# Presentation: 636823

## Study of Isospin Fluctuations at RHIC-PHENIX

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**Study of Isospin Fluctuations ****at RHIC-PHENIX**

_**Tomoaki Nakamura**_** /**** Kensuke Homma**
**for the PHENIX Collaboration**
**Hiroshima University**

**Contents**
**History of Centauro Search**
**Search Strategy**
**Observable and Analysis Method**
**Analysis Results**
**Summary and Future Plan**

## Centauro /Anti Centauro Event

**(Cosmic ray experiment)**
**(****Brazil-Japan collaboration in Bolivia)**** ****Y.Fujimoto and S.Hasegawa, Phys. Rep. 65, 151 (1980)**
**(JACEE)**** J.J.Lord and Iwai, Paper No. 515, International Conference on High Energy Physics, Dallas (1992) **

**O : Photon,    +  : Charged Particle**

- Anti Centauro

**        ****This is anomalous region assuming isospin symmetry.**

**Notes:**
In the 1970's high energy cosmic ray experiments observed anomalous events that have a large asymmetry between the number of charged and $\gamma$ clusters. 

## List of Centauro Searches

|  | Experiment | Collaboration | CM Energy | Search Region (η,φ)  |
| --- | --- | --- | --- | --- |
| 1980 | Mt. Chacaltaya | Brazil-Japan | √s≧1.7 TeV | ------------ |
| 1992 | Balloon
 | JACEE | ------------ | 5.0<η<9.0
⊿φ<2π |
| 1982 | SPPS | UA5 | √s=540 GeV | |η|<5.0 |
| 1983 | SPPS | UA1 | √s=540 GeV | |η|<3.1 |
| 1986 | SPPS | UA5 | √s=900 GeV | |η|<5.0 |
| 1996 | TEVATRON | CDF | √s=1.8 TeV | |η|<4.2, ,⊿φ<2π |
| 1997 | TEVATRON | MINIMAX | √s=1.8 TeV | 3.4<η<4.2 |
| 2000 | SPS | WA98 | √s=3.5 TeV (Pb+Pb) | 2.80<η< 3.75
⊿φ<π |
| 2001 | RHIC | PHENIX | √s=39.4 TeV 
(Run2 Au+Au) | |η| < 0.35
⊿φ<1/2π (×2 arm) |

**Notes:**
This is a list of Centauro searches. There are some approaches of searching for Centauro events after the report from cosmic ray experiment but, its candidate have never been observed in the past accelerator experiments. RHIC is the most high energy accelerator with respect to total center of mass energy. We perform this Centauro search by using PHENIX detector at RHIC. 

## PHENIX Experiment at Run2

**Using Magnetic Field-off data**
**Gamma-like Cluster (Electro-Magnetic Calorimeter)**
**Charged Track (Drift Chamber and Pad Chamber1)**

- in each arm

**Notes:**
This is the PHENIX detector. This detector has a two arm structure, each of which covers 90 degree in azimuth and $\pm$ 0.35 in pseudo rapidity, and it can detect charged tracks and $\gamma$ clusters in the same phase space. We count charged track by using Drift Chamber and Pad Chamber1, and count gamma-like cluster by using Electro Magnetic Calorimeter which is not associated charged track.

## Disoriented Chiral Condensate

**(Quench Mechanism) ****K.Rajagopal and F.Wilczek : Nucl. Phys. B379, 395 (1993)**

**quench**

**restoration**

**QCD vacuum**

**DCC**

**Chiral symmetry breaking term due to finite masses**

**Notes:**
These events, named "Centauro Event", could be explained by a generation of disoriented chiral condensates (DCC) at the chiral phase transition based on effective theories of QCD (explained by linear sigma model) . As a result, domains with large fluctuations in the neutral to charged pion ratio could be created event-by-event. In this perspective, such an event is a signature of the chiral symmetry restoration. 

## Search Strategy

**If every event could contain largely deviated domains on  isospin symmetry and most of domains per event could be detected within a limited detector acceptance,  we would be able to discuss anomaly based on the probability distribution by the statistical treatment like:**

**probability : P(f)**

**fraction : f**

**DCC (Centauro type)**

**No DCC (binomial)**

**However, we do not know domain information on the numbers and sizes a priory, and our detector acceptance is very limited. Therefore we need to search for rare events containing anomalous domain like cosmic ray experiments rather than statistical treatment above.**

**Notes:**
If every event could contain largely deviated domains on  isospin symmetry and most of domains per event could be detected within a limited detector acceptance,  we would be able to discuss anomaly based on the probability distribution by the statistical treatment like:
However, we do not know domain information on the numbers and sizes a priory, and our detector acceptance is very limited. Therefore we need to search for rare events containing anomalous domains like cosmic ray experiments rather than the statistical treatment above.

## We search for a most largely deviated domain per event  by looking at differences between number of charged and gamma-like clusters by changing regions of interest as we do by eyes, because we don’t know what the size is  and where the position is.

