RHICRHIC における多粒子相関における多粒子相関

森田健司 森田健司 (( 早大理工早大理工 )) 　　

RCNPRCNP 研究会 第研究会 第 22 回 回 RHIC, SPSRHIC, SPS での高エネルギー重イオン衝突実験の現象論的解析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 talkOutline of this talk 2 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

3 HBT

3体相関からわかること Experimental data (by STAR)

Model Analysis

Summary

HBT in R.H.I.CHBT in R.H.I.C

kk11

kk22

((xx))

q=kq=k11-k-k22

Decomposing into Decomposing into qqsideside, q, qoutout, q, qlonglong

Corresponding ‘Size’ Corresponding ‘Size’ RRsideside, R, Routout, R, Rlonglong

RRlonglong

RRsidesideRRoutout

KKTT

R.H.I.C. – Highly R.H.I.C. – Highly Dynamical SystemDynamical System

Collective Flow:Collective Flow:Symmetry of W.F.Symmetry of W.F.

Chaotic SourceChaotic Source

Meanings of Size ParametersMeanings of Size Parameters

in LCMSin LCMS

Chapman, Nix, Heinz, PRC52,2694 (’95)Chapman, Nix, Heinz, PRC52,2694 (’95)

Space-momentum correlation on transverse planeSpace-momentum correlation on transverse plane

• TransverseTransverse

suppression at suppression at x<0

enhancement at enhancement at x>0

KKTT=50 MeV=50 MeV KKTT=500 MeV=500 MeV

*K.M. et al., PRC61,034904 (2000).*K.M. et al., PRC61,034904 (2000).

Measured “size” decreases with kt

Theoretical Tool : HydrodynamicsTheoretical Tool : Hydrodynamics

(taken from PHENIX whitepaper)

• Good Agreement with v2 by assuming QGP and Hadronic phase.

• Supporting early thermalization

v2

Spectra• Consistent with the thermal picture

Best fit with Hydro+RQMD Model

Prediction: 1Prediction: 1stst order Phase Transition order Phase Transition

11stst order P.T. – Softenning of EoS order P.T. – Softenning of EoS

CCss22 = 0 at mixed phase = 0 at mixed phase

(P = Const)(P = Const)

No acceleration in No acceleration in the mixed phasethe mixed phase

Pratt (’86), Bertsch (’88)Pratt (’86), Bertsch (’88)

Lifetime of the system is Lifetime of the system is prolongedprolonged

Prediction: HBT signal of QGPPrediction: HBT signal of QGP

Rischke and Gyulassy, NPA608,479 (1996)Rischke and Gyulassy, NPA608,479 (1996)

• Scaling Hydrodynamics with Cylindrical SymmetryScaling Hydrodynamics with Cylindrical Symmetry• from 1from 1stst order P.T. to order P.T. to T ~ 0.1TcT ~ 0.1Tc• Box ProfileBox Profile• HBT radii v.s. Initial Energy DensityHBT radii v.s. Initial Energy Density

RRoutout >> R >> Rsideside

Long lifetime Long lifetime

caused by P.T.caused by P.T.

実験事実実験事実

• 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. ModelsHBT from Conventional Hydro. Models

• STAR 130AGeV STAR 130AGeV (PRL87,082301 (’01))(PRL87,082301 (’01))

• Heinz et al.: Scaling+1Heinz et al.: Scaling+1stst order order

• Zschiesche et al.: Scaling+CrossoverZschiesche et al.: Scaling+Crossover

• Morita et al.: 1Morita et al.: 1ststorder, No Boost inv.order, No Boost inv.

(NPA702,269 (’02))(NPA702,269 (’02))

(PRC65,064902 (’02))(PRC65,064902 (’02))

(PRC65,054904 (’02))(PRC65,054904 (’02))

The RHIC HBT PuzzleThe RHIC HBT Puzzle

• Strong anisotropic flow – supports local equilibrationStrong anisotropic flow – supports local equilibration

i.e. Hydrodynamic description is i.e. Hydrodynamic description is valid.valid.

• HBT radii from hydrodynamicsHBT radii from hydrodynamics

PredictionPrediction – – large Rlarge Routout due to 1 due to 1stst order phase order phase transition, transition, small Rsmall Rsideside, , large Rlarge Rlonglong from lifetime from lifetime

ExperimentExperiment – R– Routout ~ R ~ Rsideside (even R (even Routout < R < Rsideside!), !), smaller Rsmaller Rlonglong and R and Routout, larger R, larger Rsideside

• Single particle – well Single particle – well describeddescribedby reasonable initial conditionsby reasonable initial conditions

Hybrid model calculation?Hybrid model calculation?

Soff, Bass, Dumitru, PRL86, 3981 (’01)Soff, Bass, Dumitru, PRL86, 3981 (’01)

• QGP+1QGP+1stst order P.T.+Scaling order P.T.+Scaling• Hadron Phase – UrQMDHadron Phase – UrQMD

• Long-lived, Dissipative HadroniLong-lived, Dissipative Hadronic Phase Dominatesc Phase Dominates

• Increase with Increase with KKTT

• v2 and spectra - Best fit with Hydro+RQMD (hybrid) Model

STARPHENIX

hydro onlyhydro+hadronic rescatt

Hadron rescattering makes it worse!

