1. Search for Centauro Events at RHIC-PHENIX Kensuke Homma / Tomoaki Nakamura for the PHENIX Collaboration Hiroshima University Contents History of Centauro Search Search Strategy Observable and Analysis Method Analysis Results Summary and Future Plan

2. Centauro / Anti Centauro Event Cosmic ray experiments 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 an anomalous domain based on isospin symmetry.

3. List of Centauro Searches ExperimentCollaborationCM EnergySearch Region (η,φ) 1980Mt. Chacaltaya Brazil-Japan √s ≧ 1.7 TeV ------------ 1992BalloonJACEE------------5.0<η<9.0 ⊿ φ<2π 1982SPPSUA5√s=540 GeV|η|<5.0 1983SPPSUA1√s=540 GeV|η|<3.1 1986SPPSUA5√s=900 GeV|η|<5.0 1996TEVATRONCDF√s=1.8 TeV |η|<4.2,, ⊿ φ<2π 1997TEVATRONMINIMAX√s=1.8 TeV3.4<η<4.2 1998SPSWA98√s=3.5 TeV (Pb+Pb)2.80<η< 3.75 ⊿ φ<π 2001RHICPHENIX√s=39.4 TeV (Run2 Au+Au) |η| < 0.35 ⊿ φ<1/2π (×2 arm)

4. PHENIX Experiment at Run2 Using Magnetic Field-off data Gamma-like Cluster (Electro-Magnetic Calorimeter) Charged Track (BBC Z-Vertex, Drift Chamber and Pad Chamber1) |η| < 0.35 ⊿ φ < π/2 in each arm

5. Disoriented Chiral Condensate Quench Mechanism K.Rajagopal and F.Wilczek : Nucl. Phys. B379, 395 (1993) Chiral transformation Linear sigma model quench σ π V σ π V restoration QCD vacuum DCC Chiral symmetry breaking term due to finite masses

6. 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 the simple statistical treatment.

7. We search for a most largely deviated domain per event by looking at differences between number of charged and gamma 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. For example, we want to pick up this domain. We must do this search in several million events.

8. Observables Define an asymmetry between number of charged tracks and neutral clusters in event-by-event base as a function of subdivided  -  phase spaces normalized by one standard deviation for a given multiplicity class. δA I3 Domain Size Deviation Size Domain Position η,φ Domain size and domain position of largely deviated regions can be obtained at the same time by using Multi Resolution Analysis (MRA) technique.

9. Multi Resolution Analysis (MRA) Wavelet function Scaling function Level j-1 : 2 j-1 binsLevel j : 2 j bins φ(2x) = 1/√2 {φ(x) + ψ(x) } φ(2x-1) = 1/√2 {φ(x) - ψ(x) } -0.7 ＝ (－)(－) (＋)(＋) 0.7 φ(x) 0.7 ψ(x) x x 1 1 φ(2x-1) x 1 1 φ(2x) x -0.7 Total number of bins is 2 j Level j represents a resolution level

10. Signal Decomposition j : resolution level k : k-th bin Cjk : coefficients of φ Djk : coefficients of ψ Signal φψ kk + + + + 2 2020 j=4 j=3 j=2 j=1 j=0 Cjk Djk 2 4 /2 j → Domain Size k → Domain Position Cjk → Deviation Size Djk → used to pick up k Look for a maximum Djk per event

11. Quiz Where is an anomalous domain? What is the domain size? Pink dots are distributed around 0 based on Gaussian (mean=0,  =1.0) over 2 8 bins. A single domain is hidden with Gaussian (mean=N ,  =1.0)

12. Answers N  =3 j=5 N  =2 j=4 N  =1 j=3 N  =0.5 j=2

13. 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: A I3 = ~20 x 8bins ( ,  )=(3, 7) (j , j  )=(3, 2) A B Result:Correct ( ,  )=(3,7) (j ,j  )=(3,2) Result:Wrong ( ,  )=(7,1) (j ,j  )=(2,4) Example of 2-D MRA by Djkmax Select a domain with larger Djkmax in the second projection

