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WPCF07, Sonoma, California, August 2 20071 Observation of Extended Pion Sources in Relativistic Heavy Ion Collisions: extraction of source breakup time.

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Presentation on theme: "WPCF07, Sonoma, California, August 2 20071 Observation of Extended Pion Sources in Relativistic Heavy Ion Collisions: extraction of source breakup time."— Presentation transcript:

1 WPCF07, Sonoma, California, August 2 20071 Observation of Extended Pion Sources in Relativistic Heavy Ion Collisions: extraction of source breakup time & emission duration Paul Chung SUNY Stony Brook NA49 Collaboration

2 WPCF07, Sonoma, California, August 2 2007 2  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 compared to 3D HBT Long range structure in pion source @ RHIC

3 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

4 WPCF07, Sonoma, California, August 2 2007 4 Technique Devised by: D. Brown, P. Danielewicz, PLB 398:252 (1997). PRC 57:2474 (1998). Inversion of Linear integral equation to obtain source function Source function (Distribution of pair separations) Encodes FSI Correlationfunction Inversion of this integral equation ==  Source Function Emitting source 1D Koonin Pratt Eqn. Extracted S(r) in pair CM frame Hence Model-independent i.e Kernel independent of freeze-out conditions No Shape assumption for S(r)

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

6 WPCF07, Sonoma, California, August 2 2007 6 3D Analysis (3) 3D Koonin Pratt Plug in (1) and (2) into (3) (1) (2) Expansion of R(q) and S(r) in Cartesian Harmonic basis Basis of Analysis (Danielewicz and Pratt nucl-th/0501003 (v1) 2005) X=out-direction Y=side-direction Z=long-direction

7 WPCF07, Sonoma, California, August 2 2007 7 Fitting functions: Ellipsoid & 2-Gaussian Ellipsoid : S(x,y,z) = λ G(x,y,z) λ, R x, R y, R z 2-Gaussian : S(x,y,z) = λ G s. G l G s - spherically symmetric Gaussian R 0 G l - 3D Gaussian R xl, R yl, R zl f s = 1/( 1 + (r/r 0 ) 2 ) f l = (r/r 0 ) 2 /( 1 + (r/r 0 ) 2 )

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

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

10 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)

11 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

12 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 v t constant Includes all known resonance decays Emission from infinitely long cylinder transverse radius ρ max : 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

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

14 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)

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