高エネルギー重イオン衝突における時空発展とHBT効果

RHICにおける多粒子相関
森田健司 (早大理工)
RCNP研究会第2回 RHIC, SPSでの高エネルギー重イオン衝突実験の現象論的解析
Outline of this talk
 2p HBT
 Introduction – HBTでわかること
 理論的な予想と期待 – Hydrodynamical model, Phase transition
 実験事実 – kt dependece, Y dependence from RHIC experiment
 “HBT puzzle” – Why puzzle?
 “HBT puzzle” – 現状と展望
 3p HBT
 3体相関からわかること
 Experimental data (by STAR)
 Model Analysis
 Summary
HBT in R.H.I.C
Chaotic Source
r(x)
Rlong
Rside
k1
Symmetry of W.F.
KT
q=k1-k2
Rout
k2
Decomposing into qside, qout, qlong
Corresponding ‘Size’ Rside, Rout, Rlong
R.H.I.C. – Highly
Dynamical System
Collective Flow:
Meanings of Size Parameters
in LCMS
Chapman, Nix, Heinz, PRC52,2694 (’95)
Space-momentum correlation on transverse plane
• Transverse
*K.M. et al., PRC61,034904 (2000).
suppression at x<0
enhancement at x>0
KT=50 MeV
KT=500 MeV
Measured “size” decreases with kt
Theoretical Tool : Hydrodynamics
 v2
• Good Agreement with v2 by
assuming QGP and Hadronic
phase.
• Supporting early thermalization
(taken from PHENIX whitepaper)
 Spectra
• Consistent
with the
thermal picture
Best fit with Hydro+RQMD Model
Prediction: 1st order Phase Transition
Pratt (’86), Bertsch (’88)
1st order P.T. – Softenning of EoS
Cs2 = 0 at mixed phase
(P = Const)
No acceleration in
the mixed phase
Lifetime of the system is
prolonged
Prediction: HBT signal of QGP
Rischke and Gyulassy, NPA608,479 (1996)
• Scaling Hydrodynamics with Cylindrical Symmetry
• from 1st order P.T. to DT ~ 0.1Tc
• Box Profile
• HBT radii v.s. Initial Energy Density
Rout >> Rside
Long lifetime
caused by P.T.
実験事実
• pp result for 200A GeV.
• Similar to 130A GeV results.
• Excellent consistency among the
experiments.
• Strong kt dependence.
• Ro ~ Rs ~ Rl
• Ro/Rs ~ (or < 1)
実験事実 (2)
• No rapid change in the excitation
function
• Strong space-momentum correlation in
longitudinal direction
HBT from Conventional Hydro. Models
• STAR 130AGeV
(PRL87,082301 (’01))
• Heinz et al.: Scaling+1st order
(NPA702,269 (’02))
• Zschiesche et al.: Scaling+Crossover
(PRC65,064902 (’02))
• Morita et al.: 1storder, No Boost inv.
(PRC65,054904 (’02))
The RHIC HBT Puzzle
• Strong anisotropic flow – supports local equilibration
i.e. Hydrodynamic description is valid.
• Single particle – well described
by reasonable initial conditions
• HBT radii from hydrodynamics
Prediction – large Rout due to 1st order phase
transition, small Rside, large Rlong from lifetime
Experiment – Rout ~ Rside (even Rout < Rside!), smaller
Rlong and Rout, larger Rside
Hybrid model calculation?
• v2
and spectra - Best fit with Hydro+RQMD (hybrid) Model
Soff, Bass, Dumitru, PRL86, 3981 (’01)
• QGP+1st order P.T.+Scaling
• Hadron Phase – UrQMD
hydro only
hydro+hadronic rescatt
• Long-lived, Dissipative
Hadronic Phase Dominates
• Increase with KT
STAR
PHENIX
Hadron rescattering makes it
worse!
Lifetime of the system
• From experimental data
tf ~ 9 fm/c
Non-central HBT analysis:
Evolution of eccentricity – also indicate short (~9fm/c)
Lifetime
Lifetime in hydro : ~15fm/c
Phase transition?
• Origin of long lifetime of hydro. – 1st order phase transition
• Experimental data – many many indication of QGP (energy
density, jet quenching, v2, …)
No clear evidence of phase transition!
(Rapid change of observables, etc)
• Transport calculation – also supports strongly interacting high
density matter. (Lin,Ko, and Pal, Molnar and Gyulassy)
Problem – mixed and hadron phase?
• Crossover case – improve, but still fails to reproduce the
data.
• Modifying hadronic EoS
Chemical freeze-out (Hirano, ’02)
• Introducing chemical potential for each particle species
• Lifetime of fluid is reduced → Smaller Rlong, but fails Rout, Rside
Geometry?
• Positive x-t correlation
• Opaque source
(Lin,Ko and Pal, PRL89,152301,(’02))
(KM and Muroya, PTP111,93 (’04))
normal
opaque
Initial fluctuation and Continuous emission
Socolowski, Grassi, Hama, Kodama, PRL93, 182301 (’04)
1 random ev.
averaged (30)
Giving Smaller
Size!
