Elliptic Flow Fluctuations at PHOBOS

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Elliptic Flow Fluctuations at PHOBOS

Elliptic Flow Fluctuations

with the PHOBOS detector

Burak Alver

Massachusetts Institute of Technology

v 2

fluctuations at PHOBOS

Burak Alver - MIT


PHOBOS Collaboration

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 Holynski, 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 Wozniak, Shaun Wyngaardt, Bolek Wyslouch

ARGONNE NATIONAL LABORATORY

INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW

NATIONAL CENTRAL UNIVERSITY, TAIWAN

UNIVERSITY OF MARYLAND

BROOKHAVEN NATIONAL LABORATORY

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

UNIVERSITY OF ILLINOIS AT CHICAGO

UNIVERSITY OF ROCHESTER

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Motivation

High v 2

observed in

CuCu can be explained

by fluctuations in

initial collision region.

Can we test the Participant Eccentricity Model?

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Expected fluctuations

Assuming v 2 ∝ε part , participant

eccentricity model predicts

v 2 fluctuations

Expected σ v2 from fluctuations in ε part

Data

Au+Au

MC

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Measuring v 2 Fluctuations

• We have considered 3 different methods

– 2 particle correlations →

• c.f. S. Voloshin nucl-th/0606022

• σ v22 = - 2

• Do systematic errors cancel?

– 2 particle correlations → v 2

2

event by event

• Mixed event background generation is possible

• Reduces fit parameters to 1 (no reaction plane)

• Hard to untangle acceptance effects event by event

– v 2 event by event

• This is the method we are pursuing

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Measuring v 2 Fluctuations - Today’s Talk

• Measuring v 2 event by event

• Ongoing analysis on 200GeV Au-Au

• Today

– How we are planning to make the measurement

– Studies on fully simulated MC events

• Modified Hijing - Flow

• Geant

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Method Overview - Simplified Example

2 possible v 2 values

Event by Event measurement

Demonstration Demonstration

K b (u)

K a (u)

V 2b

V 2a

V 2b

V 2a

f 1

Relative abundance in sample

Demonstration

Observed u distribution in a sample

Demonstration

g(u)

u=v 2obs.

or u = v 2

2

obs.

or u = q obs.

Question: What is the relative abundance of 2 v 2 ’s in the sample?

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Method Overview - Simplified Example

2 possible v 2 values

Event by Event measurement

Demonstration Demonstration

K b (u)

K a (u)

V 2b

V 2a

V 2b

V 2a

f 1

Relative abundance in sample

Demonstration

Measured u distribution in a sample

Demonstration

g(u)

u=v 2obs.

or u = v 2

2

obs.

or u = q obs.

Question: What is the relative abundance of v 2a to v 2b in the sample?

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Method Overview - Simplified Example

2 possible v 2 values

Event by Event measurement

u=v 2obs.

V 2b

K b (u)

V 2a

K a (u)

V 2b

V 2a

V 2b

V 2a

Extracted v 2true distribution from sample Measured u distribution in a sample

f a

Demonstration

Demonstration

g(u)

f b

Demonstration Demonstration

Question: What is the relative abundance of v 2a to v 2b in the sample?

g(u)=f a K a (u) + f b K b (u)

or u = v 2

2

obs.

or u = q obs.

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Method Overview

Kernel

In real life v 2 can take

a continuum of values

K(u,v 2 )

200 GeV AuAu

Modified Hijing+Geant

u=v 2obs.

Extracted v 2true distribution from sample

Measured u distribution in a sample

200 GeV AuAu

Modified Hijing+Geant

f(v 2 )

g(u)

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Method Overview

• 3 Tasks

– Measure u event-by-event g(u)

– Calculate the kernel K(u,v 2 )

– Extract dynamical fluctuations f(v 2 )

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PHOBOS Detector

PHOBOS Multiplicity Array

-5.4


Measuring u=v 2obs Event by Event I

• Probability Distribution Function (PDF) for hit positions:

PDF

Probability of hit in η

Probability of hit in φ

u

demonstration

• Define likelihood of u and φ 0 for an event:

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Measuring u=v 2obs Event by Event II

• Maximize likelihood to find “most likely” value of u

• Comparing values of u and φ 0

– In an event, p(η i ) is same for all u and φ 0 .

– PDF folded by acceptance must be normalized to the same

value for different u and φ 0 ’s

Acceptance

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Measuring u=v 2obs Event by Event II

• Maximize likelihood to find “most likely” value of u

• Comparing values of u and φ 0

– In an event, p(η i ) is same for all u and φ 0 .

