# Presentation: 534417

## PARTICLE DENSITY FLUCTUATIONS

- Bedanga Mohanty
- Variable Energy Cyclotron Centre, Calcutta
- (for the WA98 Collaboration)

- _OUTLINE_
- Motivation
- N  and Nch multiplicity fluctuation
- N  vs. Nch   fluctuation
- Summary

## RELATIVISTIC HEAVY-ION COLLISIONS

- QCD transitions _            _
- Deconfinement
- Chiral symmetry restoration

-  At Tricritical point
-     Large e-by-e fluctuations
-      in observables

-  PRL 81 (1998) 4816; Stephanov et al.

-  NPA 663 (2000)183; Peter Braun-Munzinger

## EVENT-BY-EVENT FLUCTUATIONS

-   Thermodynamic properties of matter :
-    Total heat capacity

-     Compressibility

- Study of  thermodynamical  quantities (or fluctuations
- in experimental observables) can shed light on possible
- existence of phase transition  and its nature

- At tricritical point – singularities in thermodynamical
- observables – large e-by-e fluctuations in Expt. Obs.

-  PLB 430 (1998) 9
-  S. Mrowczynski

-  PRL 75 (1995) 1044
-  L. Stodolsky

## CHIRAL SYMMETRY RESTORATION

- Through search for disoriented
- chiral condensates
- _   _
- Study and detection of DCC :
- Nature of chiral phase transition
- Vacuum structure of strong interaction

- Look at N vs. Nch fluctuations_         _

## FLUCTUATIONS IN HEAVY-ION COLLISIONS

_**FLUCTUATIONS IN HEAVY-ION COLLISIONS**_

- Large number of particles in single event
- Large acceptance detectors
- Near Gaussian distributions
-   **Fluctuation studied by width**

- PRC 65 (2002) 054912
- WA98 Collaboration

- PLB 459 (1999) 679
- NA49 Collaboration

- WA98

- WA98

- WA98

- NA49

- SPS -> RHIC -> LHC

## MEASURES OF FLUCTUATIONS

|     Measure |   Proposed by  |     Reference |
| --- | --- | --- |
| 2/mean & 
Ratios | Baym, Heiselberg 
Jeon, Koch | PLB 469 (1999) 7; Phys. Rep. 351 (2001) 161; PRL 83 (1999) 5435  |
| Correlator | Stephanov, Rajagopal,   Shuryak | PRD 60 (1999) 114028
 |
| Fluctuation in conserved Quantities | Jeon,Koch 
Asakawa,Heinz,Muller  | PRL 85 (2000) 2076
PRL 85 (2000) 2076 |
| Balance Functions | Bass, Danielewicz,Pratt | PRL 85 (2000) 2689 |
| pT | Gazdzicki, Mrowczynski | Z. Phys. C54 (1992) 127 |
| dyn | Pruneau, Gavin ,Voloshin | nucl-ex/0204011 |

- Space-time evolution of fluctuations are important!

## FLUCTUATION STUDY IN

**SPMD : 2.35 < ******** < 3.75**

_**FLUCTUATION STUDY IN**_

**PMD : 2.9 < ******** < 4.2**

## CERN SPS : 158A GeV Pb+Pb

_**CERN SPS : 158A GeV Pb+Pb**_

- Charged Particles

-  Photons

-  Ch. particles vs. Photons

- Single event display

## MULTIPLICITY FLUCTUATIONS

- N   :    Particle Multiplicity
- Npart :  No. of participants
- ni  :     No of particles produced by ith
-            participant, accepted within the
-            acceptance of detector

- N and Nch fluctuations are studied by looking at
- the simple variable

- Centrality and pseudo-rapidity acceptance dependence

- _Participant model:_

- Compare to participant model and VENUS

## CENTRALITY SELECTION

_**CENTRALITY SELECTION**_

- Fluctuations should be calculated for narrow bins in
- centrality ( 2% cs bins ) such that fluctuations in
- number of participants are Poisson-like

