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Paul Chung SUNY Stony Brook NA49 Collaboration

Observation of Extended Pion Sources in Relativistic Heavy Ion Collisions: extraction of source breakup time & emission duration. Paul Chung SUNY Stony Brook NA49 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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Paul Chung SUNY Stony Brook NA49 Collaboration

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  1. Observation of Extended Pion Sources in Relativistic Heavy Ion Collisions: extraction of source breakup time & emission duration Paul Chung SUNY Stony Brook NA49 Collaboration WPCF07, Sonoma, California, August 2 2007

  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 WPCF07, Sonoma, California, August 2 2007

  3. Outline • Probing origin of observed long range pion structure: scan energy range available at SPS • NA49 @ SPS : 30, 80, 158 AGeV Pb+Pb collisions • Overview of 3D source function shape analysis : Cartesian Spherical Harmonic decomposition & Imaging Technique • low pT (0<pT<70MeV) pion moments in 158 AGeV central (cen<7%) Pb+Pb evnts • 3D source function extraction: Moment Imaging & Fitting • Therminator model comparison - Source breakup time & emission duration extraction from 3D source function shape @ SPS & RHIC WPCF07, Sonoma, California, August 2 2007

  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 WPCF07, Sonoma, California, August 2 2007

  5. 158 AGeV -Angle-averaged C(q) & S(r) WPCF07, Sonoma, California, August 2 2007

  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) WPCF07, Sonoma, California, August 2 2007

  7. 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 - spherically symmetric Gaussian R0 Gl - 3D Gaussian Rxl , Ryl , Rzl fs = 1/( 1 + (r/r0)2 ) fl = (r/r0)2 /( 1 + (r/r0)2 ) WPCF07, Sonoma, California, August 2 2007

  8. 158AGeV – Ellipsoid & 2-Gaussian Fit Ellipsoid shape describes data poorly Pair Fraction (2-Gaus Fit) = 0.28 => 40% increase WPCF07, Sonoma, California, August 2 2007

  9. Ellipsoid & 2-Gaus. fit for all moments WPCF07, Sonoma, California, August 2 2007

  10. 158 AGeV - 3D C(q) & S(r) Non-Gaussian tails in x x-y assymetric indicates non-zero relative emission time in LCMS Long-range exponential-like Tail in longitudinal direction Signature of blast-wave dynamics S.Pratt PRD 33, 5, 1314 (1986) WPCF07, Sonoma, California, August 2 2007

  11. 30 & 80 AGeV – 3D S(r) Less prominent tails in z @ 30 and 80 AGeV 3D source essentially Gaussian WPCF07, Sonoma, California, August 2 2007

  12. Therminator model Event Generator • A.Kisiel et al. 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 : controls sideward extent • Proper breakup time in fluid element rest frame, tau : controls longitudinal extent • Modified by Kisiel to implement emission duration Δtau : controls tails in long and out directions WPCF07, Sonoma, California, August 2 2007

  13. Therminator model comparison WPCF07, Sonoma, California, August 2 2007

  14. Conclusions • First 3D source imaging analysis at SPS: Low pT (0<pT<70MeV/c) pion moments in central sqrt_s=17.3AGeV Pb+Pb events indicate: • Prominent non-Gaussian tails in source image in longitudinal and outward directions @ sqrt_s=17.3AGeV • Less prominent tails at lower beam energies • 3D source function well described by 2-Gaussian function in good agreement with source image • 3D source image at sqrt_s=17.3AGeV in agreement with Therminator Blast-Wave calculations with tau=7.3fm/c, Δtau=3.7fm/c • 3D source image at sqrt_s=200AGeV gives tau=8.5fm/c, Δtau=2fm/c • Exponential tail in long direction: (1) verification of details of 3D dynamics (2) critical signature of blast-wave dynamics for longitudinal flow Scott Pratt PRD 33, 5, 1314-1327 (1986) WPCF07, Sonoma, California, August 2 2007

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