Event-by-event Multiplicity Fluctuations Analysis at PHOBOS

1
Event-by-event Multiplicity Fluctuations Analysis
at PHOBOS

• Zhengwei Chai
• Brookhaven National Laboratory
• for the Collaboration
• Correlations Fluctuations Workshop
• 2005 RHIC AGS Users Meeting
• (June 20-24, 2005, BNL)

2
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,
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 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
3
Outline

1. Physics motivation
2. Fluctuations variables C, ?(C) and ?2dyn
3. Analysis procedure for extracting C, ?(C) and
   ?2dyn
4. Preliminary results
5. Summary and outlook

4
Fluctuations in Particle Production

• Particle production in Au-Au collisions is
  dominated by overlapping geometry of the
  colliding ions, thus the particle multiplicity
  mainly depends on the number of participants
  Npart.
• Event-by-event multiplicity fluctuations could be
  a useful signature of the QGP-Hadron Gas phase
  transition due to the large difference of the
  degree of freedom between the two phases.
• Dynamic fluctuations other than statistical and
  Npart fluctuations may provide helpful insights
  on the intrinsic mechanisms of the particle
  production.
• Dynamic fluctuations are also related to particle
  correlations, which could be resulted from jets,
  resonances and clusters effect.

5
Event-by-event Fluctuations Observable s(C)

• Study multiplicity fluctuation using

• s(C) RMS of C distribution

• N1-N2 in definition of C ?
• Npart fluctuations suppressed in s(C)

• s2(C) s2stat s2dyn , ?2stat 1
• statistical and dynamic fluctuations
• ?(C) 1 for independent particles

• s(C) ? 1 ?non-0 dynamic fluctuations

6
Correlation Variable ?(C)

• Fluctuations variable ?(C) is a measure of the
  particles correlations
• Long range (particles in different ? bins)
  correlations reduce ?(C) from 1.
• Short range (particles usually in the same ? bin)
  correlations increase ?(C) from 1.
• Short range correlations could also have the long
  range effect if the correlated particles are
  selected into different bins.

1
2
3
7
Long Range Correlations

• Long range correlations effect in ?(C)
• Assuming ltN1gtltN2gtN, N1N22N and the
  correlation coefficient is ?
• Positive long range correlations ? ?2dynlt0 and
  ?(C)lt1

8
Short Range Correlations

• Short range correlations effect in ?(C)
• Such correlation may be treated as cluster
  effect, the cluster multiplicity k studied by UA5
  is related to ?(C)
• If particles are created in cluster with
  multiplicity k, and the total multiplicity in a
  specific ? bin is increased from N to kN
• ?2(C) ?2stat?2dyn k is a measure of cluster
  multiplicity if all the associated particles in
  cluster are included in this ? bin. ?2(C) may be
  regarded as effective cluster multiplicity if
  some of the associated particles in cluster are
  included in different bins.
• Short range correlations ? ?2dyngt0 and ?(C)gt1

9
C Distribution from HIJING Primaries
?2(C) (?2stat ?2dyn )
1.5lt?lt2.0
?(C) 1.08
C
10
C Distribution from Rec. HIJINGGEANT Hits
?2(C) (?2stat ?2dyn ) ?2det
1.5lt?lt2.0
?(C) 1.33
C
11
Extraction of Dynamic Fluctuations

• Assuming
• ?2(C) (?2stat ?2dyn ) ?2det
• ?2stat 1 by definition
• ?2det evaluated from various simulations
• ?2(C) calculated from reconstructed hits
• ?2dyn is a measure of particle correlations

12
Octagon
13
Octagon Multiplicity Detector Acceptance Coverage
?
?
Hit distribution in ?-? space with Zvtxlt10cm
14
Extracting Multiplicity Fluctuations ?(C)

• Octagon silicon sensors provide
• Number of hits (Nhit)
• Sum of the angle-corrected deposit energy dE for
  charged particles (E)
• NhitNmax(1-exp(-E/Emax))
• Emax/Nmax average dE by a charged particle in
  selected h bin
• Estimated multiplicity
• N E /(Emax/Nmax)

Number of hits (Nhit)
Deposit Energy (E)

• Multiplicities N1, N2 in forward and backward
  h bins of equal size
• N1, N2 ?
  ? s(C)