14. Data Analysis (East Arm) Magnetic Field-off Minimum bias 818,507 events number of charged tracks > 0 number of photon-like clusters >0 Charged Track BBC Z-Vertex, Drift Chamber and Pad Chamber1 associated straight-line track Photon-like Cluster Cluster of Electro-Magnetic Calorimeter 1) Photon cluster shower shape 2) Time of flight of photon 3) Not associated with charged track 4) dead and hot channels are rejected Number of Selected Charged Track Number of Selected Photon-like Clusters [uncorrected]

15. Baseline fluctuations  Binomial sample Produce hit maps (2 8 x 2 8 bins in  ) per short run segment for  clusters and charged tracks respectively from real data to reproduce inefficient area of the detector as realistic as possible. Randomly distribute  clusters and charged tracks to all  space, but if there is no entry in the hit map, discard the cluster or track until # of accepted clusters and tracks coincide with those observed in a given real event.     Map for charged tracks Map for  clusters

16. W/O hit map With hit map Example of binomial distribution  DC component of Nch-N  per event is subtracted in advance before the 2D MRA. This gives almost symmetric shape in the maximum deviation distribution, even if the slope in the correlation plot is different from one, unless a given hit map biases partial phase space. (Nch, N  )=(200,100)

17. Maximum Deviation Size Maximum Deviation Size (A.U.) PHENIX magnetic field-off data Au+Au 200 GeV 818,507 events East Arm [uncorrected] Binomial sample with hit map 100 times larger statistics using same multiplicity-set

18. Level-by-Level Deviation Size ⊿ η: 0.044 0.088 0.175 0.350 ⊿ φ : 2.813° 5.625° 11.25° 22.50° 45.00° [East Arm, uncorrected] -1.0 -0.5 0 0.5 1.0 -- Data --Binomial

19. Positive Deviation (Centauro Type) pseudo rapidity :η azimuthal angle :φ[rad] ⊿ η=0.175 ⊿ φ=22.5 pseudo rapidity :η azimuthal angle :φ[rad] ＋ : charged track = 46 ○ : photon-like cluster = 0

20. 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. Detector biases will be more rigorously studied. We will set a reasonably tight significance level to define the degree of anomaly based on realistic physical models with normal fluctuations. We will measure signal to background ratios above the significance level. We will discuss characters of those events such as centrality dependence and azimuthal correlation with respect to reaction plane.

21. Back up slides

22. Centrality Determination Event characterization in terms of impact parameter (b) in Au+Au collisions. –Large : peripheral collision –Small : central collision Coincidence between BBC and ZDC. –Determine collision centrality. –92 % of inelastic cross section can be seen. Extract variables using Glauber Model –Number of participants (N_part). Number of nucleons participate in a collision. Represents centrality. Related with soft physics. –Number of binary collisions (N_binary). Number of Nucleon-Nucleon collisions. Related with hard physics. Incoherent sum of N-N collisions becomes a baseline for A-A collisions. peripheralcentral BBC Charge Sum ZDC Total Energy b to ZDC spectator participant to BBC Central Arm

23. Normalization per centrality bin Number of Charged Tracks Number of Photon-like Clusters Centrality + Factor 10 0-10% 221.5 0.067 9 10-20% 158.3 0.079 8 20-30% 109.2 0.096 7 30-40% 72.36 0.118 6 40-50% 44.92 0.149 5 50-60% 25.88 0.196 4 60-70% 13.87 0.269 3 70-80% 7.744 0.360 2 80-90% 5.319 0.434 1 90-94% 4.223 0.487 Correlation between Nch vs. N  [uncorrected] Normalization factor per centrality

24. Centrality-by-Centrality Maximum Deviation Size -1.0 -0.5 0 0.5 1.0 Top 10% 100843 events 10-20% 101585 20-30% 98416 30-40% 98673 40-50% 98898 50-60% 98685 60-70% 92970 70-80% 68048 80-90% 42529 90-94% 5589 -1.0 -0.5 0 0.5 1.0 -- Data --Binomial