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RHIC における多粒子相関

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. 2 p 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?

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RHIC における多粒子相関

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  1. 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

  2. Outline of this talk • 2pHBT • 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

  3. Rlong Collective Flow: KT q=k1-k2 Rside Rout Decomposing into qside, qout, qlong Corresponding ‘Size’ Rside, Rout, Rlong HBT in R.H.I.C Chaotic Source k1 R.H.I.C. – Highly Dynamical System r(x) Symmetry of W.F. k2

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

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

  6. 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

  7. 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

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

  9. 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)

  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)) • Heinz et al.: Scaling+1st order • Zschiesche et al.: Scaling+Crossover • Morita et al.: 1storder, No Boost inv. (NPA702,269 (’02)) (PRC65,064902 (’02)) (PRC65,054904 (’02))

  12. Single particle – well described by reasonable initial conditions The RHIC HBT Puzzle • Strong anisotropic flow – supports local equilibration i.e. Hydrodynamic description is valid. • 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

  13. hydro only hydro+hadronic rescatt STAR PHENIX 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 • Long-lived, Dissipative Hadronic Phase Dominates • Increase with KT Hadron rescattering makes it worse!

  14. 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

  15. 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)

  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 • Lifetime of fluid is reduced → Smaller Rlong, but fails Rout, Rside

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

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

  19. √s = 130 GeV STAR PHENIX Retiere, Lisa Rout (fm) 8 Csorgo et al 4 8 Rside (fm) 4 Rlong (fm) 8 4 0.8 0.6 0.4 0.2 kT (GeV/c) Parametrization – Hint for the solution? • Blast-Wave (Retiere and Lisa, PRC70,044907 (’04)) T=106MeV, R=13fm, t=9fm/c, Dt=0.003fm/c • Buda-Lund (Csanad et al., NPA742,80(’04)) T0=210MeV, t0=7fm/c, Dt=0fm/c • Cracow (Broniowski et al., nucl-th/0212053) single freeze-out, positive <xt> • Renk ( Renk., PRC70, 021903,(’04)) Not Boost-invariance, (maybe) positive <xt>

  20. 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?

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

  22. 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., PRL91,262301 (’03) 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

  23. Strategy Extracting l from C2 and w from C3 (r3) • Assumption : dominant background – long lived resonances • “True” chaoticity – subtracting contributions from the resonances • r3 : function of C2 and C3 • Parametrization of the C2 and the C3 • Parameter Tuning w.r.t. experimental data Thermal model w ltrue • Applying models of particle production • Consistency check betweenl andw • How chaotic are the pion sources?

  24. Extraction ofl: 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)

  25. Extraction ofl: 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

  26. 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-parameterc2 fitting to experimental data

  27. 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

  28. Models Heinz and Zhang, (1997), Nakamura and Seki, (2000) e : Chaotic Fraction, a : Mean # of Coh. Sources (Poisson Dist.) • Partial Coherent • Multicoherent • Partial Multicoherent Note : 0 < e < 1

  29. Result : Partial Coherent *×0.7

  30. 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!

  31. 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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