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3D Pion Emission Sources from Au+Au collisions @ RHIC: probe of source breakup times

3D Pion Emission Sources from Au+Au collisions @ RHIC: probe of source breakup times. Paul Chung SUNY Stony Brook PHENIX Collaboration. Long range structure in pion source @ RHIC. PHENIX nucl-ex/0605032 1D Pion-Pion Correl Func Au+Au sqrt(s)=200AGeV

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3D Pion Emission Sources from Au+Au collisions @ RHIC: probe of source breakup times

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  1. 3D Pion Emission Sources from Au+Au collisions @ RHIC: probe of source breakup times Paul Chung SUNY Stony Brook PHENIX Collaboration SQM07, Levoca, Slovakia, June 27 2006

  2. Long range structure in pion source @ RHIC • PHENIX nucl-ex/0605032 • 1D Pion-Pion Correl Func • Au+Au sqrt(s)=200AGeV • Imaging source function vs 3D HBT source function • Discrepancy for r>20fm • Corresponds to q<10MeV • 30% more pions in tail above 3D HBT Gaussian source • 20% in <r> compared to 3D HBT SQM07, Levoca, Slovakia, June 27 2006

  3. Outline • Probing origin of observed 1D long range pion structure: 3D shape analysis of emission source function • Overview of 3D source function shape analysis : Cartesian Spherical Harmonic decomposition & Imaging Technique • low pT (0.2<pT<0.36 GeV) pion moments in central (cen<20%) Au+Au events @ 200 AGeV • 3D source function extraction: Moment Imaging & Fitting • Therminator event generator - Source breakup times extraction from 3D source function shape SQM07, Levoca, Slovakia, June 27 2006

  4. Emitting source Technique Devised by: D. Brown, P. Danielewicz, PLB 398:252 (1997).PRC 57:2474 (1998). Inversion of Linear integral equation to obtain source function 1D Koonin Pratt Eqn. Encodes FSI Source function (Distribution of pair separations) Correlation function No Shape assumption for S(r) Inversion of this integral equation == Source Function Extracted S(r) in pair CM frame Hence Model-independent i.e Kernel independent of freeze-out conditions SQM07, Levoca, Slovakia, June 27 2006

  5. Imaging Inversion procedure Expansion in B-spline basis Freezeout occurs after last scattering Hence only Coulomb & BE effect included in kernel SQM07, Levoca, Slovakia, June 27 2006

  6. 3D Analysis Basis of Analysis (Danielewicz and Pratt nucl-th/0501003 (v1) 2005) Expansion of R(q) and S(r) in Cartesian Harmonic basis X=out-direction Y=side-direction Z=long-direction 3D Koonin Pratt (3) Plug in (1) and (2) into (3) (1) (2) SQM07, Levoca, Slovakia, June 27 2006

  7. Moments restoredfrom Imaging • Moments decrease with increasing order for x, y and z : truncate at l=6 • Restored moments in good agreement with data moments : Imaging under control SQM07, Levoca, Slovakia, June 27 2006

  8. Fitting functions: Ellipsoid & 2-Gaussian • Ellipsoid : S(x,y,z) = λ G(x,y,z) λ , Rx , Ry , Rz • 2-Gaussian : S(x,y,z) = λ Gs . Gl Gs - 3D Gaussian Rxs , Rys , Rzs Gl - 3D Gaussian Rxl , Ryl , Rzl fs = 1/( 1 + (r/r0)2 ) fl = (r/r0)2 /( 1 + (r/r0)2 ) SQM07, Levoca, Slovakia, June 27 2006

  9. Ellipsoid & 2-Gaussian Fits 2-Gaussian shape provides better representation of data SQM07, Levoca, Slovakia, June 27 2006

  10. 2-Gaussian Fit: • All independent moments well reproduced by 2-Gaussian fit SQM07, Levoca, Slovakia, June 27 2006

  11. 3D C(q) & S(r) X-Y assymetry reflects non-zero Emission duration Long-range Exponential-like Tail in z direction: Signature of Blast-Wave dynamics S.Pratt PRD 33, 5, 1314 (1986) SQM07, Levoca, Slovakia, June 27 2006

  12. Therminator model Event Generator • Kisiel, Broniowski, Florkiowski Comput.Phys.Commun.174, 669 (2006) • Thermal model with Bjorken longitudinal expansion • Transverse Flow vt constant • Includes all known resonance decays • Emission from infinitely long cylinder transverse radius ρmax=8.92 fm – controls sideward extent • Single proper breakup time in fluid element rest frame, tau=8.55 fm/c – controls longitudinal extent SQM07, Levoca, Slovakia, June 27 2006

  13. Therminator model comparison SQM07, Levoca, Slovakia, June 27 2006

  14. Conclusions • First 3D pion source imaging analysis at RHIC: pion moments in central 200 AGeV Au+Au events indicate: • Prominent non-Gaussian tails in source image in longitudinal and outward directions • 3D source function well described by 2-Gaussian function in good agreement with source image • 3D source image in agreement with Therminator Blast- Wave calculations with transverse radius=8.92 fm, tau=8.55 fm/c, spread(tau)=2 fm/c • Exponential tail in long direction: (1) verifies details of 3D dynamics (2) critical signature of blast-wave dynamics for longitudinal flow first proposed by Scott Pratt PRD 33, 5, 1314-1327 (1986) SQM07, Levoca, Slovakia, June 27 2006

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