**We search for a most largely deviated domain per event  by looking at differences between number of charged and gamma-like clusters by changing regions of interest as we do by eyes, because we don’t know what the size is  and where the position is.**

**We want to extract this region. We must do this search in several million events.**

**Notes:**
We search for a most largely deviated domain per event  by looking at differences between number of charged and gamma-like clusters by changing regions of interest as we do by eyes, because we don’t know what the size is  and where the position is.

## Observables

**Definition of asymmetry between number of charged tracks and neutral clusters event-by-event base as a function of subdivided eta-phi phase spaces normalized by 1 sigma of standard deviation for given multiplicity.**

***δA******I3***

**Domain Size**

**Deviation Size**

**Domain Position**

**η,φ**

**Domain Size and Domain Position of large deviated region can be obtained at the same time by using Multi Resolution Analysis (MRA) technique.**

## Multi Resolution Analysis (MRA)

**Total number of bins is 2****j**
**Level j correspond to resolution level**

## Signal Decomposition

-  **j : resolution level**
**k : k-th bin in pseudo rapidity **
**Cjk  : coefficients of φ**
_**Djk : coefficients of ψ**_

**1/2****j****→ Domain Size**
**k → Phase Space Position**
**Djk → Deviation Size**

**Look for Djkmax in a event **

## Example of 2D MRA

- eta (j=4)

- phi(j=4)

**C**

- 1) projection on eta

- 2) projection on phi

- 1) projection on phi

- 2) projection on eta

- Domain C:
- AI3= ~20 x 8bins
- (, )=(3, 7)
-  (j ,  j)=(3, 2)

- A

- B

- Result:Correct
- (,)=(3,7)
- (j,j)=(3,2)
- Djkmax2
- =_4392.42_

- Result:Wrong
- (,)=(7,1)
- (j,j)=(2,4)
- Djkmax2
- =_3179.54_

_**Example of 2D MRA**_

## Binomial Distribution as a Baseline Fluctuation

**We need to define a degree of the anomaly quantitatively with a familiar statistical language.**
**Suppose that we have *****m***** charged tracks and *****n***** ********-clusters in our total detector acceptance in a given event. If we distribute them independently into the acceptance, the asymmetry found in a given subdivided phase space must follow asymmetry based on binomial distributions.**
**We apply 2-D MRA to those simple binomial samples.**
**We can get correspondence between Djkmax****2**** and probability to exclude the binomial sample.**

**#charge:100,  #gamma-like:100**

**[Djkmax****2****]**

## Correlation between Charged Tracks and Gamma-like Clusters

**uncorrected**

**uncorrected**

## Maximum Deviation Size (Djkmax2)

**0.044      0.088      0.175       0.350  :⊿η**** **

**uncorrected**

**⊿****Phi :   2.813°     **** ****5.625°****    ****11.25°   ****  ****22.50°  ****     ****45.00°**

**Data minimum bias in West Arm**

## 0.044      0.088      0.175       0.350  :⊿η 

**uncorrected**

**⊿****Phi :   2.813°     **** ****5.625°****    ****11.25°   ****  ****22.50°  ****     ****45.00°**

**Data minimum bias in East Arm**

**Red : Data**
**Black : Binomial**

**( # of charge > 1, # of gamma > 1 )**

## Maximum Deviation Size (Djkmax2)

**0.044      0.088      0.175       0.350  :⊿η**** **

**uncorrected**

**⊿****Phi :   2.813°     **** ****5.625°****    ****11.25°   ****  ****22.50°  ****     ****45.00°**

**HIJING minimum bias in West Arm**

_**Maximum Deviation Size (Djkmax**__**2**__**)**_

## 0.044      0.088      0.175       0.350  :⊿η 

**0.044      0.088      0.175       0.350  :⊿η**** **

**uncorrected**

**⊿****Phi :   2.813°     **** ****5.625°****    ****11.25°   ****  ****22.50°  ****     ****45.00°**

**HIJING minimum bias in East Arm**

**Blue : HIJING**
**Black : Binomial**

**( # of charge > 1, # of gamma > 1 )**

## Centauro Type (West)

**[eta]**

**[eta]**

**[phi]**

**[phi]**

**Djkmax****2 ****: 1.698**
**# of gamma-like : 10**
**# of charged : 55**

## Centauro Type (East)

**[eta]**

**[eta]**

**[phi]**

**[phi]**

**Djkmax****2 ****: 2.251**
**# of gamma-like : 2**
**# of charged : 49**

## Anti Centauro Type

**[eta]**

**[eta]**

**[phi]**

**[phi]**

**Djkmax****2 ****: -1.638**
**# of gamma-like : 36**
**# of charged : 28**

## Summary and Future Plan

**We have demonstrated two dimensional multi-resolution analysis on the asymmetry between the number of the charged tracks and γ-like clusters in the η-φ phase space.**** ****(See below)**
**More understanding of detector biases is necessary.**
**Set a reasonable significance level to define the degree of anomaly based on the physical models with normal fluctuations.**
**Count the anomalous events above the significance level.**
**Discuss the event characters of those events, if they are found.**