# Presentation: 479687

## Fluctuations and Correlations in Relativistic Heavy Ion Collisions 

-  Charge Fluctuations
-  Balance Functions
-  Event-by-event <pT> Fluctuations
-  Looking Ahead
-  Conclusions, Credits, Apologies

- Fluctuations and Correlations in Relativistic Heavy Ion Collisions

- Jeffery T. Mitchell
*(Brookhaven National Laboratory)*

## Charge Fluctuations

- Hadron Gas Scenario

- Quark-Gluon Plasma Scenario

- Fractional electric charges of the quarks ==>
- Charges more evenly spread in a plasma ==> Reduced net charge
- fluctuations in a small region of phase-space

- Hypothesis: Fluctuations in net charge and net baryon number may be significantly reduced if a QGP is formed in the collisions
*Asakawa, Heinz, Müller PRL 85(2000)2072; Jeon & Koch PRL 85(2000)2076*

## Summary of Charge Fluctuation Measures

**Summary of Charge Fluctuation Measures**

**Quoted in this presentation**

## Charge Fluctuation Magnitude Expectations

|  | v(Q) | D | +-,dyn
(STAR) | +-,dyn
(PHENIX) | q
(NA49) |
| --- | --- | --- | --- | --- | --- |
| Independent Particle Emission | 1.0 | 4.0 | 0.0 | 0.0 | 0.0 |
| Resonance Gas | 0.75 | 3.0 | -0.0013 | -0.006 | -0.125 |
| Quark-Gluon Plasma | 0.25 | 1.0 | -0.0038 | -0.019 | -0.375 |
| Quark Coalescence | 0.83 | 3.33 | -0.0008 | -0.004 | -0.084 |

## Charge Fluctuations vs. Rapidity Acceptance (Excitation Function): NA49

- Correction for fluctuations due to charge conservation.

**Quark Coalescence**

**Resonance Gas**

**Quark-Gluon Plasma**

**Charge Conservation**

***See poster by P. Chrisakogiou***

***Also see talk by H. Sako for new CERES results.***

## Charge Fluctuations vs. Rapidity Acceptance

****** ****= ********/2,**
**0.3 ******** p****T**** ******** 2.0 GeV/c**

**Charge Conservation**

**Quark Coalescence**

**Resonance Gas**

**Quark-Gluon Plasma**

**Phys. Rev. Lett. 89 (2002) 082301, 130 GeV.**

## Charge Fluctuations vs. Rapidity Acceptance

**Charge Conservation**

**Quark Coalescence**

**Resonance Gas**

**Quark-Gluon Plasma**

**Phys. Rev. C68 (2003) 044905, 130 GeV.**

## Balance Functions

- Bass, Danielewicz, & Pratt, Phys. Rev. Lett. **85**, 2689 (2000)

*********+ - ******(************y)****** ******= Histogram of | y(************+******) - y(************--******) |, for all possible pairs within an event. This histogram is summed over all events.***

-  Designed to determine whether hadronization from a QGP occurs early  (<1 fm/c) or late.
-  Based upon the fact that charge is conserved locally, and produced pairs are initially correlated in coordinate space.
-  **Bottom line**: The balance function is narrower in the delayed hadronization scenario.

**Early hadronization scenario**: Pairs separate in rapidity due to expansion and rescattering.

**Delayed hadronization scenario**: Pairs are more strongly correlated in rapidity.

## STAR 130 GeV Balance Function Results

- Phys. Rev. Lett. 90 (2003) 172301.

**All Charged Hadron Pairs**

**All Charged Hadron Pairs**

**Identified Pion  Pairs**

**Identified Pion  Pairs**

## STAR 200 GeV Balance Function Widths

**The balance function gets narrower in central collisions ******** Delayed hadronization scenario?**

- Increasing Centrality

***See talk tomorrow by G. Westfall***

## NA49 17 GeV Balance Function Widths

**A similar behavior AND narrowing magnitude is observed compared to the STAR data!**

**The balance function gets narrower in central collisions.**

***See talk by M. Gazdzicki***

**Preliminary**

- Increasing Centrality

## Other explanations for the broadening of the balance function

_**Resonance contributions**_
*P. Bozek, W. Broniowski, and W. Florkowski,               nucl-th/0310062*
**Computing balance functions in a thermal model with neutral resonance decay.**
**The calculations including resonances are consistent with the STAR results.**

**0-10% centrality**

**10-40% centrality**

**40-70% centrality**

**70-96% centrality**

_**Quark Coalescence Model Predictions**_
**Bialas, hep-ph/0308245.**
**Predicts a width consistent with the STAR result for central collisions with a transverse flow velocity below 0.5c.**

## Behold The <PT> Fluctuation Signal!

- Behold The <PT> Fluctuation Signal!

## Summary of Event-by-event <pT> Fluctuation Measures

- Summary of Event-by-event <pT> Fluctuation Measures

- pT

- pT

- pT,n

- FpT

- pT,dyn

- Goal of the observables:
- State a comparison to the expectation of statistically independent particle emission.

