1. Detailed HBT measurement with respect to Event plane and collision energy in Au+Au collisions Takafumi Niida for the PHENIX Collaboration University of Tsukuba Quark Matter 2012 in Washington,DC

2. T. Niida Quark Matter 2012, Aug.14, 2012 outline 2 Introduction of HBT Azimuthal HBT w.r.t v 2 plane Azimuthal HBT w.r.t v 3 plane Low energy at PHENIX Summary

3. T. Niida Quark Matter 2012, Aug.14, 2012 What is HBT ? Quantum interference between two identical particles Hadron HBT can measure the source size at freeze-out (not whole size but homogeneity region in expanding source) detector P(p 1 ) : Probability of detecting a particle P(p 1,p 2 ) : Probability of detecting pair particles 3 assuming gaussian source 〜 1/R C2C2 q [GeV/c]

4. T. Niida Quark Matter 2012, Aug.14, 2012 3D HBT radii “Out-Side-Long” system  Bertsch-Pratt parameterization Core-halo model  Particles in core are affected by coulomb interaction 4 R long : Longtudinal size R side : Transverse size R out : Transverse size + emission duration R os : Cross term between Out and Side detector R long R side R out Sliced view Beam

5. T. Niida Quark Matter 2012, Aug.14, 2012 centrality (%)  n = Measurement by PHENIX Detectors 5 05-5 ZDC/SMD  dN/d  RXN in: 1.5<|  |<2.8 & out: 1.0<|  |<1.5 MPC: 3.1<|  |<3.7 BBC: 3.0<|  |<3.9 CNT: |  |<0.35 ✰ PID by EMC&TOF ➫ charged π/K are selected ✰ Ψ n by forward detector RXN EMC TOF n=2 RXN n=3 RXN n=4 RXN n=2 MPC n=3 MPC R(q),M(q): relative momentum dist. for real and mixed pairs

6. T. Niida Quark Matter 2012, Aug.14, 2012 Azimuthal HBT w.r.t v 2 plane Final eccentricity can be measured by azimuthal HBT  It depends on initial eccentricity, pressure gradient, expansion time, and velocity profile, etc.  Good probe to investigate system evolution 6 Momentum anisotropy v 2 Initial spatial eccentricity v 2 Plane Δφ What is the final eccentricity ?

7. T. Niida Quark Matter 2012, Aug.14, 2012 Eccentricity at freeze-out ε final ≈ ε initial /2 for pion  Indicates that source expands to in-plane direction, and still elliptical shape  PHENIX and STAR results are consistent ε final ≈ ε initial for kaon  Kaon may freeze-out sooner than pion because of less cross section  Need to check the difference of m T between π/K? 7 ε final = ε initial @WPCF2011 Rs2Rs2 φ pair - Ψ 2 0π/2π R s,2 2 R s,0 2 PRC70, 044907 (2004) in-plane

8. T. Niida Quark Matter 2012, Aug.14, 2012 m T dependence of ε final ε final of pions increases with m T in most/mid-central collisions There is still difference between π/K for mid-central collisions even in same m T  Indicates sooner freeze-out time of K than π ? 8

9. T. Niida Quark Matter 2012, Aug.14, 2012 m T dependence of relative amplitude Relative amplitude of R out in 0-20% doesn’t depend on m T  Does it indicate emission duration between in-plane and out-of- plane is different at low m T ? 9 Geometric info.Temporal+Geom. in-plane out-of-plane

10. T. Niida Quark Matter 2012, Aug.14, 2012 Azimuthal HBT w.r.t v 3 plane Final triangularity could be observed by azimuthal HBT w.r.t v 3 plane(Ψ 3 ) if it exists at freeze-out  Related to initial triangularity, v 3, and expansion time, etc.  Detailed information on space-time evolution can be obtained 10 Initial spatial fluctuation (triangularity) Momentum anisotropy triangular flow v 3

11. T. Niida Quark Matter 2012, Aug.14, 2012 Centrality dependence of v 3 and ε 3 Weak centrality dependence of v 3 Initial ε 3 has centrality dependence 11 v 3 @ p T =1.1GeV/c PRL.107.252301 ε3ε3 ε2ε2 v3v3 v2v2 Npart Final ε 3 has any centrality dependence? S.Esumi @WPCF2011

12. T. Niida Quark Matter 2012, Aug.14, 2012 Azimuthal HBT radii w.r.t Ψ 3 R side is almost flat R out have a oscillation in most central collisions 12 Ψ3Ψ3 φ pair

13. T. Niida Quark Matter 2012, Aug.14, 2012 Comparison of 2 nd and 3 rd order component In 0-10%, R out have stronger oscillation for Ψ 2 and Ψ 3 than R side  Its oscillation indicates different emission duration between 0°/60° w.r.t Ψ 3 13 Average of radii is set to “10” or “5” for w.r.t Ψ 2 and w.r.t Ψ 3 Ψ2Ψ2 φ pair Ψ3Ψ3 Ψ2Ψ2 Ψ3Ψ3 Ψ2Ψ2 Ψ3Ψ3 Rside Rout

14. T. Niida Quark Matter 2012, Aug.14, 2012 Triangularity at freeze-out Relative amplitude is used to represent “triangularity” at freeze-out 14 Rs2Rs2 φ pair - Ψ 3 0π/32π/3 R s,3 2 R s,0 2 ✰ Triangular component at freeze-out seems to vanish for all centralities within systematic error

