# Presentation: 914053

## Local Charged Particle Multiplicity Fluctuations in PHENIX

**Tarun Kanti Ghosh**
**for the PHENIX Collaboration**
**Vanderbilt University**

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Motivation

-    This is famous and unusual  JACEE event
- In circle area : one charged hadrons and many photons
- Does it DCC? Do we expect to see such events at RHIC?

**O Photon    **
**+ Charged    Particle**

**Anti Centauro**

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## DCC Signal

- Likely many uncorrelated domains can be formed, then this asymmetric distribution will become Gaussian
- S0 such fluctuations should be looked in localized  or  space, localized momentum space
- We look for localized charged fluctuations in -space to isolate the rare events that may correspond to higher or lower value of  “f”.

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Wavelet : Formalism

- Wavelets jk() are the set of orthogonal functions where index j labels the scale and k labels the spatial bin
- We use Discrete Wavelet Transformation technique to extract events with localized fluctuations in eta space over large events sample
- Define Sample function      f() = 1- Nch()/Nch()
- Expansion for a given scale j     fj() =  fjk jk()
- Wavelet coefficients          fjk = 2j f()jk() d
- Power                                       Pj  = (1/2j) |fjk|2

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Wavelet : stairwell function

**Wavelet functions  ********jk****(********) = ********(2****j ******** - k)**
**               ****1        for 0   ********   x   ******** 1/2**
******(x) =    -1        for 1/2  ********  x  ********    1**
**               ****0         otherwise**
**            **j           k
-                 0          0
-                 1          0
-                  1         1
-                  2         0
-                  2          1
-                  2         2
-                  2         3

_****__**  **__**=0                                       **__****__**=1                        **_

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Wavelet Transform: Daubechies

- We are using D-4 wavelets in the DWT
- Linear operation that operates on a data vector : a[n]
- Length n of the data vector is an integer power of 2
- Transform to a numerically different vector of same length
- A particular set of wavelets are specified by a particular set of numbers : wavelet filter coefficients
- Daubechies ( D-4) : c0, c1, c2, c3

- This is what a D-4 wavelet basis
- Looks like at j=2

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Simulation: FFC

- Wavelet coefficients
-     fjk = 2j f()jk() d
-    plotted at different scale j
- Simulated data with  fluctuation size  = 30% where  = Ncand ./Nmult
- Distributions become wider by adding the fluctuations in simulated data wih HIJING

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Acceptance pseudo-rapidity

- We looked for PHENIX global tracks projected on three pad chamber detectors
- Gap at Z=0 for PC2 & PC3
- PC3 further away from PC1
- PC2 only in one side

-  = .7   j=1     = .7/21   = .35
-                j=5     = .7 / 25  = .022

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Wavelet Coefficients @200 GeV

**    **tracks projected to PC1: PHENIX data is not significantly different from simulated data and mixed events.

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Wavelet Coefficients @200 GeV

**    **tracks projected to PC2: PHENIX data is not significantly different from simulated data and mixed events.

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Wavelet Coefficients @200 GeV

**    **tracks projected to PC3 : PHENIX data is not significantly different than the simulated data and mixed events

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Power Spectrum@200 GeV

- Correlation in power spectrum is similar for PHENIX data, mixed events, and in simulated data.  Random sample shows a flat power spectrum.
- This is work in progress. This sample has 60K PHENIX events and 120K mixed events.

**power spectrum is convolution of    physics results and detector effects**** **

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh

## Summary

- DWT can be effective tool to look for Charged particle fluctuations in pseudo-rapidity space
- Analysis was performed for a small fraction of 200 GeV Au+Au data and current status of this analysis is work in progress
- Comparison is made with simulated and mixed events using similar cuts
- Correlation in power spectrum is consistent with the detector acceptance for this sample of minimum bias PHENIX data
-  Rare events can be searched from the tail of ffc distribution

- APS meeting / Albuquerque  04/20/02

- T. K. Ghosh