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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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3 p correlation at rhic
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
motivation chaotic or coherent

‘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)

3 p correlation an alternative tool
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

analysis by star col

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
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
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
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
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
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 l true
Results of ltrue

lexp = 0.5 (STAR, PRL87,082301 (’01))

0.817 < l < 0.896

extraction of w correlation functions
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

q 3 dependence of r 3
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
Results
  • Model I and II
  • Model III

0 < e < 0.26

4.71 < a < 8.62

All models show partial coherent source

conclusion
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?
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