1. RHIC における多粒子相関 森田健司 ( 早大理工 ) 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

2. Outline 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

3. HBT in R.H.I.C k1k1k1k1 k2k2k2k2 (x)(x)(x)(x) q=k 1 -k 2 Decomposing into q side, q out, q long Corresponding ‘Size’ R side, R out, R long R long R side R out KTKTKTKT R.H.I.C. – Highly Dynamical System Collective Flow: Symmetry of W.F. Chaotic Source

4. Meanings of Size Parameters in LCMS Chapman, Nix, Heinz, PRC52,2694 (’95)

5. Space-momentum correlation on transverse plane Transverse Transverse suppression at suppression at x<0 enhancement at enhancement at x>0 K T =50 MeV K T =500 MeV *K.M. et al., PRC61,034904 (2000). Measured “size” decreases with k t

6. Theoretical Tool : Hydrodynamics (taken from PHENIX whitepaper) Good Agreement with v 2 by assuming QGP and Hadronic phase. Supporting early thermalization v 2 Spectra Consistent with the thermal picture Best fit with Hydro+RQMD Model

7. Prediction: 1 st order Phase Transition 1 st order P.T. – Softenning of EoS C s 2 = 0 at mixed phase (P = Const) No acceleration in the mixed phase Pratt (’86), Bertsch (’88) Lifetime of the system is prolonged

8. Prediction: HBT signal of QGP Rischke and Gyulassy, NPA608,479 (1996) Scaling Hydrodynamics with Cylindrical Symmetry Scaling Hydrodynamics with Cylindrical Symmetry from 1 st order P.T. to  T ~ 0.1Tc from 1 st order P.T. to  T ~ 0.1Tc Box Profile Box Profile HBT radii v.s. Initial Energy Density HBT radii v.s. Initial Energy Density R out >> R side Long lifetime caused by P.T.

9. 実験事実  result for 200A GeV. Similar to 130A GeV results. Excellent consistency among the experiments. Strong k t dependence. Ro ~ Rs ~ R l Ro/Rs ~ (or < 1)

10. 実験事実 (2) No rapid change in the excitation function Strong space-momentum correlation in longitudinal direction

11. HBT from Conventional Hydro. Models STAR 130AGeV (PRL87,082301 (’01)) STAR 130AGeV (PRL87,082301 (’01)) Heinz et al.: Scaling+1 st order Heinz et al.: Scaling+1 st order Zschiesche et al.: Scaling+Crossover Zschiesche et al.: Scaling+Crossover Morita et al.: 1 st order, No Boost inv. Morita et al.: 1 st order, No Boost inv. (NPA702,269 (’02)) (PRC65,064902 (’02)) (PRC65,054904 (’02))

12. The RHIC HBT Puzzle Strong anisotropic flow – supports local equilibration Strong anisotropic flow – supports local equilibration i.e. Hydrodynamic description is valid. HBT radii from hydrodynamics HBT radii from hydrodynamics Prediction – large R out due to 1 st order phase transition, small R side, large R long from lifetime Experiment – R out ~ R side (even R out < R side !), smaller R long and R out, larger R side Single particle – well described Single particle – well described by reasonable initial conditions

13. Hybrid model calculation? Soff, Bass, Dumitru, PRL86, 3981 (’01) QGP+1 st order P.T.+Scaling QGP+1 st order P.T.+Scaling Hadron Phase – UrQMD Hadron Phase – UrQMD Long-lived, Dissipative Hadronic Phase Dominates Long-lived, Dissipative Hadronic Phase Dominates Increase with K T Increase with K T v2 and spectra - Best fit with Hydro+RQMD (hybrid) Model STAR PHENIX hydro only hydro+hadronic rescatt Hadron rescattering makes it worse!

14. 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

15. Phase transition? Origin of long lifetime of hydro. – 1 st 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)

16. 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 Introducing chemical potential for each particle species Lifetime of fluid is reduced → Smaller R long, but fails R out, R side Lifetime of fluid is reduced → Smaller R long, but fails R out, R side

17. Geometry? Positive x-t correlation (Lin,Ko and Pal, PRL89,152301,(’02)) Opaque source (KM and Muroya, PTP111,93 (’04)) normal opaque

18. Initial fluctuation and Continuous emission Socolowski, Grassi, Hama, Kodama, PRL93, 182301 (’04) 1 random ev.averaged (30) Giving Smaller Size!