15. T. Niida Quark Matter 2012, Aug.14, 2012 v2v2 v3v3 v4v4 v 4 (Ψ 4 ) Spatial anisotropy by Blast wave model 15 ☞ Similar results with HBT Blast wave fit for spectra & v n  Parameters used in the model s 2 and s 3 correspond to final eccentricity and triangularity  s 2 increase with going to peripheral collisions  s 3 is almost zero T f : temperature at freeze-out ρ 0 : average velocity ρ n : anisotropic velocity s n : spatial anisotropy Initial vs Final spatial anisotropy Poster, Board #195 Sanshiro Mizuno

16. T. Niida Quark Matter 2012, Aug.14, 2012 Image of initial/final source shape 16

17. T. Niida Quark Matter 2012, Aug.14, 2012 Low energy at PHENIX No significant change beyond systematic error in 200GeV, 62GeV and 39GeV for centrality and m T dependence 17 200GeV 62GeV 39GeV

18. T. Niida Quark Matter 2012, Aug.14, 2012 Volume vs Multiplicity Product of 3D HBT radii shows the volume of homogeneity regions Consistent with global trends 18 Poster, Board #246 Alex Mwai

19. T. Niida Quark Matter 2012, Aug.14, 2012 Summary Azimuthal HBT radii w.r.t v 2 plane  Final eccentricity increases with increasing m T, but not enough to explain the difference between π/K ☛ Difference may indicate faster freeze-out of K due to less cross section  Relative amplitude of R out in 0-20% doesn’t depend on m T ☛ It may indicate the difference of emission duration between in-plane and out-of-plane Azimuthal HBT radii w.r.t v 3 plane  First measurement of final triangularity have been presented. It seems to vanish at freeze-out by expansion.  while Rout clearly has finite oscillation in most central collisions ☛ It may indicate the difference of emission duration between Δφ=0°/60° direction Low energy in Au+Au collisions  No significant change between 200, 62 and 39 [GeV]  Volume is consistent with global trends 19

20. T. Niida Quark Matter 2012, Aug.14, 2012 Thank you for your attention! 20 Japanese rice ball has just “triangular shape” !! Elliptical shape is minor …

21. T. Niida Quark Matter 2012, Aug.14, 2012 Back up 21

22. T. Niida Quark Matter 2012, Aug.14, 2012 Relative amplitude of HBT radii Relative amplitude is used to represent “triangularity” at freeze-out Relative amplitude of Rout increases with increasing Npart 22 Rμ2Rμ2 φ pair - Ψ 3 0π/32π/3 R μ,3 2 R μ,0 2 ✰ Triangular component at freeze- out seems to vanish for all centralities(within systematic error) Geometric info.Temporal+Geom.

23. T. Niida Quark Matter 2012, Aug.14, 2012 Higher harmonic event plane Initial density fluctuations cause higher harmonic flow v n Azimuthal distribution of emitted particles: 23    Ψ n : Higher harmonic event plane φ : Azimuthal angle of emitted particles

24. T. Niida Quark Matter 2012, Aug.14, 2012 Charged hadron v n at PHENIX v 2 increases with increasing centrality, but v3 doesn’t v 3 is comparable to v 2 in 0-10% v 4 has similar dependence to v 2 24 PRL.107.252301

25. T. Niida Quark Matter 2012, Aug.14, 2012 v 3 breaks degeneracy v 3 provides new constraint on hydro-model parameters  Glauber & 4πη/s=1 : works better  KLN & 4πη/s=2 : fails 25 V2V2 V3V3 PRL.107.252301

26. T. Niida Quark Matter 2012, Aug.14, 2012 Azimuthal HBT radii for kaons Observed oscillation for R side, R out, R os Final eccentricity is defined as ε final = 2R s,2 / R s,0  26 in-plane out-of- plane PRC70, 044907 (2004) @WPCF2011

27. T. Niida Quark Matter 2012, Aug.14, 2012 k T dependence of azimuthal pion HBT radii in 20-60% Oscillation can be seen in R s, R o, and R os for each kT regions 27

28. T. Niida Quark Matter 2012, Aug.14, 2012 k T dependence of azimuthal pion HBT radii in 0-20% 28

29. T. Niida Quark Matter 2012, Aug.14, 2012 Centrality / m T dependence have been measured for pions and kaons  No significant difference between both species 29 The past HBT Results for charged pions and kaons m T dependence centrality dependence

30. T. Niida Quark Matter 2012, Aug.14, 2012 Analysis method for HBT Correlation function  Ratio of real and mixed q-distribution of pairs q: relative momentum Correction of event plane resolution  U.Heinz et al, PRC66, 044903 (2002) Coulomb correction and Fitting  By Sinyukov‘s fit function  Including the effect of long lived resonance decay 30

31. T. Niida Quark Matter 2012, Aug.14, 2012 Azimuthal HBT radii for pions Observed oscillation for R side, R out, R os Rout in 0-10% has oscillation  Different emission duration between in-plane and out-of-plane? 31 out-of-plane in-plane

32. T. Niida Quark Matter 2012, Aug.14, 2012 Model predictions 32 S.Voloshin at QM11 T=100[MeV], ρ=r’ρ max (1+cos(nφ)) Blast-wave model AMPT Out Side S.Voloshin at QM11 Side Out Both models predict weak oscillation will be seen in R side and R out. n=2 n=3 Out-Side