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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

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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

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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]

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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

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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

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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 ?

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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

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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

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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

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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

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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

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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

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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

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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

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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

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

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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

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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

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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

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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 …

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

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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.

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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

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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

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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

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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

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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

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

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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

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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

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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

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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

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