Lifetime of the system• From experimental data

f ~ 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)Chemical freeze-out (Hirano, ’02)

• Introducing chemical potential for each particle speciesIntroducing chemical potential for each particle species

• Lifetime of fluid is reduced → Smaller RLifetime of fluid is reduced → Smaller Rlong, long, but fails Rbut fails Routout, R, Rsideside

Geometry?• Positive x-t correlation (Lin,Ko and Pal, PRL89,152301,(’02))

• Opaque source (KM and Muroya, PTP111,93 (’04))

normal opaque

Initial fluctuation and Continuous emissionSocolowski, 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, =9fm/c, =0.003fm/c

• Buda-Lund (Csanad et al., NPA742,80(’04))

T0=210MeV, 0=7fm/c, =0fm/c

√s = 130 GeV STAR PHENIX

4

8

0.2 0.4 0.6 0.8kT (GeV/c)

4

8

4

8

Ro

ut (

fm)

Rsi

de (

fm)

Rlo

ng (

fm)

Retiere, LisaCsorgo et al

• Cracow (Broniowski et al., nucl-th/0212053)

single freeze-out, positive <xt>

• Renk ( Renk., PRC70, 021903,(’04))

Not Boost-invariance,

(maybe) positive <xt>

Summary (I)Summary (I)

• 実験結果実験結果 : : Rs~Ro~Rl~ 6-7 fmRs~Ro~Rl~ 6-7 fm

• 実験結果実験結果 : : Strong space-momentum correlationStrong space-momentum correlation

• 実験結果実験結果 : : ~ 9fm/c~ 9fm/c

• HBT puzzleHBT puzzle – hydro – hydro の結果とは合わないの結果とは合わない

• 原因 – 相転移（以降）原因 – 相転移（以降）

• 他の測定量とは他の測定量とは consistent – consistent – 実験では”相転移”は見実験では”相転移”は見えていないえていない

• 打開へ向けて打開へ向けてmore realistic EoS, Hadronic Stage の理解 , Rescattering?

33 correlation – Measure of the chaoticity correlation – Measure of the chaoticity

•2-2-body:body:

(HBT Effect)(HBT Effect)

‘Measure’ :

Suffer from many effects (Long-lived resonance, Coulomb int., etc...)Cohere

ntChaotic

•3-3-body:body:‘Measure’ :

Not affected by long-lived resonances

=1 for chaotic source

Analysis by STAR Col.Analysis by STAR Col.

quadratic/quartic fit to extract quadratic/quartic fit to extract

Extraction of from r3(Q3)

Chaotic fraction

Using Partial Coherent Model

STAR Coll., PRL91,262301 (’03)STAR Coll., PRL91,262301 (’03)

~ 0.8(80% of pions come from the chaotic source)

Central Mid-Central

but...

= 0.91-0.97

from the above exp = 0.5 @ Central Au+Au 130A GeV

Consistency ?

StrategyStrategyExtracting from C2 and from C3 (r3)

• Assumption : dominant background – long lived resonances

• “True” chaoticity – subtracting contributions from the resonances

Thermal model

true

• r3 : function of C2 and C3

• Parametrization of the C2 and the C3

Parameter Tuning w.r.t. experimental data

• Applying models of particle production• Consistency check between and • How chaotic are the pion sources?

Extraction ofExtraction of : long-lived : long-lived resonancesresonances

at at q q ~0, contributions from such resonances can be ~0, contributions from such resonances can be neglected.neglected.

Gyulassy and Padula, (1988), Heiselberg, (1996), Csorgo et al., (1996)Gyulassy and Padula, (1988), Heiselberg, (1996), Csorgo et al., (1996)

qq : : ~ ~ 5-10 MeV in the experiment5-10 MeV in the experiment

Estimate # of long-lived resonances – Statistical Estimate # of long-lived resonances – Statistical modelmodel

Braun-Munziger et al., (1996,1999,2001)Braun-Munziger et al., (1996,1999,2001)

(up to *(1385) )

→ < 5 MeV

Performing 2 fitting to particle ratio

Extraction ofExtraction of : long-lived : long-lived resonances (2)resonances (2)• Particle ratio from stat. model – integrated w.r.t. momentum

• exp – measured in each pt bin

Assumption : True chaoticity does not depend on particle momenta

Averaging exp as

Then, Get true using Experimental Data

Extraction of Extraction of : How to? : How to? - Constructing C2 and C3 consistent with the experiment

Simple model source function : Simultaneous emission, spherically symmetric source

“gauss”

“exp”

“cosh”

3-parameter 2 fitting to experimental data

• Themal fit : T=158±9 MeV, B=36±6 MeV, 2/dof=2.4/5

• exp = 0.57±0.06,true = 0.93±0.08 (22% pions from long-lived resonances)

Result : Au+Au@RHIC, STARResult : Au+Au@RHIC, STAR

• minimum 2 : cosh

• R=15.2 fm, =0.71, =0.64

• =0.872±0.097

ModelModelssChaotic FractionChaotic FractionMean # of Coh. Sources (Poisson Dist.)Mean # of Coh. Sources (Poisson Dist.)

Heinz and Zhang, (1997), Nakamura and Seki, (2000)Heinz and Zhang, (1997), Nakamura and Seki, (2000)

NoteNote : 0 < : 0 < < < 11

1. Partial Coherent

2. Multicoherent

3.3. Partial MulticoherentPartial Multicoherent

Result : Partial CoherentResult : Partial Coherent

pc From From (×0.8) From

S+Pb 0.75±0.12 0.41±0.05* 0.14±0.24

Pb+Pb (NA44)

0.84±0.11 0.53±0.04 ---

Pb+Pb (WA98)

--- 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 MulticoherentResult : Partial Multicoherent Au+Au

×0.8

= 0.75±1.02

= 0.77±7.08

No “Best fit” Solution

large solution is excluded!

Summary (2)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 ), 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.