n n
n n
F F d
B B d
η η φ φ
η η φ φ
∆ = ∆ ∆ ∆
∆ = ∆ ∆ ∆
∫∫
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Correlations & Fluctuations Workshop in Florence, Italy 187/7/2006
Phenomenological model - Clustering
A phenomenological model of particle production in high energy collisions:Non-perturbative gluons split into qqbar pairs;Neighboring qqbar combine into color singlet cluster;Clusters decay into final-state hadrons;
Assumption of independent cluster emission
QCD and Collider Physics, p190, Ellis, Stirling and Webber, 1996
Hadronization via clusters
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Correlations & Fluctuations Workshop in Florence, Italy 197/7/2006
where is characterized by a Gaussian distribution:
Cluster model and Two-particle rapidity C.F.
1 2
(2),η ηΓ
If there are c clusters in an event and ki particles in a cluster, the two particle density:
Pairs from one cluster
Pairs from different clusters
1 2
( ) (2) ( ) ( )1 2 , 1 2
1 1 1
1( , ) ( ){ ( 1) ( ) ( )}( 1)
n c cII I I
n i i i j n nc i i j
P c k k k kn n η ηρ η η ρ η ρ η
= = ≠ =
= − Γ +− ∑ ∑ ∑
21 2
2
( )exp( )4
η ηδ−
−
Particle 1
Particle 2
Particle 1
Particle 2
(Nucl.Phys.B, 78:541, 1974)
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Correlations & Fluctuations Workshop in Florence, Italy 207/7/2006
where is characterized by a Gaussian distribution:
Cluster model and Two-particle rapidity C.F.
1 2
(2),η ηΓ
If there are c clusters in an event and ki particles in a cluster, the two particle density:
Pairs from one cluster
Pairs from different clusters
1 2
( ) (2) ( ) ( )1 2 , 1 2
1 1 1
1( , ) ( ){ ( 1) ( ) ( )}( 1)
n c cII I I
n i i i j n nc i i j
P c k k k kn n η ηρ η η ρ η ρ η
= = ≠ =
= − Γ +− ∑ ∑ ∑
21 2
2
( )exp( )4
η ηδ−
−
1 2
(2)( ), 1 21 2
1 2 ( ) ( ) ( ) ( )1 2 1 2
( , )( , )( , ) ( 1)( 1) [ 1]( ) ( ) ( ) ( )
IIII n
I I I In n n n
R n η η η ηρ η ηη η αρ η ρ η ρ η ρ η
Γ=< − − >= −
( 1)K KK
α < − >=
< >
Two-particle rapidity correlation function:
where:
Particle 1
Particle 2
Particle 1
Particle 2
(Nucl.Phys.B, 78:541, 1974)
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Correlations & Fluctuations Workshop in Florence, Italy 217/7/2006
where is characterized by a Gaussian distribution:
Cluster model and Two-particle rapidity C.F.
1 2
(2),η ηΓ
If there are c clusters in an event and ki particles in a cluster, the two particle density:
Pairs from one cluster
Pairs from different clusters
1 2
( ) (2) ( ) ( )1 2 , 1 2
1 1 1
1( , ) ( ){ ( 1) ( ) ( )}( 1)
n c cII I I
n i i i j n nc i i j
P c k k k kn n η ηρ η η ρ η ρ η
= = ≠ =
= − Γ +− ∑ ∑ ∑
21 2
2
( )exp( )4
η ηδ−
−
1 2
(2)( ), 1 21 2
1 2 ( ) ( ) ( ) ( )1 2 1 2
( , )( , )( , ) ( 1)( 1) [ 1]( ) ( ) ( ) ( )
IIII n
I I I In n n n
R n η η η ηρ η ηη η αρ η ρ η ρ η ρ η
Γ=< − − >= −
( 1)K KK
α < − >=
< >
Two-particle rapidity correlation function:
where:
2
1 KeffK K
Kσα= + =< >+< >
An effective cluster size can be defined as:
Particle 1
Particle 2
Particle 1
Particle 2
(Nucl. Phys. B 86:201, 1975)
(Nucl.Phys.B, 78:541, 1974)
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Correlations & Fluctuations Workshop in Florence, Italy 227/7/2006
Cluster model and Two-particle rapidity C.F.( )( ) [ 1]( )
IIRB
ηη αη
Γ ∆∆ = −
∆A fit to the C.F. to extract cluster:
Keff=1.73, δ=0.61
Raw PYTHIA 200Gev
2
2
( )( ) exp( )4ηηδ∆
Γ ∆ ∝ −
∆η
RII (∆η)
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Correlations & Fluctuations Workshop in Florence, Italy 237/7/2006
Cluster model and Two-particle rapidity C.F.( )( ) [ 1]( )
IIRB
ηη αη
Γ ∆∆ = −
∆
UA5 ppbar 540Gev
A fit to the C.F. to extract cluster:
Keff=1.73, δ=0.61
2
2
( )( ) exp( )4ηηδ∆
Γ ∆ ∝ −
∆η
RII (∆η)
Raw PYTHIA 200Gev
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Correlations & Fluctuations Workshop in Florence, Italy 247/7/2006
∆η
Cluster model and Two-particle rapidity C.F.
