# Presentation: 383294

## PANIC 05,  Santa Fe, NM, October, 2005 Probing Collision Dynamics with Fluctuation and Correlation Studies at RHIC

- Claude A Pruneau
- For the STAR Collaboration
- Physics & Astronomy Department
- Wayne State University
- Detroit, Michigan, USA

- Net Charge Fluctuations
- Transverse Momentum Fluctuations

## Why Study E-by-E Fluctuations ?

- Net Charge Fluctuations
- Prediction by Jeon & Koch, PRL83 (99) 5435,  + others...
- Net charge fluctuations ***dramatically reduced*** in a QGP compared to a hadron or resonance gas.
- Published STAR results at 130 GeV:  C. Adler, *et al.*, Phys. Rev. **C68**, 044905 (2003).
- Momentum Fluctuations
- Predictions by M. Stephanov *et al* PRL81 (98) 4816; S. Mrowczynski, PLB314 (93) 118.
- Large Transverse Momentum Fluctuations
- Sensitive to 1st order phase transition - QGP Droplets.
- Sensitive to 2nd order phase transition Near critical point.
- Excitation Function Study submitted by STAR to PRC

| Model | D | +-,dyn |
| --- | --- | --- |
| Poisson, Hadron Gas | 4 | 0 |
| Resonance Gas (Koch et al) | 2.8 | -1.2/nch |
| Quark Coalescence (Bialas) | 3.33 | -0.7/nch |
| QGP (Koch et al) | 0.75 | -3.25/nch |
| Lattice | 1 | -3/nch
 |

- Study beam energy & collision centrality dependence

- Claude A. Pruneau, STAR, QM05

## Event-by-event Fluctuations at STAR

- Au + Au @ **s****NN****1/2**** = 20, 62, 130, 200 GeV**
- TPC data || < 1.0.
- Collision centrality charged particle multiplicity ||<0.5.
- Centrality slices 0-5%, 5-10%, 10-20 %, ...
- Use Glauber MC model to estimate number of participants.

- Claude A. Pruneau, STAR, QM05

## Specific Fluctuation Measures

- Instead of measuring the variance of a yield ratio,

- Study the “dynamical fluctuations”:

- Side Note:

**p****t**** Fluctuations**

**Net Charge & K/******** Fluctuations**

- Claude A. Pruneau, STAR, QM05

## Useful Properties

- Independent Particle Production (Poisson):
- Superposition of M  “N+N” collisions without re-scattering of secondaries:
- Robustness
- Independent of detection efficiency

- Claude A. Pruneau, STAR, QM05

## Dynamical Net Charge and pt Fluctuations

- Dynamical Net Charge and pt Fluctuations

- ||<0.5; 0.2 < pt < 5.0 GeV/c

- Net Charge

- Finite Dynamical Fluctuations
- Dilution increases with Npart
- Energy dependence ?

- <pt,1pt,2>

- Npart

- Npart

- Claude A. Pruneau, STAR, QM05

## QGP Signature?  1/N Scaling?

**QGP Signature?  1/N Scaling?**

***Koch/Jeon QGP ~ -3.***

- Magnitude of net charge “compatible” with resonance and coalescence models.
- Finite Centrality Dependence but note dN/d/(Npart/2) changes with Npart.

- Claude A. Pruneau, STAR, QM05

## 1/Npart Scaling?

- Npart +-dyn exhibits small dependence on Npart
- Npart <pt,1, pt,2> exhibits large dependence on Npart

- Claude A. Pruneau, STAR, QM05

## Pt Fluctuations In/Out of Plane

***STAR Cut : |************| < 1.0;  ************ = 360************; 0.1 < p******t****** < 2 GeV***
**STAR with PHENIX Cuts: *****|************| < 0.35; ************ = 2x90************; 0.2 < p******t****** < 2 GeV***

- In plane

- Out-of-plane

- Puts in question PHENIX’s  (PRL 93 (04) 092301 ) Jet Quenching Interpretation.

