elliptic flow fluctuations · 2011. 10. 20. · elliptic flow fluctuations and non-flow...

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Elliptic Flow Fluctuationsand

Non-Flow Correlations

Burak Alver for the collaboration

Massachusetts Institute of Technology

(alver@mit.edu) ‏

The 20th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter 2008)

February 4-10, 2008, Jaipur, India

1Burak Alver (MIT)

PHOBOS Collaboration

Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts,Richard Bindel, Wit Busza (Spokesperson), Vasundhara Chetluru, Edmundo García,Tomasz Gburek, Joshua Hamblen, Conor Henderson, David Hofman, Richard Hollis,Roman Hołyński, Burt Holzman, Aneta Iordanova, Chia Ming Kuo, Wei Li, Willis Lin,

Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen,Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Christof Roland,

Gunther Roland, Joe Sagerer, Peter Steinberg, George Stephans, Andrei Sukhanov,Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier,

Gábor Veres, Peter Walters, Edward Wenger, Frank Wolfs, Barbara Wosiek,Krzysztof Woźniak, Bolek Wysłouch

ARGONNE NATIONAL LABORATORY BROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER

46 scientists, 8 institutions, 9 PhD students

2Burak Alver (MIT)

Quark Matter 2005 |η| < 1

Statisticalerrors

High v2 observed in Cu+Cu Especially most central events

Au+Au, 200 PRL 94 122303 (2005) ‏Cu+Cu, 200 PRL 98 242302 (2007)

Cu+Cu

PHOBOSAu+Au

3Burak Alver (MIT)

Quark Matter 2005

Participants

x'y'Participant Eccentricity

b x

y

Au+AuCu+Cu

PHOBOS Glauber MC

Au+Au, 200 PRL 94 122303 (2005) ‏Cu+Cu, 200 PRL 98 242302 (2007)

|η| < 1

Statisticalerrors

High v2 observed in Cu+Cu Especially most central events

Fluctuations in initial collisionregion can lead to largeeccentricity

Cu+Cu

PHOBOSAu+Au

4Burak Alver (MIT)

Quark Matter 2005

Participants

x'y'Participant Eccentricity

b x

y

Au+AuCu+Cu

PHOBOS Glauber MC

Cu+CuAu+Au

|η| < 1

Statisticalerrors

|η| < 1 Statisticalerrors

Cu+CuAu+Au

Au+Au, 200 PRL 94 122303 (2005) ‏Cu+Cu, 200 PRL 98 242302 (2007)

PHOBOS

PHOBOS

5Burak Alver (MIT)

Quark Matter 2006Kernel – Response Functionv2

obs distribution in “data”

Extracted true 〈v2〉 and σ(v2)

!

g(v2obs) = K(v2

obs,v2)f(v2)dv2"

Event-by-event measurement Determination of response in MC Extraction of true 〈v2〉 and σ(v2)

arXiv:nucl-ex/0702036〈v2〉

2σ(v2)

6Burak Alver (MIT)

Quark Matter 2006 Relative v2 fluctuations of approximately 40%

Correlated particle production (non-flowcorrelations) can broaden the v2

obs distributionand affect the fluctuation measurement.

Au+Au200GeV

7Burak Alver (MIT)

Quark Matter 2006 Estimate non-flow contribution with HIJING

We used response function calculated fromHIJING with correlations preserved to estimatenon-flow effect.

Au+Au200GeV

Measuredfluctuations

HIJINGNon-flow

Correction(very small)

8Burak Alver (MIT)

Quark Matter 2008 We have made a data-based measurement of

non-flow Separating flow and non-flow

• Flow magnitude is a function of η• Flow correlates particles at all Δη ranges• Non-flow is dominated by short range correlations - small Δη

Idea: Use unique acceptance of PHOBOS to do asystematic study of Δϕ correlations at different Δηranges.

Finally: flow fluctuations corrected for non-flowcorrelations

9Burak Alver (MIT)

Correlation function Rn

Calculate Δϕ=ϕ1-ϕ2 correlations between two particles attwo η windows, η1 and η2. Foreground: hit pairs in the same event Background: hit pairs in mixed events

!

Rn"#( ) =

F("#)

B("#)$1

!

F("#) =1

npairssame

dnpairssame

d"#

!

B("#) =1

npairsmixed

dnpairsmixed

d"#

Au-Au 200GeV0-6% central

PHOBOSMC

η1 η2

PRL 91, 052303 (2003)

10Burak Alver (MIT)

Correlation function Rn

Calculate Δϕ=ϕ1-ϕ2 correlations between two particles attwo η windows, η1 and η2. Foreground: hit pairs in the same event Background: hit pairs in mixed events

!

Rn"#( ) =

F("#)

B("#)$1

!

F("#) =1

npairssame

dnpairssame

d"#

!

B("#) =1

npairsmixed

dnpairsmixed

d"#

!

