Angular correlations at PHOBOS v7Correlations & Fluctuations Workshop in 7/7/2006 Florence, Italy 3 Overview ¾Motivation: Clusters from F&B multiplicity correlations at PHOBOS; ¾Two-particle

7/7/2006Correlations & Fluctuations Workshop in

Florence, Italy 1

Angular correlations at PHOBOS

Wei LiMassachusetts Institute of Technology

for the collaboration

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


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.


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


∆η

Two-particle angular correlations

PYTHIA 200Gev at -3<η<3 without weak decay

∆φ

RII (∆η,∆φ

)


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:


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.


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∆ ∆


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


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


∆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

)


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

)


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

)


Correcting the secondary effects

— =

HIJING+GEANT Correction functionRAW HIJING

Then, we build correction function from HIJING



— =

HIJING+GEANT

PYTHIA+GEANT

Correction functionRAW HIJING




— =

≈

HIJING+GEANT

Raw PYTHIA Corrected PYTHIAPYTHIA+GEANT

Correction functionRAW HIJING

Correction almost recovers the original correlations!


More quantitative comparison will be discussed later

subtracted


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

∆ = ∆ ∆ ∆

∆ = ∆ ∆ ∆

∫∫


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


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)




1 2

(2),η ηΓ




1 2

( ) (2) ( ) ( )1 2 , 1 2

1 1 1

1( , ) ( ){ ( 1) ( ) ( )}( 1)

n c cII I I



= = ≠ =

= − 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)




1 2

(2),η ηΓ




1 2

( ) (2) ( ) ( )1 2 , 1 2

1 1 1

1( , ) ( ){ ( 1) ( ) ( )}( 1)

n c cII I I



= = ≠ =

= − 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)


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)


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


∆η


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)


∆η


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)


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


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



Clusters in pp collisionsCluster decay width δ vs s

Almost remains constant with energy



Clusters in pp collisionsCluster decay width δ vs s

Almost remains constant with energy

PHOBOS 200Gev and 410Gevwith high stat. from RHIC



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!


Outlook:

Two-particle angular correlation in Heavy Ion


Two-particle correlations in AAMod. HIJING CuCu 200Gev with triangular-shaped v2

RII (∆η,∆φ

)


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


Backups


Various definition of correlation function


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


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:


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.

Documents

Angular correlations at PHOBOS v7Correlations & Fluctuations Workshop in 7/7/2006 Florence, Italy 3 Overview ¾Motivation: Clusters from F&B multiplicity correlations at PHOBOS; ¾Two-particle