15
Preliminary Fluctuations Analysis Result(K.W. et
el, QM04)

• Data s(C) similar to
• Rec.HijingGeant s(C)
• Data and Rec. MC s(C)
• dominated by detector
• responses
• Estimated systematic
• error 5 (not shown)

Phobos Prelim. Data Rec. HijingGeant Hijing
(half f)
s(C)
16
Preliminary Fluctuations Analysis Result(K.W. et
el, QM04)
s(C)

• Data and Rec. MC s(C)
• are similar
• Hijing s(C) increases
• with the separation in
• pseudo-rapidity space
• Estimated systematic
• error 5(not shown)

h
17
Preliminary Fluctuations Analysis Result(K.W. et
el, QM04)
s(C)

• Data and Rec. MC s(C)
• increase with the h bin
• size
• Hijing s(C) increases
• with the h bin size
• Estimated systematic
• error 5(not shown)

Dh
18
Fluctuations Sources in Rec. MC Multiplicity

• Acceptance Effects
• Secondaries
• dE/dx Fluctuations
• Landau fluctuation
• Velocity (b) variation
• Statistical fluctuations
• Model non-statistical
• fluctuations

19
Extraction of Dynamic Fluctuations

• Acceptance gap effects suppression with C offset
• ?-dependent dE/dx cuts to suppress contribution
  
• from secondary particles
• 1st order detector effects adjustment for
  dynamic
• fluctuations extraction

20
Acceptance Gap Effects in ?(C)

• Acceptance gap ?
• asymmetric multiplicities
• At vertex A
• N1A gt N2A ? ltCgt gt 0
• At vertex B
• N1B lt N2B ? ltCgt lt 0
• Asymmetric forward and
• backward multiplicities
• ? varying mean of C in
• small Zvtx bin
• ? significant ?(C) increase
• in bigger Zvtx bin

N1A
N2A
N1B
N2B
-Z
Z
A
B
21
Acceptance Gap Effects Suppression

• Event-by-event C offset
• -?C is the mean of C distribution in a specific
• (Zvtx, ?, Centrality) bin.
• ?C suppresses the acceptance gap effects by
  reducing the ltCgt variation while keeping other
  fluctuations unchanged.

22
?lt0.5
?lt0.5
C
C
w/o offset correction
w/ offset correction
Zvtx
Zvtx
ltCgt
?(C)
Zvtx
Zvtx
23
dE/dx Distributions of MC HitsBlack
Primaries Secondaries, Red Secondaries,
Blue Primaries
-3.0lt?lt-2.5
-0.5lt?lt0.0
24
Detector Effects from ModelGeant Simulations
?2det ?2(C) - (?2stat ?2dyn )
25
?2det 1st order dependence on ?2dyn
Mod. HIJING (randomized ? sign)
Std. AMPT
0-20 Central
Std. HIJING
1.5lt?lt2.0 half ? acc.
26
Extracting Dynamic Fluctuations Using Detector
Effects from Simulations

• General equation
• ?2(C) ?2stat ?2dyn ?2det
• Use MC to evaluate detector effects
• ?2det ?2(C) - (?2stat ?2dyn)
• ?2det ?2det0(1 - ??2dyn)
• Use the adjusted detector effects to extract
  dynamic fluctuations
• ?2(C) ?2stat ?2dyn ?2det0(1 - ? ?2dyn)
• Multiply the extracted dynamic fluctuations by 2
  to extrapolate it from half to full ? acceptance

27
Extracted and True Model Dynamic Fluctuations
28
Extracted and True Model Dynamic Fluctuations
29

• Procedure for extraction of dynamic fluctuations
• tested with 3 simulations.
• 200GeV AuAu data dynamic fluctuations coming
• out soon

30
Summary and Outlook

• Analyzed multiplicity fluctuations of the
  charged particle production
• in AuAu collisions at 200GeV over a
  wide pseudo-rapidity
• range (-3.0 lt h lt 3.0)
• The preliminary fluctuations in the Data are
  similar to that in
• reconstructed AuAu MC (HIJINGGEANT)
• The physics fluctuations grow with increasing
  bin separation (h)
• and width (Dh) and may be explained by
  intrinsic correlations in
• particle production.
• Established a reliable procedure for extracting
  the dynamic
• fluctuations from PHOBOS multiplicity
  measurement.
• Results of dynamic fluctuations compared with
  models to be released.