# Presentation: 201465

## 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)****      **

##                    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 Hołyński, 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 Woźniak, Shaun Wyngaardt, 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

- Zhengwei Chai

- 06-21-2005

## Outline

- Physics motivation
- Fluctuations variables *C*, ***(C)* and ***2**dyn*
- Analysis procedure for extracting *C*, ***(C)* and ***2**dyn*
- Preliminary results
- Summary and outlook

- Zhengwei Chai

- 06-21-2005

## Fluctuations in Particle Production

- 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 *N**part* 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.

**Fluctuations in Particle Production**

- Zhengwei Chai

- 06-21-2005

## Event-by-event Fluctuations Observable (C)

-  Study multiplicity fluctuation using

-  ***(C) = RMS* of *C* distribution

-  *****(C) = **σ****stat* + *σ**2**dyn** **,  * ***2**stat* = *1*
-    statistical and dynamic fluctuations
* ****(C) = 1 *for independent particles

-  *N**1**-N**2* in definition of *C* 
*   **N**part* fluctuations suppressed in ***(C)*

***(C) * *1* non-0 dynamic fluctuations

- Zhengwei Chai

- 06-21-2005

## 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**

- Zhengwei Chai

- 06-21-2005

## Long Range Correlations

- Long range correlations effect in ***(C)*
- Assuming  <*N**1*>=<*N**2*>=*N*, *N**1*+*N**2*=*2N *and the correlation coefficient is* ***
- Positive long range correlations  ***2**dyn**<0* and ***(C)<1*

- Zhengwei Chai

- 06-21-2005

## 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)= ****2**stat**+****2**dyn** = 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  ***2**dyn**>0 *and (C)>1

- Zhengwei Chai

- 06-21-2005

## C Distribution from HIJING Primaries

***C***** Distribution from HIJING Primaries**

**C**

- 1.5<||<2.0

*********(C) = 1.08***

***2**(C) = (****2**stat** + ****2**dyn** )*

- Zhengwei Chai

- 06-21-2005

## C Distribution from Rec. HIJING+GEANT Hits

***C***** Distribution from Rec. HIJING+GEANT Hits**

- 1.5<||<2.0

**C**

*********(C) = 1.33***

***2**(C) = (****2**stat** + ****2**dyn** )+ ****2**det*

- Zhengwei Chai

- 06-21-2005

## Extraction of Dynamic Fluctuations

- Assuming
- 		***2**(C) = (****2**stat** + ****2**dyn** )+ ****2**det*
***2**stat** = 1* by definition
***2**det*   evaluated from various simulations
***2**(C)* calculated from reconstructed hits
***2**dyn* is a measure of particle correlations

- Zhengwei Chai

- 06-21-2005

## Octagon

**Octagon**

## Octagon Multiplicity Detector Acceptance Coverage

**Octagon Multiplicity Detector Acceptance Coverage**

****

****

**Hit distribution in ********-******** space with |Z****vtx****|<10cm**

- Zhengwei Chai

- 06-21-2005

## Extracting Multiplicity Fluctuations (C)

- Octagon silicon sensors  provide
- Number of hits (*N**hit*)
- Sum of the angle-corrected deposit energy *dE *for charged particles (*E*)
*N**hit**=N**max**(1-exp(-E/E**max**))*
*E**max**/N**max*: average *dE* by a charged particle in selected ** bin
- Estimated multiplicity
-                 *N = E /(E**max**/N**max**)*

-    Multiplicities *N**1*, *N**2* in forward and backward ** bins of equal size
-      		*N**1*, *N**2*                                      ***(C)*

***Deposit Energy (E)***

***Number of hits (N******hit*****)**

- Zhengwei Chai

- 06-21-2005

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

-  Data ***(C)* similar to
-   Rec.Hijing+Geant ***(C)*
-  Data and Rec. MC ***(C)*
-   dominated by detector
-   responses
-  Estimated systematic
-   error 5% (not shown)

- Phobos Prelim. Data
- Rec. Hijing+Geant
- Hijing (half )

******(C)**

- Zhengwei Chai

- 06-21-2005

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

-   are similar
-  Hijing ***(C) *increases
-   with the separation in
-   pseudo-rapidity space
-  Estimated systematic
-   error 5%(not shown)

