# Presentation: 445636

## Correlations and Fluctuationsin STAR

- Balance Function
- Excitation Function for *p**t* Fluctuations
- Net Charge Fluctuations
- Discrete Wavelet Analysis

- Quark Matter 2004Gary D. Westfall*Michigan State University**For the STAR Collaboration*

- Gary Westfall for STAR

## The Balance Function

- Theoretical expectations for *B(****y)*
- PYTHIA representing p+p collisions shows a characteristic width of about 1 unit of ***y*
- Bjorken thermal model representing delayed hadronization shows narrower balance function width
**Nucleon-nucleon ******** wide**
**Delayed hadronization ******** narrow**
- Experimental considerations
- Use  for all charged particles
- We will show centrality dependence for Au+Au and d+Au
- Use all centralities for p+p

- Bass, Danielewicz, and Pratt, PRL **85**, 2689 (2000)

- Gary Westfall for STAR

## Balance Function for Au+Au at 200 GeV

**Balance Function for Au+Au at 200 GeV**

- Gary Westfall for STAR

## Balance Function Widths

**Balance Function Widths**

- Balance function for Au+Au narrows in central collisionsHIJING shows little centrality dependenceSmooth dependence on *N**part*

- Width is defined as weighted average of  for *0.1 **** **** **** 2.0*

- Gary Westfall for STAR

## Balance Function for qinv

- Fits are thermal +*K**0* decay
- Thermal distribution is

**Balance Function for q****inv**

- Narrowing of *B(****)* may be caused by transverse flowUse *B(q**inv**)* to remove reference frame dependenceAllow more direct comparison with thermal models

- Gary Westfall for STAR

## Width of Balance Function using qinv

**Width of Balance Function using q****inv**

- Balance function *B(q**inv**)* for pions and kaons narrows in central collisions even when using Lorentz invariant observable

- Gary Westfall for STAR

## Theoretical Predictions for the Balance Function

**Theoretical Predictions for the Balance Function**

- Cheng, Petriconi, Pratt, and Skoby, nucl-th/0401008
- Includes HBT, Coulomb, resonances, strong interactions, radial flow, conservation of S,Q,B
- Uses STAR acceptance filter
- The agreement with the measured narrow balance function in central collisions suggests that charge conservation remains highly localized at breakup

- Au+Au 200 GeV

- Gary Westfall for STAR

## pt and Net Charge Fluctuations

- Search for dynamical fluctuations motivated by predictions
- Fluctuations in energy density due to localized deconfinement
- Increased fluctuations in energy density due to long range correlations
- Proximity to tri-critical and critical points would lead to changes in fluctuation patterns
- Production of DCCs
- Fluctuations from jet production

- Gary Westfall for STAR

## Au+Au at 20, 130, and 200 GeV
5% most central bin using min bias data, || < 1.0
Real is wider than mixed
 Dynamical fluctuations

- 5% most central bin using min bias data, *|****| < 1.0*
- Real is wider than mixed
-  Dynamical fluctuations

**Histograms of *****<p******t******>***

- See poster by Claude Pruneau

- Gary Westfall for STAR

## <pt,i pt,j> as a Function of Incident Energy

***<************p******t,i****** ************p******t,j******>***** as a Function of Incident Energy**

- Compare Au+Au at 20,130, and 200 GeV
*|****| < 1*
- Compare with filtered HIJING

- Gary Westfall for STAR

## <pt,i pt,j>1/2/<<pt>> as a Function of Incident Energy

***<************p******t,i****** ************p******t,j******>******1/2******/******<******<p******t******>******>***** as a Function of Incident Energy**

- Compare Au+Au at 20, 130, 200 GeV, *|****| < 1*
- Compare with CERES result from SPS, 17 GeV Pb+Pb

**<********p****t,i**** ********p****t,j****>****1/2****/<<p****t****>>**

- Gary Westfall for STAR

## Different Scaling Methods for <pt,i pt,j> 

**Different Scaling Methods for *****<************p******t,i****** ************p******t,j******>***** **

- Scale with *N**part*

- Scale with *dN/d*** - compare to ***pt*

- Centrality dependence may be sign of the onset of equilibration in central Au+Au collisions

- Gary Westfall for STAR

## Comparison to Fpt

- 200 GeV Au+AuSTAR withPHENIX Cuts
*|****| < 0.35**** = 2x90****0.2 < p**t** < 2 GeV*

- 200 GeV Au+AuSTAR Cuts
*|****| < 1.0**** = 360****0.1 < p**t** < 2 GeV*

- Acceptance matters

- Gary Westfall for STAR

## Net Charge Fluctuations - Centrality Dependence

**Net Charge Fluctuations - Centrality Dependence**

- Increased dilution of correlation with increasing *N**part*
*|****+-,dyn**|* larger at 20 GeV than 130 and 200 GeV
- Peripheral Au+Au in agreement with inclusive p+p
*1/N* scaling violation

- See poster by Claude Pruneau

- Gary Westfall for STAR

## Net Charge Fluctuations - Dependence on  Acceptance

**Net Charge Fluctuations - Dependence on ******** Acceptance**

- 50-70% Central

- 0-10% Central

- 50-70% Au+Au quite similar to p+p
- 0-10% Monotonic increase of correlation strength with beam energy
- Flow is important (sensitivity to velocity profile)

- || acceptance

- Ratio to || < 1

- Ratio to || < 1

- Gary Westfall for STAR

## Net Charge Fluctuations - Scaling

**Net Charge Fluctuations - Scaling**

- Participant Scaling

- Binary Scaling

*dN/d*** Scaling

- Multiplicity Scaling

- Gary Westfall for STAR

## Discrete Wavelet Analysis

**Discrete Wavelet Analysis**

- See poster by Mikhail Kopytine

- Suppression of
- correlation observed at high pt
- Approaches thermalization

- Gary Westfall for STAR

## Conclusions

- Balance functions
*B(****)*, *B(****y)*, and *B(q**inv**)* narrow in central Au+Au collisions
- Consistent with trends of models incorporating late hadronization
*p**t* correlations
- Dynamic correlations observed at Au+Au collisions at 20, 130, and 200 GeV
- Correlations/particle increase with incident energy
- Correlations/pair show little incident energy dependence
- May show onset of equilibration in central Au+Au collisions
- Net Charge Fluctuations
- Larger *|****+-,dyn**|* for Au+Au at 20 GeV than 130 and 200 GeV
*|****+-,dyn**|**Au+Au*  *N* *|****+-,dyn**|**p+p*
*N**bin* scaling observed
- Discrete wavelet analysis
- Evidence for suppression of jet-like phenomena in central Au+Au collisions in the longitudinal direction

- Gary Westfall for STAR

## Extra Slides

- Gary Westfall for STAR

## Balance Function for p+p and d+Au at 200 GeV

**Balance Function for p+p and d+Au at 200 GeV**

- p+p

- d+Au

- Gary Westfall for STAR

## Delayed Hadronization

- Early Hadronization
-  Large 

- Late Hadronization
-  Small 

- Suppose we could identify balancing charges

- After Scott Pratt

- Gary Westfall for STAR

## Definition of <pt,i pt,j> 

- Gary Westfall for STAR

## Dynamical Net Charge Fluctuations

**Dynamical Net Charge Fluctuations**

- Independent Particle (Poisson) Limit

- Definition:

- Measurement:

- Key Properties:

- Sensitive to two-particle correlations

- Independent Particle Production

- Independent N+N Collisions

- Gary Westfall for STAR

## Ratio of <pt,i pt,j>  using Pairs withqinv < 0.1 GeV to All Pairs

- Gary Westfall for STAR