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/

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-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

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/  ~ 0.8 (80% of pions come from the chaotic source) CentralMid-Central but... = from the above  exp = Central Au+Au 130A GeV Consistency ?

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

Models Heinz and Zhang, PRC56, 426(’97), Nakamura and Seki, PRC61, (’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)

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 

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!

Correction for long-lived resonances Statistical model T = ,  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,  ’ 

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

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

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  :

Results Model I and II Model IModel II From <  pc < <  m < 8.62 From  <  pc < <  m < 9.91 Model III 0 <  < <  < 8.62 All models show partial coherent source

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 Not fully chaotic but small coherence still 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?