# Presentation: 947826

## AGS/RHIC User Meeting - June 2005 Probing Collision Dynamics with Fluctuation and Correlation Studies at RHIC

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

## Talk Outline

- Net Charge Fluctuations
- Transverse Momentum Fluctuations
- K/ Fluctuations (Proof of principle)
- Questions:
- Smoking gun for QGP, phase transition ?
- Threshold Effects with beam energy?
- What can we learn about collision dynamics ?
- Resonances
- Radial Flow Velocity + Profile
- Role of Jets ?
- Issues
- E, p conservation
- HBT & Coulomb effects

- Claude A Pruneau, Wayne State

## Why Study E-by-E Fluctuations ?

- Net Charge Fluctuations
- Prediction by Jeon & Koch, PRL83 (99) 5435,  + others)
- Net charge fluctuations ***reduced*** in a QGP compared to a hadron or resonance gas.
- 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.
- Strangeness Fluctuations
- Large strangeness fluctuations
- QGP Droplets

| 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
 |

- NA49

- Claude A Pruneau, Wayne State

## Event-by-event Fluctuations at STAR

- M. Anderson et al. NIMA499 (2003)

- Suprya Das, *et al.*

- Gary Westfall, *et al.*, STAR

- G. Westfall *et al*

- Claude A Pruneau, Wayne State

## Anatomy of Fluctuations

- Probability to find a correlated pair:
- Distribution of associated particle per trigger

**Anatomy of Fluctuations**

**Differential Observables**

**Integral Observables**

**1-, 2-Particle Integrals**
- Weighted Integrals:
- Variance:
- Covariance:
- Correlation Coefficient:

- 1-particle distribution

- 2-particle distribution

- Claude A Pruneau, Wayne State

## Net Charge, and K/ Fluctuations

- Instead of measuring the variance of a yield ratio,

- Study the “dynamical fluctuations”:

- Side Note:

- <pt> Fluctuations

- Claude A Pruneau, Wayne State

## 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, Wayne State

## Data Sets - STAR

- Au + Au
- sNN1/2 = 20, 62, 130, 200 GeV
- Collision Centrality Determination based on all charged particle multiplicity ||<0.5.
- Centrality slices 0-5%, 5-10%, 10-20 %, ...
- Use Glauber model/MC to estimate the corresponding number of participants.
- Events analyzed  for |zvertex|<MAX.
- DCA < DCAMAX cm.
- Track quality Nhit>15; Nfit/Nhit>0.5.
- Fluctuations studied in finite rapidity, pt, and azimuthal ranges.

- Claude A Pruneau, Wayne State

## Dynamical Fluctuations in Au + Au Collisions

- Dynamical Fluctuations in Au + Au Collisions

- Au +Au

- || < 1.0; 0.15< pt< 2.0 GeV/c

- G. Westfall *et al.*, Submitted to PRC.

- Au + Au 200 GeV

- ||<0.5; 0.2 < pt < 5.0 GeV/c

- ||<0.5;

- Net Charge

- K vs 
- Au+Au 200 GeV

- S.Das, G. Westfall, *et al.*, Work in progress

- C. P. *et al.*, Work in progress.

- Finite Fluctuations @ all measured energies.
- Increased dilution with increasing Npart
- Energy dependence ?

- <pt,1pt,2>

- Claude A Pruneau, Wayne State

## QGP Signature?  1/N Scaling?

**PHOBOS - PRC65, 061901R**
**Au + Au sqrt(s****NN****)=130 and 200 GeV.**

- No Correlations

- G. Westfall *et al.*, Submitted to PRC.

- C. P. *et al.*, Work in progress.

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

- Koch/Jeon QGP ~ -3.

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

- Claude A Pruneau, Wayne State

## 1/Npart Scaling?

- G. Westfall *et al.*, Submitted to PRC.

- C. P. *et al.*, Work in progress.

- Claude A Pruneau, Wayne State

## Comparison to PHENIX, Fpt

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

- PHENIX 130 GeV Au+Au; STAR 200 GeV Au+Au

- G. Westfall (STAR), QM’04

- In plane

- Out-of-plane

**Shengli Huang (STAR)**

- Claude A Pruneau, Wayne State

## 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

- Need to correct for charge conservation effects!

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

- Possible “Threshold” Effect at lowest SPS/CERES energy.

- 5% Central Au+Au

- Claude A Pruneau, Wayne State

## <ptpt> Beam Energy Dependence

- <ptpt> Beam Energy Dependence

- HIJING still does _**not**_ agree with  the data.

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

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

**<********p****t****,********p****t****>****1/2**** scaled by <p****t****> exhibits small or no beam energy dependence.**

- G. Westfall *et al.*, Submitted to PRC.

- Claude A Pruneau, Wayne State

## K/ Fluctuations Beam Energy Dependence

| Experiment | Ratio type | data | mixed | dyn |
| --- | --- | --- | --- | --- |
| STAR | K/ | 17.78% | 17.23% | 4.6%±0.025 |
| STAR | K+/+ | 24.29% | 24.10% | 3.06%±0.066 |
| STAR | K-/- | 24.81% | 24.55% | 3.61%±0.055 |

- STAR
- 200 GeV

- Supriya Das et al, work in progress

- Claude A Pruneau, Wayne State

## What Can We Learn About Reaction Dynamics ?

- Thermalization
- Role of resonance production
- Collective Flow
- Jets
- etc

## Thermalization

- S. Gavin, Nucl. Dyn 2004.