******(C)**

- 

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

- Zhengwei Chai

- 06-21-2005

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

-   increase with the ** bin
-   size
-  Hijing ***(C) *increases
-   with the ** bin size
-  Estimated systematic
-   error 5%(not shown)

******(C)**

- 

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

- Zhengwei Chai

- 06-21-2005

## Fluctuations Sources in Rec. MC Multiplicity

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

- Zhengwei Chai

- 06-21-2005

## Extraction of Dynamic Fluctuations

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

- Zhengwei Chai

- 06-21-2005

## Acceptance Gap Effects in (C)

**A**

- B

**-Z**

**+Z**

***N******1A***

***N******2A***

***N******1B***

***N******2B***

-  Acceptance gap 
-    asymmetric multiplicities
-  At vertex A:
-       *N**1A* > *N**2A*  *<C>* > *0*
-    At vertex B:
-       *N**1B* < *N**2B ** <C> **<** 0*
-  Asymmetric forward and
-    backward multiplicities
-     varying mean of *C *in
-         small *Z**vtx* bin
-     significant (C) increase
-         in bigger *Z**vtx* bin

- Zhengwei Chai

- 06-21-2005

## Acceptance Gap Effects Suppression

- Event-by-event *C* offset
*-****C* is the mean of *C* distribution in a specific
-     (*Z**vtx**, ****, Centrality*) bin.
***C* suppresses the acceptance gap effects by reducing the *<C>* variation while keeping other fluctuations unchanged.

- Zhengwei Chai

- 06-21-2005

## ||<0.5

**|********|<0.5**

**|********|<0.5**

- w/o offset correction

- w/ offset correction

***C***

***C***

***Z******vtx***

***Z******vtx***

***Z******vtx***

***Z******vtx***

***<C>***

*********(C)***

- Zhengwei Chai

- 06-21-2005

##  dE/dx Distributions of MC HitsBlack: Primaries + Secondaries,  Red: Secondaries,  Blue:  Primaries

-  **dE/dx Distributions of MC Hits**Black: Primaries + Secondaries,  Red: Secondaries,  Blue:  Primaries

**-3.0<********<-2.5**

**-0.5<********<0.0**

- Zhengwei Chai

- 06-21-2005

## Detector Effects from Model+Geant Simulations

***2**det** = ****2**(C) - (****2**stat** + ****2**dyn** )*

- Zhengwei Chai

- 06-21-2005

## 2det 1st order dependence on 2dyn

*********2******det***** 1****st**** order dependence on ***********2******dyn***

**1.5<|********|<2.0 & half ******** acc.**

**Mod. HIJING (randomized ******** sign)**

**Std. AMPT**

**Std. HIJING**

**0-20% Central**

- Zhengwei Chai

- 06-21-2005

## Extracting Dynamic Fluctuations Using Detector Effects from Simulations

- General equation:
*	**	****2**(C) = ****2**stat **+ ****2**dyn **+ ****2**det*
- Use MC to evaluate detector effects:
*	**	****2**det *= ***2**(C) - (****2**stat **+ ****2**dyn**)  *
*	**	****2**det **= ****2**det0**(1 - ******2**dyn**)*
- Use the adjusted detector effects to extract dynamic fluctuations: *	**	*
*	**	****2**(C) = ****2**stat **+ ****2**dyn **+ ****2**det0**(1 - **** ****2**dyn**)*
- Multiply the extracted dynamic fluctuations by 2 to extrapolate it from half to full  acceptance

- Zhengwei Chai

- 06-21-2005

## Extracted and True Model Dynamic Fluctuations

- Zhengwei Chai

- 06-21-2005

## Extracted and True Model Dynamic Fluctuations

- Zhengwei Chai

- 06-21-2005

##  Procedure for extraction of dynamic fluctuations

-  Procedure for extraction of dynamic fluctuations
-    tested with 3 simulations.
-  200GeV Au+Au data dynamic fluctuations coming
-    out soon...

- Zhengwei Chai

- 06-21-2005

## Summary and Outlook

-  Analyzed multiplicity fluctuations of the charged  particle production
-    in Au+Au collisions at        =200GeV over a wide pseudo-rapidity
-    range (-3.0 < **< +*3.0*)
-  The preliminary fluctuations in the Data are similar to that in
-    reconstructed Au+Au MC (HIJING+GEANT)
-  The physics fluctuations grow with increasing bin separation (**)
-    and width (**) 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.

- Zhengwei Chai

- 06-21-2005