Parametrization – Hint for the solution?
• Blast-Wave
(Retiere and Lisa, PRC70,044907 (’04))
T=106MeV, R=13fm, t=9fm/c, Dt=0.003fm/c
(Csanad et al., NPA742,80(’04))
T0=210MeV, t0=7fm/c, Dt=0fm/c
Rout (fm)
• Buda-Lund
√s = 130 GeV STAR
PHENIX
Retiere, Lisa
Csorgo et al
8
4
single freeze-out, positive <xt>
• Renk
( Renk., PRC70, 021903,(’04))
Not Boost-invariance,
(maybe) positive <xt>
Rside (fm)
(Broniowski et al., nucl-th/0212053)
8
4
Rlong (fm)
• Cracow
8
4
0.2
0.6
0.4
kT (GeV/c)
0.8
Summary (I)
• 実験結果 : Rs~Ro~Rl~ 6-7 fm
• 実験結果 : Strong space-momentum correlation
• 実験結果 : t ~ 9fm/c
• HBT puzzle – hydroの結果とは合わない
• 原因 – 相転移（以降）
• 他の測定量とはconsistent – 実験では”相転移”は見
えていない
• 打開へ向けて
more realistic EoS, Hadronic Stageの理解, Rescattering?
3p correlation – Measure of the chaoticity
(HBT Effect)
•2-body:
‘Measure’ : l
Coherent
Chaotic
Suffer from many effects (Longlived resonance, Coulomb int.,
etc...)
•3-body:
‘Measure’ :
=1 for chaotic source
Not affected by long-lived resonances
Analysis by STAR Col.
STAR Coll., PRL91,262301 (’03)
Extraction of w from r3(Q3)
Central
Mid-Central
Chaotic fraction e
Using Partial Coherent Model
e ~ 0.8
(80% of pions come from the chaotic
source)
but...
l = 0.91-0.97
from the above e
quadratic/quartic fit to extract w
lexp = 0.5 @ Central
Au+Au 130A GeV
Consistency ?
Strategy
Extracting l from C2 and w from C3 (r3)
• Assumption : dominant background
– long lived resonances
• r3 : function of C2 and C3
• “True” chaoticity – subtracting
contributions from the resonances
Parameter Tuning w.r.t. experimental data
• Parametrization of the C2 and the C3
Thermal model
ltrue
•
•
•
w
Applying models of particle production
Consistency check between l and w
How chaotic are the pion sources?
Extraction of l : long-lived resonances
Gyulassy and Padula, (1988), Heiselberg, (1996), Csorgo et al., (1996)
at q ~0, contributions from such resonances can be neglected.
dq : ~ 5-10 MeV in the experiment
→ G < 5 MeV
Estimate # of long-lived resonances – Statistical model
(up to S*(1385) )
Performing c2 fitting to particle ratio
Braun-Munziger et al., (1996,1999,2001)
Extraction of l : long-lived resonances (2)
• Particle ratio from stat. model – integrated w.r.t. momentum
• lexp – measured in each pt bin
Assumption : True chaoticity does not depend on particle momenta
Averaging lexp as
Then, Get ltrue using
Experimental Data
Extraction of w : How to?
- Constructing C2 and C3 consistent with the experiment
Simple model source function : Simultaneous emission, spherically symmetric source
“gauss”
“exp”
“cosh”
3-parameter c2 fitting to experimental data
Result : Au+Au@RHIC, STAR
• Themal fit : T=158±9 MeV, mB=36±6 MeV, c2/dof=2.4/5
• lexp = 0.57±0.06, ltrue = 0.93±0.08 (22% pions from long-lived resonances)
• minimum c2 : cosh
• R=15.2 fm, l=0.71, n=0.64
• w=0.872±0.097
Models
Heinz and Zhang, (1997), Nakamura and Seki, (2000)
e : Chaotic Fraction, a : Mean # of Coh. Sources (Poisson Dist.)
1. Partial Coherent
Note : 0 < e < 1
2. Multicoherent
3. Partial Multicoherent
Result : Partial Coherent
epc
From l
From l (×0.8)
From w
S+Pb
0.75±0.12
0.41±0.05*
0.14±0.24
Pb+Pb
(NA44)
Pb+Pb
(WA98)
0.84±0.11
0.53±0.04
---
---
0.58±0.05
0.51±0.12
RHIC
0.73±0.14
0.49±0.07
0.65±0.10
*×0.7
Result : Partial Multicoherent
Au+Au
l×0.8
e = 0.75±1.02
a = 0.77±7.08
No “Best fit” Solution
large e solution is excluded!
Summary (2)
• Develop simultaneous analysis framework of C2 and C3
• Applied to S+Pb@SPS, Pb+Pb@SPS, Au+Au@RHIC
• As system size and bombarding energy increase, the system
becomes close to a chaotic (thermalized) source
• Still large uncertainty (especially in l), but systematic behavior
seem to be appeared.
• From a multicoherent source picture of view, chaoticity in the small
system comes from chaotic background, while many “clusters” may be
formed in the large and high energy system.

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