1. 3  Correlation at RHIC 森田健司 ( 早大理工 ) 室谷心 ( 徳山女子短大 ) 中村博樹 ( 早大理工 ) 1.Introduction 2.Models 3.Effect of long-lived resonances on the 2  correlation 4.Q 3 dependence of the 3  correlation 5.Results 6.Summary Reference : nucl-th/0310057

2. 2-body:2-body: (Local) equilibrium? / Exotic phenomena? Intensity Correlation as a ‘Measure’ Motivation – Chaotic or Coherent? “HBT Puzzle” affected by other effects (Long-lived resonance, Coulomb int., etc...) HBT Effect ‘Measure’ : chaoticity  CoherentChaotic (=random relative phase) Chaoticity of the source and Information on geometry (size)

3. 3-body:3-body: ‘Measure’ : =1 for chaotic source 3  Correlation : An Alternative Tool in experiments weight factor Chaoticity and asymmetry of the source Not affected by long-lived resonances

4. Analysis by STAR Col. quadratic/quartic fit to extract  Extraction of  from r 3 (Q 3 )Chaotic fraction  Using Partial Coherent Model STAR Coll., nucl-ex/0306028  ~ 0.8 (80% of pions come from the chaotic source) CentralMid-Central but... = 0.91-0.97 from the above  exp = 0.5 @ Central Au+Au 130A GeV Consistency ?

5. In this work... Check consistency of 2  and 3  correlations 3 partial coherent source model -distinguish production mechanism ? 2  correlation – Correction for long-lived resonance decays Q 3 dependence of r 3

6. Models Heinz and Zhang, PRC56, 426(’97), Nakamura and Seki, PRC61, 054905 (’00) Note : 0 <  pc < 1 Each of the models contains single parameter only. Model I : Partial Coherent Parameter: chaotic fraction  pc  pc  pc Model II : Multicoherent Parameter: mean # of coh. sources  m (Poisson Distribution)

7. Models (contd)  Chaotic Fraction  Mean # of Coh. Sources (Poisson Dist.) Note : 0 <  < 1 Model III : Partial Multicoherent Parameter:two parameters  Consistent determination of  and  from and 

8. Apparent reduction of by long-lived resonances :  production point x :  production point Semi-classical description: Gyulassy and Padula, PLB217,181 (’88), Heiselberg, PLB379,27 (’96), Csorgo et al., Z.Phys.C71, 491 (’96) average on lifetime  Experimental resolution of q : ~ 5 MeV Resonances with larger  cannot be resolved!

9. Correction for long-lived resonances Statistical model T =160-180,  B = 40-50,  S = 9,  I3 = -1 [MeV] Cleymans and Redlich (1999), Broniowski and Florkowski (2001), Braun-Munziger et al., (2001) (up to  *(1385) ) Need : Estimation of # of long-lived resonances K s 0,  ’ 

10. Results of true (T,  ) [MeV] eff true (160,40)0.6120.817 (170,45)0.5830.857 (180,50)0.5580.896 exp = 0.5 (STAR, PRL87,082301 (’01)) 0.817 <  < 0.896

11. Extraction of  : Correlation functions r 3 (Q 3 )/2 : Constructed from C 2 (Q ij ) and C 3 (Q 3 ) Need to establish functional form of C 2 and C 3 to obtain r3(0)/2 fit with

12. Q 3 dependence of r 3 Experiment : decrease with Q 3 2 Chaotic Source : ~1 at small Q 3 2 increase at large Q 3 2 Decrease with Q 3 – coherent components must exist due to projection Value of  : 0.873 - 0.892

13. Results Model I and II Model IModel II From 0.572 <  pc < 0.6784.46 <  m < 8.62 From  0.648 <  pc < 0.6807.70 <  m < 9.91 Model III 0 <  < 0.26 4.71 <  < 8.62 All models show partial coherent source

14. Conclusion 2- and 3- pion Correlation – Degree of Coherence. 2- and 3- pion Correlation – Degree of Coherence. 3-type of Source Models. 3-type of Source Models. Correction for Long-Lived Resonance Decays. Correction for Long-Lived Resonance Decays. @RHIC: Not fully chaotic but small coherence still exists. @RHIC: Not fully chaotic but small coherence still exists. All of models gives the consistent result. All of models gives the consistent result. Future Problem: Future Problem:  As a function of multiplicity  Distinction among models?