**Quoted in this presentation**

## How To Measure A Fluctuation

**Red: Random Expectation           (******** distribution)**
**Blue: STAR acceptance fluctuation of:**
******pT****=52.6 MeV,**
** ****F****pT****=14%, **
******2****pT,dyn****=52.3 (MeV/c****2****),**
******pT****=9.8%**

- MpT = Event-by-Event Average pT

- Gamma distribution calculation for statistically independent particle emission with input parameters taken from the inclusive spectra. *See M. Tannenbaum, Phys. Lett. B498 (2001) 29.*

## A Positive Signal is Observed!Known contributions to the <pT> fluctuation signal should be subtracted.

_**Contributions from Known Processes**_
**HBT – too small (NA49, STAR, CERES)**
**Resonances – too small (NA49, STAR)**
**Elliptic Flow – too small/negligible (PHENIX, CERES, NA49)**
**Hard Processes...**
**Or onset of thermalization...**

*A Schematic Illustration of Elliptic Flow*

## A Possible Explanation of the Signal: A System in Near-local Thermal Equilibrium

*Sean Gavin, nucl-th/0308067, see his talk tomorrow for more details.*

## The onset of thermalization?

***See talks tomorrow by S. Gavin (model) and G. Westfall (data)***

## A Large Fluctuation Contribution at high pT

- A Large Fluctuation Contribution at high pT

**An increase in observed fluctuations grows primarily in a p****T**** region where number fluctuations vary little.**

**0.2 < p****T**** < p****T****max**

**Preliminary**

_**Increases from p**__**T**__**max**__**=1.0 to 2.0 GeV/c**_** **
**PHENIX Fluctuations: 243%**
**CERES Fluctuations: 34%**
**<N>: < 15%**

**20-25% centrality**

**20-30% centrality**

**This trend is observed at all centralities.**

***See talk by H. Sako***

**0.1 < p****T**** < p****T****max**

***See talk by M. Tannenbaum***

## Fluctuations: A Jet Contribution?

**Jets inherently add particles that are correlated in p****T**** to the event, so a contribution due to hard processes is expected, but how much? What about jet suppression?**

*A Schematic Illustration of Jet Suppression*

## Jet Simulation Results: PHENIX at 200 GeV

**20-25% centrality**

- PHENIX Data: nucl-ex/0310005

**Results from a 2-component hybrid simulation.**
_**Component 1**_**: Reproduce soft processes by sampling the inclusive p****T**** and N data distributions.**
_**Component 2**_**: Embed PYTHIA hard scattering events at a given rate per particle produced in Part 1. Keep the rate fixed, or scale it by R****AA****.**

**This decrease is due to the signal competing with the M****pT**** width increase for low N.**

**This decrease is due to jet suppression?**

***See poster by J. T. Mitchell***

## Jet Simulation Results: STAR at 130 GeV

**STAR data: nucl-ex/0308033**
**Error bars are the quoted total systematic error.**

**The simulation predicts ~15-20% increase when going from 130 to 200 GeV**

## Jet Simulation Results: NA49 at 17 GeV

- NA49 Preliminary Data: See poster by          K. Grebieszkow & M. Rybczynski

## Estimate of the Magnitude of Residual Event-by-Event Temperature Fluctuations

| Measurement | sqrt(sNN) | T/<T>,
Most central | T/<T>,
At the peak |
| --- | --- | --- | --- |
| PHENIX | 200 | 1.8% | 3.7% |
| STAR | 130 | 1.7% | 3.8% |
| CERES | 17 | 1.3% | 2.2% |
| NA49 | 17 | 0.6% | 1.7% |

- R. Korus and S. Mrowczynski,
- Phys. Rev. C64 (2001) 054908.

*p ****inclusive p**T**, ****(p,b), p~1*

## Add a dimension: 2-point transverse momentum correlations

**STAR Preliminary**

*HBT and Coulomb interaction*

*Higher ****p******t******  ****pairs from*
*hard scattering ?*

- Like sign

**In PHENIX, x(1.5 GeV/c) ~ 0.93**

**NA49 17 GeV Pb+Pb**

**Thermal Fluctuation Model Simulations**

**STAR Preliminary 130 GeV Au+Au**

**Data**

******(T) = 5 MeV**

******(T) = 10 MeV**

******(T) = 20 MeV**

**hep-ex/0311009**

***L. Ray, DNP 2003, see his poster***

## Coming Soon: A Multi-dimensional Analysis

**STAR Preliminary**

***(centrality, p******T,1******, p******T,2******, pseudorapidity, azimuth)***

**Same side**

**Opposite side**

***See poster by D. Prindle***

***Elliptic flow has been removed.***

***T. Trainor, DNP 2003***

## Synopsis

- _Charge fluctuations:_
- SPS results and RHIC-PHENIX results are close to the random expectation after correcting for charge conservation.
- RHIC-STAR results are consistent with a quark coalescence model prediction in central collisions.
- _Balance Functions:_
- Both SPS (NA49) and RHIC (STAR) results show a narrowing of the balance function in central collisions.
- The narrowing is indicative of delayed hadronization.
- The narrowing may also be explained within the quark coalescence picture, or by resonance decay contributions.
- _<p__T__> Fluctuations:_
- A positive fluctuation signal that decreases for more central collisions is seen at the SPS and at RHIC.
- The signal can be explained within a model that simulates jet production, however, a jet suppression scenario must be introduced to describe the most central collisions at RHIC.
- The signal can also be explained within a thermalization onset scenario.
- Stay tuned for more exciting results soon!

## Acknowledgements

- Many thanks to H. Appelshauser (CERES), M. Gazdzicki (NA49), S. Gavin, D. Prindle (STAR), L. Ray (STAR), C. Roland (NA49), H. Sako (CERES), T. Trainor (STAR), G. Westfall (STAR), for providing input into this presentation.

- But wait! There’s more!

** ****Multiplicity Fluctuations**
** ****Spatial Fluctuations, or “Event Texture”**
** ****Charge/Neutral (Isospin) Fluctuations**
** ****Particle Ratio Fluctuations**

***The following topics could not be covered in this presentation.***

## Fluctuations According to HIJING

**HIJING cannot reproduce the centrality dependence of the fluctuations.**
**One problem is that <N> changes depending on the HIJING settings – not matched to the observed dataset.**
**Example for 0-5% centrality: <N> = 93.0 for jet suppression, 76.6 without suppression, and 51.2 without jets.**

**20-25% centrality**

**Auxiliary Slide**