19. 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)) T 0 =210MeV,  0 =7fm/c,  =0fm/c √s = 130 GeVSTAR PHENIX 4 8 0.2 0.4 0.6 0.8 k T (GeV/c) 4 8 4 8 R out (fm) R side (fm) R long (fm) Retiere, Lisa Csorgo et al Cracow (Broniowski et al., nucl-th/0212053) single freeze-out, positive Renk ( Renk., PRC70, 021903,(’04)) Not Boost-invariance, (maybe) positive

20. Summary (I) 実験結果 : Rs~Ro~Rl~ 6-7 fm 実験結果 : Rs~Ro~Rl~ 6-7 fm 実験結果 : Strong space-momentum correlation 実験結果 : Strong space-momentum correlation 実験結果 :  ~ 9fm/c 実験結果 :  ~ 9fm/c HBT puzzle – hydro の結果とは合わない HBT puzzle – hydro 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 consistent – 実験では ” 相転移 ” は見えて いない 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 打開へ向けて more realistic EoS, Hadronic Stage の理解, Rescattering?

21. 3  correlation – Measure of the chaoticity 3  correlation – Measure of the chaoticity 2-body:2-body: (HBT Effect) ‘Measure’ :  Suffer from many effects (Long- lived resonance, Coulomb int., etc...) CoherentChaotic 3-body:3-body: ‘Measure’ : Not affected by long-lived resonances =1 for chaotic source

22. Analysis by STAR Col. quadratic/quartic fit to extract  Extraction of  from r 3 (Q 3 )Chaotic fraction  Using Partial Coherent Model STAR Coll., PRL91,262301 (’03)  ~ 0.8 (80% of pions come from the chaotic source) CentralMid-Central but... = 0.91-0.97 from the above  exp = 0.5 @ Central Au+Au 130A GeV Consistency ?

23. Strategy Extracting from C 2 and  from C 3 (r 3 ) Assumption : dominant background – long lived resonances “True” chaoticity – subtracting contributions from the resonances Thermal model true r 3 : function of C 2 and C 3 Parametrization of the C 2 and the C 3 Parameter Tuning w.r.t. experimental data  Applying models of particle production Consistency check between  and  How chaotic are the pion sources?

24. Extraction of : long-lived resonances at q ~0, contributions from such resonances can be neglected. Gyulassy and Padula, (1988), Heiselberg, (1996), Csorgo et al., (1996)  q : ~ 5-10 MeV in the experiment Estimate # of long-lived resonances – Statistical model Braun-Munziger et al., (1996,1999,2001) (up to  *(1385) ) →  < 5 MeV Performing  2 fitting to particle ratio

25. Extraction of : long-lived resonances (2) Particle ratio from stat. model – integrated w.r.t. momentum exp – measured in each p t bin Assumption : True chaoticity does not depend on particle momenta Averaging exp as Then, Get true using Experimental Data

26. Extraction of  : How to? - Constructing C 2 and C 3 consistent with the experiment Simple model source function : Simultaneous emission, spherically symmetric source “ gauss ” “ exp ” “ cosh ” 3-parameter  2 fitting to experimental data

27. 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, STAR minimum  2 : cosh R=15.2 fm, =0.71, =0.64  =0.872±0.097

28. Models  Chaotic Fraction  Mean # of Coh. Sources (Poisson Dist.) Heinz and Zhang, (1997), Nakamura and Seki, (2000) Note : 0 <  < 1 1.Partial Coherent 2.Multicoherent 3.Partial Multicoherent

29. Result : Partial Coherent  pc From From (×0.8) From  S+Pb 0.75 ± 0.120.41 ± 0.05 * 0.14 ± 0.24 Pb+Pb (NA44) 0.84 ± 0.110.53 ± 0.04 --- Pb+Pb (WA98) --- 0.58 ± 0.050.51 ± 0.12 RHIC0.73±0.140.49±0.070.65±0.10 *×0.7

30. Result : Partial Multicoherent Au+Au × 0.8  = 0.75±1.02  = 0.77±7.08 No “Best fit” Solution large  solution is excluded!

31. Summary (2) Develop simultaneous analysis framework of C 2 and C 3 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.