- Fluctuations in number of  participants increases
- with increasing  % cs but for 2% cs bins ~ 1

## CENTRALITY DEPENDENCE OF MULTIPLICITY FLUCTUATIONS

- Data agree fairly well with model calculations

## PSEUDO-RAPIDITY ACCEPTANCE DEPENDENCE OF MULTIPLICITY FLUCTUATIONS

_**PSEUDO-RAPIDITY ACCEPTANCE DEPENDENCE OF MULTIPLICITY FLUCTUATIONS**_

- Data agree fairly well with model
- calculations based on binomial sampling

-  Int. J. Mod. Phys. A 17 (2002) 675

## N vs. Nch FLUCTUATIONS       

- Results from data compared to mixed events and simulation

-  Top 5% central events  ONLY
-  Bins in 
-  Discrete Wavelet Analysis
-  Correlation Analysis:

_**N**__****__** **__***vs***__**. N**__**ch**__** FLUCTUATIONS**__       _

## MIXED EVENTS

- different contributions to fluctuations

_**MIXED EVENTS**_

| Type | PMD -  | SPMD - ch | Behavior |
| --- | --- | --- | --- |
| M1 | Mix hits | Mix hits | Does not preserve correlated or individual fluctuations. |
| M2 | Unaltered hits
Event mixing | Unaltered hits Event mixing | Does not preserve the correlated physics fluctuation. |
| M3- | Unaltered hits | Mix hits | Fluctuations due to photons are preserved. |
| M3-ch | Mix hits | Unaltered hits | Fluctuations due to charged particles preserved. |

## COMPARISON OF RMS WIDTH  OF DATA, M1-MIXED EVENTS AND SIMULATION

_**COMPARISON OF RMS WIDTH  OF DATA, M1-MIXED EVENTS AND SIMULATION**_

- Mix hits in PMD and SPMD separately
- Maintain global correlation

-  _**Presence of**_
_** **__**localized fluctuations.**_
_** **_
**Possibilities in:**
- N
- Nch
- Correlated fluctuation

- Data widths larger than M1-mixed

## CORRELATED FLUCTUATIONS ?

_**DATA  AND M2-MIXED EVENTS**_

- Mix one event of PMD with
- Another event of SPMD
- Hits unaltered in an event
- N– Nch correlation maintained

- Data matches with M2-mixed

_**Absence of**_
_**Correlated fluctuations.**_
_** **_

## DO BOTH  N  and Nch CONTRIBUTE ?

_** **__**DATA AND M3-MIXED EVENTS **_

- Mix hits in one detector only
- Hits unaltered in other detector
- This case is in between M1 and M2
- Maintain global correlation

- M3-mixed between Data & M1.

_**Presence of individual**_
_**Fluctuations in both :**_
**N******
**N****ch**

## CENTRALITY DEPENDENCE OF LOCALIZED CHARGE-NEUTRAL FLUCTUATIONS

- Total localized fluctuations
- in photon and charged
- particle decreases with
- decrease in centrality

- Ref : nucl-ex/0206017

- Not detectable

## UPPER LIMIT ON DCC 

_**PRODUCTION AT SPS**_

- Based on a simple model of
-  DCC

- Ref : nucl-ex/0206017

- Differences between data
- and M2 (event mixing)
- assumed solely due to DCC

## SUMMARY

- Systematic study of centrality dependence of multiplicity fluctuations of photons and charged particles for the full acceptance of the detectors do not show any evidence of  significant non-statistical contribution

- Ref : PRC 65 (2002) 054912

- A model independent analysis using mixed events indicates non-statistical localized fluctuations in data  for limited regions of azimuthal angle

- No e-by-e correlated fluctuations (DCC-type) observed in photons and charged particles

- Ref : PRC 64 (2001) 011901 (R)

- Ref : nucl-ex/0206017

- Upper limit on DCC production at SPS set at 90% C.L.