3 p Correlation at RHIC

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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

• 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?