R "#( ) = n $1( )F("#)

B("#)$1

%

& '

(

) *

PRC 75 054913 (2007)

Technical note: Correction for secondaries are doneusing R(Δϕ) which is not diluted by multiplicity.

See Wei Li’s talk for details at session XIX

n=number of hits

11Burak Alver (MIT)

Au-Au 200GeV0-6% central

PHOBOS

MC events withflow+correlations

Short and long range correlationsMC

MCPRL 91, 052303 (2003)Large Δη

Small Δη

12Burak Alver (MIT)

Au-Au 200GeV0-6% central

PHOBOS

MC events with only flow

FlowMC

MCPRL 91, 052303 (2003)Large Δη

Small Δη

13Burak Alver (MIT)

Calculating v22(η1,η2)

Calculate 2nd Fouriercoefficient of Rn(Δϕ) :

!

Rn"#( ) = 2v

2

2cos(2"#)

!

v2

2 "1,"

2( ) = v2"1( ) # v2 "2( )

If there is no non-flow:

MC

MC Large Δη

Small Δη

14Burak Alver (MIT)

Calculating v22(η1,η2)

!

Rn"#( ) = 2v

2

2cos(2"#)

!

v2

2 "1,"

2( ) = v2"1( ) # v2 "2( ) + $("

1,"

2)

flow

In general:

non-flow

MC

MC Large Δη

Small Δη

15Burak Alver (MIT)

Calculating v22(η1,η2)

!

Rn"#( ) = 2v

2

2cos(2"#)

!

v2

2 "1,"

2( ) = v2"1( ) # v2 "2( ) + $("

1,"

2)

flow

In general:

non-flow

DATA

DATA Large Δη

Small Δη

16Burak Alver (MIT)

Separating flow and non-flow Assume non-flow is small for

Residual δ(η1,η2) in data estimated using HIJING Fit to find flow component of v2

2:

!

v2"1( ) # v2 "2( ) = v

2

2 "1,"

2( ) $%("1,"2) "1$"

2> 2

Au-Au 200GeV40-45% central

Au-Au 200GeV40-45% central

(flow⊕non-flow) flow

!

"1#"

2> 2

Fit here

17Burak Alver (MIT)

Separating flow and non-flow Subtract to find δ(η1,η2) at all ranges:

!

"(#1,#

2) = v

2

2 #1,#

2( ) $ v2 #1( ) % v2 #2( )

non-flow

Au-Au 200GeV40-45% central

Au-Au 200GeV40-45% central

flow⊕non-flow flow

Au-Au 200GeV40-45% central

Au-Au 200GeV40-45% central

18Burak Alver (MIT)

δ as a function of centrality Average δ(η1,η2) over all hit pairs

!

" =

"(#1,#2)dn

d#1

dn

d#2d#1d#2$

dn

d#1

dn

d#2d#1d#2$

• Non-flow in data islarger than in HIJING• These values are validfor PHOBOS geometry

Au+Au200GeV

19Burak Alver (MIT)

Non-flow effect on fluctuations Non-flow correlations are quantified by δ

Verified in MC studies

!

" = cos 2#$( ) arXiv:0708.0800

!

"# (v2)= # /2

Fluctuationsmeasured inevents with

constant flow

20Burak Alver (MIT)

Expected fluctuations from non-flow

Calculate expected fluctuations: Scale with 〈v2〉 to match fluctuation results

!

"# (v2) = # /2

Au+Au200GeV

21Burak Alver (MIT)

Subtracting non-flow How do non-flow and fluctuations add?

Empirical fit matches MC results better thanaddition in quadrature.

Cluster MC

!

"(v2)total ="(v2)flow +" (v2)non -flow # exp $" (v2)flow" (v2)non -flow

%

& '

(

) *

Addition in quad.Empirical fit

The difference isincluded in

systematic errorsPHOBOS

22Burak Alver (MIT)

Subtracting non-flow in data

σ(v2) non-flow

σ(v2) flow⊕non-flow

Au+Au 200GeV40-45% central

23Burak Alver (MIT)

Subtracting non-flow in data

σ(v2) non-flow

σ(v2) flow⊕non-flow

σ(v2) flow extracted

Au+Au 200GeV40-45% central

24Burak Alver (MIT)

Flow fluctuations

Au+Au200GeV

First results of flow fluctuations correctedfor non-flow correlations measured in data.

25Burak Alver (MIT)

Model comparison

Au+Au200GeV

Results are in agreement with both Glauber andCGC calculations within errors

CGC: arXiv:0707.0249

26Burak Alver (MIT)

Conclusions We have performed a systematic

measurement of Δϕ correlations atdifferent Δη ranges allowing the separationof flow and non-flow correlations.

We have presented the first measurementof flow fluctuations corrected for non-flow.

Our results agree both with the participanteccentricity and with CGC calculations ofinitial geometry fluctuations within errors.