1. QM06, Shanghai, China, Nov 19 20061 Evidence of non-Gaussian tail in Pion Emission Source @ SPS: Sensitivity to source formation & emission duration Paul Chung SUNY Stony Brook NA49 Collaboration

2. QM06, Shanghai, China, Nov 19 2006 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. 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

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

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

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

8. QM06, Shanghai, China, Nov 19 2006 8 Imaging C 0 : 40 AGeV & 160 AGeV Difference at q Difference at r > 20 fm

9. QM06, Shanghai, China, Nov 19 2006 9 Imaging C x2 : 40 AGeV & 160 AGeV Negative Moment in q => Positive Moment in r

10. QM06, Shanghai, China, Nov 19 2006 10 Imaging C y2 : 40 AGeV & 160 AGeV Positive Moment in q => Negative Moment in r

11. QM06, Shanghai, China, Nov 19 2006 11 Fitting functions: Ellipsoid & 2-Src model Ellipsoid : S(x,y,z) = λ G(x,y,z) λ, R x, R y, R z 2-Src model : S 1 = λ s g s + λ l g l λ s, R xs, R ys, R zs, λ l, R xl, R yl, R zl S(x,y,z) = λ s 2 G s + λ l 2 G l + 2 λ s λ l G sl

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

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

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

15. QM06, Shanghai, China, Nov 19 2006 15 Interpretation of large space-time extents x-direction: R x /R y > 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

16. 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) R x /R y > 1 due to finite non-zero emission duration (2) tail in z related to source formation duration time ~ 10fm/c 3D HBT technique gives R x /R y =1 at low pT due to Gaussian shape assumption inability to describe non-Gaussian tail of source function.