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3 p Correlation at RHIC Reference : nucl-th/0310057 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 ) Introduction Models Effect of long-lived resonances on the 2 p correlation Q 3 dependence of the 3 p correlation Results Summary ‘Measure’ : chaoticity l “HBT Puzzle” HBT Effect
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3p Correlation at RHIC Reference : nucl-th/0310057 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) • Introduction • Models • Effect of long-lived resonances on the 2p correlation • Q3 dependence of the 3p correlation • Results • Summary
‘Measure’ : chaoticity l “HBT Puzzle” HBT Effect Coherent Chaotic (=random relative phase) affected by other effects (Long-lived resonance, Coulomb int., etc...) Motivation – Chaotic or Coherent? (Local) equilibrium? / Exotic phenomena? Intensity Correlation as a ‘Measure’ • 2-body: Chaoticity of the source and Information on geometry (size)
3p Correlation : An Alternative Tool • 3-body: Chaoticity and asymmetry of the source ‘Measure’ : weight factor =1 for chaotic source in experiments Not affected by long-lived resonances
but... l = 0.91-0.97 from the above e lexp = 0.5 @ Central Au+Au 130A GeV Consistency ? Analysis by STAR Col. STAR Coll., nucl-ex/0306028 Extraction of w from r3(Q3) Chaotic fraction e Central Mid-Central Using Partial Coherent Model e ~ 0.8 (80% of pions come from the chaotic source) quadratic/quartic fit to extract w
In this work... • Check consistency of 2p and 3p correlations • 3 partial coherent source model -distinguish production mechanism ? • 2p correlation – Correction for long-lived resonance decays • Q3 dependence of r3
Models Heinz and Zhang, PRC56, 426(’97), Nakamura and Seki, PRC61, 054905 (’00) Model I : Partial Coherent Parameter: chaotic fractionepc epc Note : 0 < epc < 1 1-epc Parameter: mean # of coh. sources am Model II : Multicoherent (Poisson Distribution) Each of the models contains single parameter only.
Models (contd) Model III : Partial Multicoherent Parameter: two parameters e : Chaotic Fraction, a : Mean # of Coh. Sources (Poisson Dist.) Note : 0 < e < 1 l w Consistent determination of e and a from l and w
Apparent reduction of l by long-lived resonances Gyulassy and Padula, PLB217,181 (’88), Heiselberg, PLB379,27 (’96), Csorgo et al., Z.Phys.C71, 491 (’96) x : p production point Semi-classical description: average on lifetime t Experimental resolution ofq : ~ 5 MeV Resonances with larger G cannot be resolved!
Correction for long-lived resonances Need : Estimation of # of long-lived resonances Statistical model Ks0, h, h’, f, L, S, X (up to S*(1385) ) T=160-180 , mB = 40-50, mS = 9, mI3 = -1 [MeV] Cleymans and Redlich (1999), Broniowski and Florkowski (2001), Braun-Munziger et al., (2001)
Results of ltrue lexp = 0.5 (STAR, PRL87,082301 (’01)) 0.817 < l < 0.896
Extraction of w : Correlation functions r3(Q3)/2 : Constructed from C2(Qij) and C3(Q3) Need to establish functional form of C2 and C3 to obtain r3(0)/2 fit with
Q3 dependence of r3 Experiment : decrease with Q32 Chaotic Source : ~1 at small Q32 increase at large Q32 due to projection Decrease with Q3 – coherent components must exist Value of w : 0.873 - 0.892
Results • Model I and II • Model III 0 < e < 0.26 4.71 < a < 8.62 All models show partial coherent source
Conclusion • 2- and 3- pion Correlation – Degree of Coherence. • 3-type of Source Models. • Correction for Long-Lived Resonance Decays. • @RHIC: Not fully chaotic but small coherence still exists. • All of models gives the consistent result. • Future Problem: • As a function of multiplicity • Distinction among models?