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Study of Fluctuations on Isospin Symmetry in Au+Au Collisions at RHIC-PHENIX

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Study of Fluctuations on Isospin Symmetry in Au+Au Collisions at RHIC-PHENIX

Tomoaki Nakamura / Kensuke Homma

Hiroshima Univ.

for the PHENIX Collaboration

Tomoaki Nakamura Hiroshima Univ.

- Physics Motivation
- PHENIX Experiment
- Multi Resolution Analysis (MRA)
- Result
- Summary

Tomoaki Nakamura Hiroshima Univ.

Anti Centauro

(High Energy 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)
(High Energy Accerarator Experiment)

- (UA5) K. Alpgard rt al., Phys. Lett. 115B, 71 (1982)
- (CDF) P.L.Melese for the CDF Collaboration XIth Topical Workshop on ppbar Collider Physics (1996)
- (MINIMAX)T.C.Brooks et al., Phys. Rev. D 55, 5667 (1997)
(High Energy Heavy Ion Experiment)

- (WA98)Tapan K. Nayak et al., Nucl.Phys.A663:745-748, (2000)

O : Photon, + : Charged Particle

Tomoaki Nakamura Hiroshima Univ.

V

V

π

π

σ

σ

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

Restoration

Quench

QCD vacuum

DCC

Fluctuation of Asymmetry as a function of pseudo rapidity

Chiral Transformation

Linear sigma model

Tomoaki Nakamura Hiroshima Univ.

Rejected EMCal Cluster

Associated PC3 Cluster

PC1 Cluster

BBC Z-Vertex

Z

Using Magnetic Field-off data

Gamma like Cluster (EMC)

Charged Track (PC1, PC3)

Pad Chamber 1 (PC1)

Pad Chamber 2 (PC2)

Lead Grass Electro-Magnetic Calorimeter (EMC)

Tomoaki Nakamura Hiroshima Univ.

(Real Data)

(MC with Full Reconstruction)

Tomoaki Nakamura Hiroshima Univ.

Domain Size

δAI3

Deviation Size

Domain Position

pseudo rapidity

Tomoaki Nakamura Hiroshima Univ.

Levelj-1: 2j-1bins

Levelj : 2jbins

φ(x)

0.7

Scaling function

x

1

φ(2x)

1

φ(2x-1)

(＋)

-0.7

＝

1

x

1

x

ψ(x)

(－)

-1

0.7

-1

Wavelet function

x

φ(2x)= 1/√2 {φ(x)+ψ(x)}

φ(2x-1)= 1/√2 {φ(x)- ψ(x)}

-0.7

Tomoaki Nakamura Hiroshima Univ.

Signal

j=4

22

20

φ

ψ

Cjk

Djk

j=3

+

j=2

+

j=1

+

j=0

+

k

k

j : resolution level

k : k-th bin in pseudo rapidity

Cjk : coefficients of φ

Djk : coefficients of ψ

j → Domain Size

k → Phase Space Position

Djk → Deviation Size

Tomoaki Nakamura Hiroshima Univ.

j=5

Δη=0.0219

j=4

Δη=0.0438

j=3

Δη=0.0875

j=2

Δη=0.1750

j=1

Δη=0.3500

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

[Djk max]

Red : Real Data PHENIXB-field off data √sNN =130GeV Selected 44,180 events from minimum bias 700k events.

Blue : MC with Full reconstructionHIJING √sNN =130GeV Selected 25,281 events from minimum bias 200k events

Tomoaki Nakamura Hiroshima Univ.

Djk Max (J=5) (Nch = 10, Nγ=10)

99.95% exclude

99.98% exclude

99.999% exclude

[Djk max]

Binomial Distribution

Tomoaki Nakamura Hiroshima Univ.

Asymmetry (-) Asymmetry (+)

PC1

PC1

j=5Δη=0.0219

Phi [rad]

Phi [rad]

PC3

PC3

Z [cm]

Z [cm]

Phi [rad]

Phi [rad]

Z [cm]

Z [cm]

EMC

EMC

Phi [rad]

Phi [rad]

Z [cm]

Z [cm]

Tomoaki Nakamura Hiroshima Univ.

PC1

PC1

j=4Δη=0.0438

j=3Δη=0.0875

Phi [rad]

Phi [rad]

PC3

PC3

Z [cm]

Z [cm]

Phi [rad]

Phi [rad]

Z [cm]

Z [cm]

EMC

EMC

Phi [rad]

Phi [rad]

Z [cm]

Z [cm]

Tomoaki Nakamura Hiroshima Univ.

PC1

PC1

j=2Δη=0.1750

j=1Δη=0.3500

Phi [rad]

Phi [rad]

PC3

PC3

Z [cm]

Z [cm]

Phi [rad]

Phi [rad]

Z [cm]

Z [cm]

EMC

EMC

Phi [rad]

Phi [rad]

Z [cm]

Z [cm]

Tomoaki Nakamura Hiroshima Univ.

j=5 Δη=0.0219

j=4 Δη=0.0438

j=3 Δη=0.0875

j=2 Δη=0.1750

j=1 Δη=0.3500

[GeV]

Total Energy of Electro-Magnetic Calorimeter

Tomoaki Nakamura Hiroshima Univ.

(# of anomalous events) / (selected total # of events) : 153 / 44,180

- The total 155 anomalous events are found by MRA. The definition of “anomalous events” is the events above thresholds which exclude 99.999% of normal events, if those normal events are based on combination of the binominal distributions.
- We are investigating the nature of the events with large deviation from binomial, whether those are coming from PHYSICS or detector.

Tomoaki Nakamura Hiroshima Univ.

Tomoaki Nakamura Hiroshima Univ.

PC1

PC1

j=1Δη=0.3500

Raw Cluster

Phi [rad]

Phi [rad]

PC3

PC3

Z [cm]

Z [cm]

Phi [rad]

Phi [rad]

Z [cm]

Z [cm]

EMC

EMC

Phi [rad]

Phi [rad]

Z [cm]

Z [cm]

Tomoaki Nakamura Hiroshima Univ.

associated PC3 cluster

PC3 cluster

PC1 cluster

associated PC1 cluster

Z

Z

Rejected EMC cluster

BBC-Zvertex

Tomoaki Nakamura Hiroshima Univ.

A symmetric structure

appears in wrong level

Shift the start bin at each

resolution level.

Find djk max among all of levels.

This can determine the level

(domain size) with the largest

deviation size.

djk is lower

should appear here !

Tomoaki Nakamura Hiroshima Univ.

Success probability that a correct domain size is found

Domain size

of 28 / 2j

j=1

j=2

j=3

j=4

j=5

j=6

j=7

Deviation size Ns

Tomoaki Nakamura Hiroshima Univ.