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

- Solves Boltzmann equation
- Parameterize particle correlations
- Spatial
- Rapidity
- Momentum

- Claude A Pruneau, Wayne State

## Resonance Contributions - An Example 

- Generating functions:

**Resonance Contributions - An Example **

******+-,dyn**

**Probability - f****3**

-  ~ 0.17
- kos 	~ 0.12
- 	~ 0.08 effective
- 	with DCA < 3cm.
- Resonances   0.3

- Claude A Pruneau, Wayne State

## Particle Correlations in “Elementary”  NN-collision. 

**Produced particles are correlated due to:**
**Local charge(s) conservation, **
**Resonances,**
**Fluctuations in number of produced “strings”, e.g. number of qq-collisions.**

- x

- y

- rapidity

- Distribution of “correlated” pairs:

- Distribution of “associated”particles (2) per “trigger”particle (1)

- “Probability” to find a “correlated” pair

- ISR

- The probability  to find a particle at mid-rapidity is about 60% larger if a particle has been already detected.

- Claude A Pruneau, Wayne State

## Particle Correlations in A+A   Radial flow

- Particle Correlations in A+A   Radial flow

**Hypothesis:**
- All particles produced in the same NN-collisionor “qq-string” subject to
- Same transverse/radial “push”.
- Same radial direction + magnitude
**Consequences:**
- Induced correlations in phi
- Induced position-momentum correlation in AA
- not present in N+N
- Induced pt correlations.
**Specifics**
- Long range rapidity correlations
- Narrow in  and wide in , charge independent
- Stronger 2-particle pt correlation in narrow bins
- Narrowing of the charge balance function
- Increase in mt & decrease in rapidity separation
- Similar to S. Pratt et al, “late hadronization scenario”
- Increase in Charge correlations in  .
- Azimuthal Balance function
- Correlation observables all evolving with centrality (radial flow)

- x

- y

- rapidity

- Claude A Pruneau, Wayne State

## Longitudinal Correlations

- Au + Au @ 200 GeV

**Longitudinal Correlations**

- G. Westfall *et al.*, QM04

**RADIAL FLOW **
**DELAYED HADRONIZATION ???**

- Claude A Pruneau, Wayne State

## Model of Transverse radial expansion

**Blast wave parameterization** of the source at freeze-out: d3n/d3p ~ e-E/T
- Schnedermann, Sollfrank, Heinz, PRC 48, 2462 (1993)

- STAR, PRL 92, 112301 (2004)

- Hypotheses:
- Uniform source density for r<R.
- Unique Temperature, T,
- Velocity profile: **v****t**** *****r *****n**

- _x_

- n=1

- S. Voloshin, nucl-th/0312065

- Claude A Pruneau, Wayne State

## Correlations Induced by Radial Flow

- n=1,  T=110 MeV

- First and second harmonics

- No dilution factor and No momentum conservation effects included

- S. Voloshin, nucl-th/0312065

**Excluded based on estimates non flow contributions to v****2**

**No velocity profile discrimination**

**Good velocity profile discrimination**

**k=1**

**v****t**** *****r *****n**

- Claude A Pruneau, Wayne State

## Transverse Momentum Correlations 

- Scale <pt,1pt,2>, divide by <<pt>>2 and number of participants.
- Compare to Blastwave calculation by S. Voloshin

**Caveats: **
**Neglecting Diffusion, **
**Finite Thermalization Time**
**Used “simple” Spatial Source Profile**
**Simple N****coll**** Scaling**

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

**v****t****   *****r *****n**

- Claude A Pruneau, Wayne State

## Effect of radial flow on Net Charge Azimuthal Correlations Monte Carlo Toy Model

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

- Multinomial production of +, -, 0, K0.

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

**No K****o****, Low mass ******** or ********, v****r**** = 0.**

**0.95c**

**0.9c**

**0.8c**

**0.7c**

**0.6c**

- Claude A Pruneau, Wayne State

## Net Charge - Azimuthal Dependence

- Au+Au @ sNN1/2 = 62 GeV

- Resonance Gas - Toy Model

- T=0.18 GeV; +, -, , K0s, vr as shown

- Pythia 25 pp + Radial Flow

**Indications of resonance + flow effects**
**Interpretation requires detailed model comparisons**

**0.95c**

**0.9c**

**0.8c**

**0.7c**

**0.6c**

- Claude A Pruneau, Wayne State

## Summary

- Net Charge fluctuations
- No smoking gun for reduced fluctuations as predicted by Koch *et al*.
- No beam energy dependence
- Bulk of observed correlations likely due to resonance decays.
- Sensitivity to radial flow.
- Pt fluctuations
- No smoking gun for large fluctuations.
- No beam energy dependence.
- Sensitivity to radial velocity profile
- K/ Yield fluctuations
- Super-poissonian
- No beam energy dependence ?
- Suggestion: Bulk correlation properties invariant with beam energy 15 < s1/2NN < 200 GeV ?

- Claude A Pruneau, Wayne State