Raw PYTHIA after cutting off the region: |∆φ|<5.625,|∆η|<0.3
Keff=1.73, δ=0.61
Rejected region is small that Keff and δ stay unchanged
Keff=1.73, δ=0.61
RII (∆η)
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Correlations & Fluctuations Workshop in Florence, Italy 257/7/2006
∆η
Cluster model and Two-particle rapidity C.F.
Raw PYTHIA after cutting off the region: |∆φ|<5.625,|∆η|<0.3
Correction is mainly located in the most central bin;Detector effects are eliminated reasonable well.
Keff=1.73, δ=0.61
Rejected region is small that Keff and δ stay unchanged
Keff=1.73, δ=0.61
Keff=1.71, δ=0.59
∆η
RII (∆η)
RII (∆η)
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Correlations & Fluctuations Workshop in Florence, Italy 267/7/2006
Clusters in pp collisionsKeff vs s
Nucl. Phys. B 86:201, 1975Nucl. Phys. B 155:269, 1979Z. Phys. - Particle and Fields C 37:191, 1988
Resonance gas
Resonance gas is not enough to explain the observed cluster multiplicity
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Correlations & Fluctuations Workshop in Florence, Italy 277/7/2006
Clusters in pp collisionsKeff vs s
Resonance gas
Resonance gas is not enough to explain the observed cluster multiplicity
PHOBOS 200Gev and 410Gevwith high stat. from RHIC
Nucl. Phys. B 86:201, 1975Nucl. Phys. B 155:269, 1979Z. Phys. - Particle and Fields C 37:191, 1988
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Correlations & Fluctuations Workshop in Florence, Italy 287/7/2006
Clusters in pp collisionsCluster decay width δ vs s
Almost remains constant with energy
Nucl. Phys. B 86:201, 1975Nucl. Phys. B 155:269, 1979Z. Phys. - Particle and Fields C 37:191, 1988
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Correlations & Fluctuations Workshop in Florence, Italy 297/7/2006
Clusters in pp collisionsCluster decay width δ vs s
Almost remains constant with energy
PHOBOS 200Gev and 410Gevwith high stat. from RHIC
Nucl. Phys. B 86:201, 1975Nucl. Phys. B 155:269, 1979Z. Phys. - Particle and Fields C 37:191, 1988
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Correlations & Fluctuations Workshop in Florence, Italy 307/7/2006
Summary
Overall correlation structure from two- particle angular correlation at a broad range in phase space. Two- particle rapidity correlation function is interpreted in the context of cluster model. The information of cluster multiplicity and decay width can be extracted;Review of the previous cluster measurements in pp collisions and perspectives of PHOBOS;
Results for pp at PHOBOS will be ready soon!
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Correlations & Fluctuations Workshop in Florence, Italy 317/7/2006
Outlook:
Two-particle angular correlation in Heavy Ion
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Correlations & Fluctuations Workshop in Florence, Italy 327/7/2006
Two-particle correlations in AAMod. HIJING CuCu 200Gev with triangular-shaped v2
RII (∆η,∆φ
)
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Correlations & Fluctuations Workshop in Florence, Italy 337/7/2006
Two-particle correlations in AA
Comprehensive study of two-particle correlation structure in pp, dA and AAwill help disentangle different effects in complex heavy ion collision system!
Projecting into ∆ηfrom 0<|∆φ|<180
Projecting into ∆φfrom 0<|∆η|<6
Flow effects <v22>
Clusters in AA
RII (∆φ
)R
II (∆η)
RII (∆η,∆φ
)
Mod. HIJING CuCu 200Gev with triangular-shaped v2
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Correlations & Fluctuations Workshop in Florence, Italy 347/7/2006
Backups
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Correlations & Fluctuations Workshop in Florence, Italy 357/7/2006
Various definition of correlation function
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Correlations & Fluctuations Workshop in Florence, Italy 367/7/2006
The range of secondary effects
Rejected region: |∆φ|<5.625,|∆η|<0.3
Pick out one slice of 2D C.F. at ∆φ=0 and ∆η=0 respectively and compare Raw PYTHIA and PYTHIA+GEANT
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Correlations & Fluctuations Workshop in Florence, Italy 377/7/2006
Secondary effects to the high peak
At the region of |∆φ|<5.625,|∆η|<0.3:
primary-primary pairs:438 primary-secondary pairs:2828 secondary-secondary pairs: 2030 PID distribution:
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Correlations & Fluctuations Workshop in Florence, Italy 387/7/2006
V1 contribution to two-particle C.F.
HIJING CuCu 200Gev with flat v1 and v2 V1 enhances near-side and decreases away-side for small ∆η,vice versa for large ∆η.