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Paul Chung SUNY Stony Brook NA49 Collaboration

Evidence of non-Gaussian tail in Pion Emission Source @ SPS: Sensitivity to source formation & 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. Evidence of non-Gaussian tail in Pion Emission Source @ SPS:Sensitivity to source formation & emission duration Paul Chung SUNY Stony Brook NA49 Collaboration QM06, Shanghai, China, Nov 19 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 QM06, Shanghai, China, Nov 19 2006

  3. Outline • Probing origin of observed long range pion structure: scan energy range available at SPS • NA49 @ SPS : 20, 40, 80, 160 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 40 & 160GeV central (cen<7%) Pb+Pb evnts • 3D source function extraction: Moment Imaging & Fitting @40&160GeV • Source formation & emission duration link to source function shape QM06, Shanghai, China, Nov 19 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 QM06, Shanghai, China, Nov 19 2006

  5. 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) QM06, Shanghai, China, Nov 19 2006

  6. Correlation moments: 40AGeV Choice of low pT pairs exclude effect of Lorentz γ boost QM06, Shanghai, China, Nov 19 2006

  7. Correlation moments: 160AGeV QM06, Shanghai, China, Nov 19 2006

  8. Imaging C0 : 40 AGeV & 160 AGeV Difference at q < 10 MeV => Difference at r > 20 fm QM06, Shanghai, China, Nov 19 2006

  9. Imaging Cx2 : 40 AGeV & 160 AGeV Negative Moment in q => Positive Moment in r QM06, Shanghai, China, Nov 19 2006

  10. Imaging Cy2 : 40 AGeV & 160 AGeV Positive Moment in q => Negative Moment in r QM06, Shanghai, China, Nov 19 2006

  11. Fitting functions: Ellipsoid & 2-Src model • Ellipsoid : S(x,y,z) = λ G(x,y,z) λ , Rx , Ry , Rz • 2-Src model : S1 = λs gs + λl glλs , Rxs , Rys , Rzs , λl , Rxl , Ryl , Rzl S(x,y,z) = λs2 Gs + λl2 Gl + 2 λsλl Gsl QM06, Shanghai, China, Nov 19 2006

  12. 40AGeV – Ellipsoid & 2-Src Fit Ellipsoid shape represents data poorly Pair Fraction (2-Src Fit) = 0.292 => 12% increase QM06, Shanghai, China, Nov 19 2006

  13. 160AGeV – Ellipsoid & 2-Src Fit Ellipsoid shape describes data poorly Pair Fraction (2-Src Fit) = 0.28 => 40% increase QM06, Shanghai, China, Nov 19 2006

  14. 3D Image & Fit S(r): 40 & 160 AGeV rms Rz=11fm rms Rz=12fm rms Rx/Ry = 1.2±0.1 rms Rx/Ry = 1.3±0.1 Source Image & 2-Src Fit in good agreement Prominent non-Gaussian tails in z-direction @ both energies Non-Gaussian tail in x-direction @ 160GeV QM06, Shanghai, China, Nov 19 2006

  15. Interpretation of large space-time extents • x-direction: Rx/Ry > 1 => Finite non-zero pion emission duration => Measure of pion source emission lifetime • z-direction: rms pair separation = 12fm @ 160AGeV, 11fm @ 40AGeV Lorentz-contracted nuclear diameter = 1.5fm @ 160AGeV, 3fm @ 40AGeV => rms pair separation due to created pion source = 10.5fm @ 160AGeV, 8fm @ 40AGeV => rms spatial extent of source emission points due to nuclear passage (vel=c) => Measure of formation time of emission points = 10 fm/c @ 160AGeV , 8fm/c @ 40AGeV QM06, Shanghai, China, Nov 19 2006

  16. Conclusions • Low pT (0<pT<70MeV/c) pion moments in central 40 & 160 GeV Pb+Pb events : gradual evolution of deformations with beam energy (1) x-moment changes sign from 40 to 160 GeV (2) z-extension increases from 40 to 160GeV • Prominent non-Gaussian tails in source image along z @ 40 & 160GeV and along x @ 160GeV • Non-Gaussian tails in source images well described by a 2-Src fit model at 40 & 160 GeV • Interpretation of extracted space-time extents @ 160geV: (1) Rx/Ry > 1 due to finite non-zero emission duration (2) tail in z related to source formation duration time ~ 10fm/c • 3D HBT technique gives Rx/Ry =1 at low pT due to Gaussian shape assumption inability to describe non-Gaussian tail of source function. QM06, Shanghai, China, Nov 19 2006

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