1. Hadron emission source functions measured by PHENIX Workshop on Particle Correlations and Fluctuations The University of Tokyo, Hongo, Japan, September 22, 2011 Oak Ridge National Laboratory Akitomo Enokizono 9/22/2011 A. Enokizono - WPCF2011 1

2. Outline Physics motivation Imaging procedure 1D and 3D source functions for charged pion 1D source function for charged kaon Experimental systematic uncertainties Theoretical descriptions Summary 9/22/2011 A. Enokizono - WPCF2011 2

3. Many reasons not to be a simple Gaussian Traditional HBT analyses assume the Gaussian source, but no reason for the emission source to be Gaussian, and more reasonable to expect the source is a non-Gaussian shape in relativistic heavy-ion collisions due to resonance decay, rescattering effect, time-dependent expansion etc… halo Core “Core-Halo” model Anomalou diffusion Normal diffusion Lavy type distribution 9/22/2011 A. Enokizono - WPCF2011 3 M. Csanád, T. Csörgő and M. Nagy hep-hp/0702032 Coulomb Strong FSI BEC p-p correlation function

4. Imaging correlation function is kernel which can be calculated from BEC and known final state interactions of pairs. is source function which represents the emission probability of pairs at r in the pair CM frame. D.A. Brown and P. Danielewicz, Phys. Rev. C 64, 014902 (2001) 9/22/2011 A. Enokizono - WPCF2011 4

5. Optimization (parameters) r max : Maximum r (minimum q) to be imaged. q scale =  /2Δr Image Restore 9/22/2011 A. Enokizono - WPCF2011 5

6. 1D source for charged pions The imaged source function deviate from the 3D angle averaged Gaussian source function at > 15-20 fm. Resonance (omega) effect?, Kinetic effect? PHENIX Au+Au 200GeV Phys. Rev. Lett. 98, 132301 (2007) 9/22/2011 A. Enokizono - WPCF2011 6

7. Centrality and momentum dependence of non-Gaussian Long components (R lr ) depend on both k T and centrality. Not consistent with a naïve assumption of omega resonance contribution. PHENIX Au+Au 200GeV Phys. Rev. Lett. 98, 132301 (2007) 9/22/2011 A. Enokizono - WPCF2011 7

8. Theoretical explanation (1) 9/22/2011 A. Enokizono - WPCF2011 8 D.A. Brown, R. Soltz, J. Newby, A. Kisiel Phys. Rev. C 76, 044906 (2007) It is hard to figure out the origin of non-Gaussian structure just by looking at 1-D space. Each component (e.g. life time, omega, kinetics. etc) seems to have different magnitude of contribution in the 3-D space.

9. Pion 3D source function Charged pion 3D S(r) is measured for the central Au+Au collision at 200GeV and compared with blast-wave model. A model calculation with resonance decay + a finite emission duration agrees with the experimental result. 9/22/2011 A. Enokizono - WPCF2011 9 PHENIX Au+Au 200GeV Phys. Rev. Lett. 100, 232301 (2008) Outwards Sidewards Longitudinal

10. 1D source for charged kaons The result is suggesting non-Gaussian structure in kaon emission function also. Experimental systematic errors are big… 9/22/2011 A. Enokizono - WPCF2011 10 PHENIX Au+Au 200GeV Phys. Rev. Lett. 103, 142301 (2009)

11. Experimental Uncertainties (1) Two track separation capability Significant at low-q (large r) region PID (e.g pion/kaon separation) Pion contamination into Kaon data is more significant Normalization factor (N) C2 = N*A/B is obtained from 3D Gaussian (core-halo) fit. Can avoid the uncertainty by imaging directly raw distributions (A. Kisiel & D.A Brown, Phys. Rev. C 80, 064911 (2009)) 9/22/2011 A. Enokizono - WPCF2011 11

12. Experimental Uncertainties (2) Momentum resolution: Real pair and background pair q distributions are smeared and enhance pairs in small-q. Z vertex resolution: Only background pairs are are affected by finite Zvertex. resolution for mixed event, and enchance pair in small-q. Central AuAu (~0.7mm), p+p (~2-3cm) Smeared/Unsmeard Num. of Pair 9/22/2011 A. Enokizono - WPCF2011 12

13. Theoretical explanation (2) The time dependent mean free path naturally creates non- Gaussian tails which depends on PID (largest for kaons - that have the smallest cross sections) M. Csanád, T. Csörgő and M. Nagy, hep-hp/0702032 9/22/2011 A. Enokizono - WPCF2011 13 The tail by hadronic rescattering reproduce the experimental non- Gaussian structure. (the Core- Core rescattering creates a significant non-Gaussian part)

14. Theoretical explanation (3) 9/22/2011 A. Enokizono - WPCF2011 14 Without hadronic scattering and decay With hadronic scattering and decay Without hadronic scattering and decay With hadronic scattering and decay Pion Kaon T. Hirano, WPCF2010

15. Summary PHENIX has measured 1D source function for charged pions, kasons and 3D source function for charged pions in Au+Au 200GeV Non-Gaussian tails are observed for both pions and kaons which still has a large experimental uncertainty Non-Gaussian tail is not simply explained by omega resonance decay only. Data are reasonably reproduced by hydro models with resonance decay + rescattering Need to be careful about the experimental systematic errors which is most significant at small q, i.e large r of the S(r). 9/22/2011 A. Enokizono - WPCF2011 15