# Presentation: 119258

## Event-by-Event Fluctuations from PHENIX

**Tomoaki Nakamura**
**for the PHENIX collaboration **
**Hiroshima University**
-  Correlations & Fluctuations Workshop at
- 2005 RHIC & AGS Annual User’s Meeting

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Phase transition

- According to the classical                                classification of the phase                                          transition by Ehrenfest, the                                        order of phase transition is                                       defined by the discontinuity                                             in the derivative of free                                                  energy.
- In this context, discontinuity in the variables of statistical mechanics or order parameter as a function of the temperature or time evolution is useful to search the critical point of phase transition.
- In particular, the second order phase transitions are often accompanied by the divergence with respect to variables of statistical mechanics or order parameters as critical phenomena.

- Specific heat of liquid Helium (He4)

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Variables of statistical mechanics as order parameters

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Event-by-event fluctuations in heavy-ion collisions measured by PHENIX

- Some variables of statistical mechanics and order parameters of phase can be obtained from event-by-event fluctuations.
- Correlation length can be extracted from the event-by-event multiplicity fluctuations by scanning the phase-space.
- Specific heat can be calculated from the results of event-by-event average *p**T* fluctuation.
- We have performed measurements of these fluctuations to explore the QCD phase transition accompanied by critical phenomena using the PHENIX spectrometer at RHIC.

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Multiplicity fluctuations by variance

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Multiplicity fluctuations in PHENIX

_**Multiplicity fluctuations in PHENIX**_

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Charged particle multiplicity distribution and negative binomial distribution (NBD)

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Negative binomial distribution (NBD)

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Charged particle multiplicity distributions in PHENIX

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## NBD k parameteras a function of average multiplicity

_**NBD k parameter**__**as a function of average multiplicity**_

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## NBD k parameteras a function of number of participants

_**NBD k parameter**__**as a function of number of participants**_

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Extraction of the correlation length from NBD k parameter

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Random particle emission pattern based on NBD

_**Random particle emission pattern based on NBD**_

- Detector 1

- Detector 2

- Emission source

- In the case of there are no correlation about the particle emission, the value of NBD k parameters are summed up.

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Correlated particle emission pattern into the phase-space

_**Correlated particle emission pattern into the phase-space**_

- Detector 1

- Detector 2

- Emission source

- If there are correlations, NBD k parameters do not increase according to the size of detector acceptance.

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## δηdependence of NBD k parameter

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Number of participants dependence of correlation length ξ

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Linear behavior of NBD k as a function of logarithmic δη

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Correlation functions and correlation length

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## δpT (pT>0.2 GeV/c) dependence of NBD k

_**δ**__***p***__***T***__** (**__***p***__***T***__**>0.2 GeV/c) dependence of NBD k**_

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Comparison for Au+Au, d+Au and p+p

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Average pT fluctuationPublished by Phys. Rev. Lett. 93, 092301 (2004)

**Already, famous!**
**It’s not a Gaussian...**
**it’s a Gamma distribution!**

**M.J. Tannenbaum, **
**Phys. Lett. B 498 (2001) 29**

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Result of average pT fluctuations in Au+Au 200 GeV and comparison with HIJING

- HIJING 1.35, default parameters

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Contribution of Jet/Jet suppression to the average pT fluctuation

**This decrease due to jet suppression?**

- PYTHIA based simulation, which contains scaled hard-scattering probability factor (Sprob) by the nuclear modification factor (RAA), well agree with the measured FpT. It might be indicate that jet suppression might contribute to the average pT fluctuation.

- centrality 20-25%

- FpT is adjusted at the open circle for this simulation

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Estimation of the magnitude of residual temperature fluctuations

| Experiment | √sNN | σT/<T> 
(most central) |
| --- | --- | --- |
| PHENIX | 200 | 1.8% |
| STAR | 130 | 1.7% |
| CERES | 17 | 1.3% |
| NA49 | 17 | 0.7% |

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Conclusions

- Charged particle multiplicity fluctuation
- Different behavior about the normalized variance of multiplicity distribution as a fluctuation of number of participants are observed at PHENIX as compared to SPS energy.
- NBD k parameters as an observable of the multiplicity fluctuation are not scaled by the mean multiplicity but scaled by the number of participants.
- There are no difference on the multiplicity fluctuation with respect to the sign of electric charge for each particles.
- Correlation length could be extracted from the multiplicity fluctuation.
- Different pseudo rapidity gap dependence of NBD k parameter has been observed as compared to the past experiment.
- Average *p**T* fluctuation
- PYTHIA based simulation with scaling the hard-scattering probability factor by the nuclear modification factor well reproduce the Au+Au 200 GeV data.
- It is suggested that jet suppressions contribute to the average *p**T* fluctuations
- No anomaly was found about the residual temperature fluctuations from the SPS energy to RHIC energy.

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Outlooks for QM2005

- Further new results will be presented at QM2005
- Systematic study of multiplicity fluctuations with respect to the collision system using Cu+Cu 200 GeV.
- Detailed study about extraction of the correlation length by the different correlation functions and the behavior of the correlation length as a function of number of participants.
- Jet suppression effects and extraction of specific heat in the average *p**T* fluctuation with Au+Au 62GeV and Cu+Cu 200GeV.
- The other observables of event-by-event fluctuations and correlations, e.g. *p**T**-p**T* correlation.
- We are willing to analyze the data on the event-by-event fluctuations for the QM. See you again at the Budapest.

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Backup Slide

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Normalized factorial moment Fq

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## NBD k and factorial moment Fq

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Integral of correlation function and normalized factorial moments

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Elliptic flow contribution by simulation

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005

## Specific heat from average pT fluctuation

- Tomoaki Nakamura - Hiroshima Univ.

- 6/21/2005