Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow...
Transcript of Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow...
![Page 1: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/1.jpg)
0
Elliptic Flow Fluctuationsand
Non-Flow Correlations
Burak Alver for the collaboration
Massachusetts Institute of Technology
The 20th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter 2008)
February 4-10, 2008, Jaipur, India
![Page 2: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/2.jpg)
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
![Page 3: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/3.jpg)
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
![Page 4: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/4.jpg)
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
![Page 5: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/5.jpg)
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
![Page 6: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/6.jpg)
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)
![Page 7: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/7.jpg)
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
![Page 8: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/8.jpg)
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)
![Page 9: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/9.jpg)
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
![Page 10: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/10.jpg)
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)
![Page 11: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/11.jpg)
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
![Page 12: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/12.jpg)
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
![Page 13: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/13.jpg)
12Burak Alver (MIT)
Au-Au 200GeV0-6% central
PHOBOS
MC events with only flow
FlowMC
MCPRL 91, 052303 (2003)Large Δη
Small Δη
![Page 14: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/14.jpg)
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
![Page 15: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/15.jpg)
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
![Page 16: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/16.jpg)
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
![Page 17: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/17.jpg)
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
![Page 18: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/18.jpg)
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
![Page 19: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/19.jpg)
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
![Page 20: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/20.jpg)
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
![Page 21: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/21.jpg)
20Burak Alver (MIT)
Expected fluctuations from non-flow
Calculate expected fluctuations: Scale with 〈v2〉 to match fluctuation results
!
"# (v2) = # /2
Au+Au200GeV
![Page 22: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/22.jpg)
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
![Page 23: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/23.jpg)
22Burak Alver (MIT)
Subtracting non-flow in data
σ(v2) non-flow
σ(v2) flow⊕non-flow
Au+Au 200GeV40-45% central
![Page 24: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/24.jpg)
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
![Page 25: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/25.jpg)
24Burak Alver (MIT)
Flow fluctuations
Au+Au200GeV
First results of flow fluctuations correctedfor non-flow correlations measured in data.
![Page 26: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/26.jpg)
25Burak Alver (MIT)
Model comparison
Au+Au200GeV
Results are in agreement with both Glauber andCGC calculations within errors
CGC: arXiv:0707.0249
![Page 27: Elliptic Flow Fluctuations · 2011. 10. 20. · Elliptic Flow Fluctuations and Non-Flow Correlations Burak Alver for the collaboration Massachusetts Institute of Technology (alver@mit.edu)](https://reader035.fdocuments.in/reader035/viewer/2022071301/60a1a79f56fcd945876bac3b/html5/thumbnails/27.jpg)
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.