– PDF folded by acceptance must be normalized to the same

value for different u and φ 0 ’s

Acceptance

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Measuring u=v 2obs Event by Event III

Observed u distribution in a sample

Mean and RMS of u in slices of v 2

200 GeV AuAu

Modified Hijing+Geant

g(u)

Error bars show RMS

200 GeV AuAu

Modified Hijing+Geant

Next Step: Construct the Kernel to unfold g(u)

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Calculating the Kernel I

• Simple: Measure u distribution in bins of v 2

• 2 small complications

– Kernel depends on multiplicity: K(u,v 2 ,n)

• n = number of hits on the detector

• Measure u distribution in bins of v 2 and n.

– Statistics in bins can be combined by fitting

smooth functions

200 GeV AuAu

Modified Hijing+Geant

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Calculating the Kernel II

• In a single bin of v 2 and n

u distribution with for fixed v 2 and n

200 GeV AuAu

Modified Hijing+Geant

(a, b) ↔ (,σ u

)

• Distribution is not Gaussian

• But can be parameterized by and σ u

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Calculating the Kernel III

• Measure and σ u in bins of v 2 and n

• Fit smooth functions

K(u,v 2 ,n)

200 GeV AuAu

Modified Hijing+Geant

K(u,v 2 ,n)

200 GeV AuAu

Modified Hijing+Geant

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Calculating the Kernel IV

• Multiplicity dependence can be integrated out

K(u,v 2 ,n)

200 GeV AuAu

Modified Hijing+Geant

K(u,v 2 )

200 GeV AuAu

Modified Hijing+Geant

N(n) = Number hits distribution in sample

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Extracting dynamical fluctuations

known ?

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Extracting dynamical fluctuations

Ansatz with two parameters:

known ?

Ansatz for f(v 2 )

ansatz

Ansatz

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Extracting dynamical fluctuations

Ansatz with two parameters:

known ?

Ansatz for f(v 2 )

ansatz

Ansatz

integrate

Expected g(u) for Ansatz

200 GeV AuAu

Modified Hijing+Geant

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Extracting dynamical fluctuations

Ansatz with two parameters:

known ?

Ansätze for f(v 2 )

ansatz

Expected g(u) for Ansätze

200 GeV AuAu

integrate

Modified Hijing+Geant

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Extracting dynamical fluctuations

Ansatz with two parameters:

known ?

Ansätze for f(v 2 )

ansatz

Comparison with sample

200 GeV AuAu

integrate

Modified Hijing+Geant

Compare expected g(u) for Ansatz with measurement

Minimum χ 2 → and σ v2

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Method Summary

K(u,v 2 ,n)

Many MC events

MC

MC

A Small Sample

f in (v 2 )

=0.05

σ v2 =0.02

measurement

N(n) K(u,v 2 )

MC

MC

Minimize χ 2 in integral

measurementintegration

MC

MC

=0.048

σ v2 = 0.023

g(u)

f out (v 2 )

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Verification

• Ran this analysis on Modified Hijing

– v 2 (η) = v 2 (0) • (1-|η|/6)

• Same as the assumption in our fit

– v 2 (0) given by a Gaussian distribution in each sample

• Same as our Ansatz

– Analysis done in 10 collision vertex bins

• Final results are averaged

– 0-40% central events used to construct Kernel

– 15-20% central events used as sample

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Verification

• Ran this analysis on Modified Hijing

– The input fluctuations are reconstructed

successfully

= 0.050

200 GeV AuAu

15-20% central

Modified Hijing+Geant

σ out

= 0.020

0.04

0.02

= 0.030

0.04

σ out

0.02

σ in

0.02 0.04

Only statistical errors shown

(from combining vertex bins)

= 0.040

0.04

σ out

σ in

0.02 0.04

0.02

0.02 0.04

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σ in


Conclusion / Outlook

• A new method to measure elliptic flow

fluctuations is developed.

Fluctuations in MC simulations are

successfully reconstructed.

• Ready to apply the method to extract

dynamical fluctuations in DATA.

– Important part will be to estimate systematic

uncertainties due to the MC/DATA differences

• dN/dη(η)

• v 2 (η)

• Non-flow in data

– Should show up in reaction plane resolutions

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Likelihood Fit Normalization

Acceptance

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Calculating the Kernel. Functions observed to fit the Kernel

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