- Claude A. Pruneau, STAR, QM05

## Net Charge Fluctuations - Beam Energy Dependence

- W. Busza, et al., Phobos, nucl-ex 0410035

- STAR ||<0.5
- PHENIX ||<0.35, =/2
- CERES 2.0<  <2.9

**Finite system size + charge conservation correction -****PRC 66 (02) 044904. **

- Nch,tot(200,5%) ~ 5092
- Nch,tot(130,5%) ~ 3900
- Nch,tot/Npart~”constant” at a given energy

**Flat except for possible “Threshold” Effect at lowest SPS/CERES energy.**

**5% Central Au+Au**

- Claude A. Pruneau, STAR, QM05

## pt Fluctuations - Beam Energy Dependence

- Adamova et al., Nucl. Phys. A727, 97 (2003)

- exhibits small or no beam energy dependence.

**p****t**** Fluctuations - Beam Energy Dependence**

- Claude A. Pruneau, STAR, QM05

## Thermalization

- S. Gavin, Nucl. Dyn 2004, QM04.

**“****Partial thermalization describes trends.”**

- Sololution of Boltzmann equation
- Parameterization of particle correlations
- Spatial, Rapidity, Momentum

- However does not explicitly include resonances & radial + elliptical flow
-  ~ 0.17
- kos ~ 0.12
- Resonances   0.3

- Claude A. Pruneau, STAR, QM05

## Radial Flow Induced Correlations in A + A

**Consequences:**
- Induced correlations in phi
- Induced position-momentum correlation in AA
- Induced pt correlations.
- ...

**Hypothesis:**
- All particles produced in the same NN-collisionor “qq-string” subject to
- Same transverse/radial “push”.
- Same radial direction + magnitude

- A+A

- p+p

- Claude A. Pruneau, STAR, QM05

## Pt Correlations Induced by Radial Flow

- Poor velocity profile discrimination

- pt pt> correlation enables velocity profile discrimination.

**Radial Velocity Profile: ****   v****t**** *****r *****n**

**1- and 2- Particle Blast wave parameterization of the source at freeze-out: **
**S. Voloshin, nucl-th/0312065**

- Transverse Rapidity

- Claude A. Pruneau, STAR, QM05

## Study of Velocity Profile based on Transverse Momentum Correlations 

**Scale ****<********p****t,1********p****t,2****> ****by <<p****t****>>****2**** and number of participants.**
**Compare to Blastwave calculation by S. Voloshin**

- Caveats:
- Neglecting Diffusion,
- Finite Thermalization Time
- Fixed Spatial Source Profile
- Simple Ncoll Scaling

- Data: G. Westfall *et al*, STAR, submitted to PRC
- Calculation: S. Voloshin, nucl-th/0312065

**v****t****   *****r *****n**

- Suggestion of a “soft” velocity profile

- Claude A. Pruneau, STAR, QM05

## Effect of radial flow on Net Charge Azimuthal CorrelationsBased on  range used to integrate +-,dyn .

**Effect of radial flow on Net Charge Azimuthal Correlations****Based on ******** range used to integrate ********+-,dyn ****.**

- Isotropic source; Maxwell Boltzman Dist.; T = 0.18 GeV;

**0.95c**

**0.9c**

**0.8c**

**0.7c**

**0.6c**

**Fixed radial flow velocity, v****r**

**Monte Carlo T****oy Model**

**Data - Au+Au @ s****NN****1/2 ****= 62 GeV **

- Production of +, -, 0, K0.

- Strong Radial Flow Effects on the net charge correlation

- Claude A. Pruneau, STAR, QM05

## Summary

- No dramatic reduction of net charge fluctuations “a la Koch *et al*.”
*Qualitative Agreement with Quark Coalescence Model (Bialas)*
- No beam energy dependence for either net charge or pt fluctuations.
- 2-Particle Correlation Strength Invariance ?
*New handles on radial flow velocity and profile*
- Strong radial flow effects on angular correlations
- Soft Velocity Profile: v~rn,  n~0.5

- Claude A. Pruneau, STAR, QM05

## K vs  multiplicity fluctuations

- Au + Au @ 200 GeV

- K/

- Finite Dynamical k vs  Fluctuations

- Claude A. Pruneau, STAR, QM05