Detailed HBT measurement with respect to Event plane and collision energy in Au+Au collisions

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

2. outline • Introduction of HBT • Azimuthal HBT w.r.t v2 plane • Azimuthal HBT w.r.tv3 plane • Low energy at PHENIX • Summary

3. What is HBT ? • Quantum interference between two identical particles • Hadron HBT can measure the source size at freeze-out (not whole size buthomogeneity region in expanding source) P(p1) : Probability of detecting a particle P(p1,p2) : Probability of detecting pair particles assuming gaussian source C2 detector 〜1/R detector q [GeV/c]

4. 3D HBT radii • “Out-Side-Long” system • Bertsch-Pratt parameterization • Core-halo model • Particles in core are affected by coulomb interaction Beam Rlong detector detector Sliced view Rside Rlong: Longtudinal size Rside: Transverse size Rout: Transverse size + emission duration Ros: Cross term between Out and Side Rout

5. Measurement by PHENIX Detectors CNT: |h|<0.35 n=2 RXN EMC n=3 RXN TOF n=4 RXN n=2 MPC n=3 MPC n = <cosn(n(meas.) - n(true))> RXN in: 1.5<|h|<2.8 & out: 1.0<|h|<1.5 dN/d MPC: 3.1<|h|<3.7 BBC: 3.0<|h|<3.9 ZDC/SMD R(q),M(q): relative momentum dist. for real and mixed pairs -5 0 5  centrality (%) • PID by EMC&TOF • charged π/K are selected • Ψnby forward detector RXN

6. v2 Plane Azimuthal HBT w.r.tv2 plane Initial spatial eccentricity • 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 Δφ Momentum anisotropyv2 What is the final eccentricity ?

7. Eccentricity at freeze-out @WPCF2011 PRC70, 044907 (2004) • εfinal≈ εinitial/2for pion • Indicates that source expands to in-plane direction, and still ellipticalshape • PHENIX and STAR results are consistent • εfinal≈ εinitialfor kaon • Kaon may freeze-out sooner than pion because of less cross section • Needto check the difference of mTbetween π/K? εfinal= εinitial in-plane Rs,22 Rs2 Rs,02 0 π/2 π φpair- Ψ2

8. mT dependence of εfinal • εfinal of pions increases with mT in most/mid-central collisions • There is still difference between π/K for mid-central collisions even in same mT • Indicates sooner freeze-out time of K than π ?

9. mT dependence of relative amplitude • Relative amplitude of Rout in 0-20% doesn’t depend on mT • Does it indicate emission duration between in-plane and out-of-plane is different at low mT? Geometric info. Temporal+Geom. out-of-plane Temporal+Geom. in-plane

10. Azimuthal HBT w.r.t v3 plane Initial spatial fluctuation(triangularity) Momentum anisotropytriangular flow v3 • Final triangularitycould be observed by azimuthal HBT w.r.t v3 plane(Ψ3) if it exists at freeze-out • Related to initial triangularity, v3, and expansion time, etc. • Detailed information on space-time evolution can be obtained

11. Centrality dependence of v3 and ε3 PRL.107.252301 • Weak centrality dependence of v3 • Initial ε3 has centrality dependence v3 @pT=1.1GeV/c S.Esumi @WPCF2011 ε2 ε3 v2 v3 🍙Finalε3 has any centrality dependence? Npart

12. Azimuthal HBT radii w.r.t Ψ3 • Rside is almost flat • Rout have a oscillation in most central collisions φpair Ψ3

13. Ψ2 Ψ2 Ψ2 Comparison of 2nd and 3rd order component • In0-10%, Rout have stronger oscillation for Ψ2 and Ψ3 than Rside • Its oscillationindicates different emission duration between 0°/60°w.r.t Ψ3 Average of radii is set to “10” or “5”for w.r.t Ψ2 and w.r.t Ψ3 Rout φpair φpair φpair Rside φpair φpair φpair Ψ3 Ψ3 Ψ3

14. Triangularity at freeze-out • Relative amplitude is used to represent “triangularity” at freeze-out Rs,32 Rs2 Rs,02 • Triangular component at freeze-out seems to vanish for all centralitieswithin systematic error 0 π/3 2π/3 φpair- Ψ3

15. Spatial anisotropy by Blast wave model • Blast wave fit for spectra & vn • Parameters used in the model • s2 and s3 correspond to final eccentricity and triangularity • s2 increase with going to peripheral collisions • s3 is almost zero Tf : temperature at freeze-out ρ0 : average velocity ρn: anisotropic velocity sn : spatial anisotropy v2 v3 v4 v4(Ψ4) Initial vs Final spatial anisotropy Poster, Board #195 SanshiroMizuno • Similar results with HBT

16. Image of initial/final source shape

17. Low energy at PHENIX 200GeV 62GeV • No significant change beyond systematic error in 200GeV, 62GeV and 39GeV for centrality and mT dependence 39GeV

18. Volume vs Multiplicity • Product of 3D HBT radii shows the volume of homogeneity regions • Consistent with global trends Poster, Board #246 Alex Mwai

19. Summary • Azimuthal HBT radii w.r.t v2 plane • Final eccentricity increases with increasing mT, 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 Rout in 0-20% doesn’t depend on mT • It may indicate the difference of emission duration between in-plane and out-of-plane • Azimuthal HBT radii w.r.t v3 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

20. Thank you for your attention! Japanese rice ball has just “triangular shape” !! Elliptical shape is minor …

21. Back up

22. Relative amplitude of HBT radii • Relative amplitude is used to represent “triangularity” at freeze-out • Relative amplitude of Rout increases with increasing Npart Geometric info. Temporal+Geom. Temporal+Geom. Rμ,32 Rμ2 Rμ,02 • Triangular component at freeze-outseems to vanish for all centralities(within systematic error) 0 π/3 2π/3 φpair- Ψ3

23. Higher harmonic event plane Ψ3 • Initial density fluctuations cause higher harmonic flow vn • Azimuthal distributionof emitted particles: Ψ2 Ψ4 Ψn: Higher harmonic event plane φ : Azimuthal angle of emitted particles

24. Charged hadron vn at PHENIX PRL.107.252301 • v2 increases with increasing centrality, but v3 doesn’t • v3 is comparable to v2 in 0-10% • v4 has similar dependence to v2

25. v3 breaks degeneracy PRL.107.252301 • v3 provides new constraint on hydro-model parameters • Glauber & 4πη/s=1 : works better • KLN & 4πη/s=2 : fails V2 V3

26. Azimuthal HBT radii for kaons • Observed oscillation for Rside, Rout, Ros • Final eccentricity is defined as εfinal= 2Rs,2 / Rs,0 PRC70, 044907 (2004) in-plane out-of-plane @WPCF2011

27. kT dependence of azimuthal pion HBT radii in 20-60% • Oscillation can be seen in Rs, Ro, and Rosfor each kT regions

28. kTdependence of azimuthal pion HBT radiiin 0-20%

29. The past HBT Results for charged pions and kaons • Centrality / mTdependence have been measured for pions and kaons • No significant difference between both species mT dependence centrality dependence

30. 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 correctionand Fitting • BySinyukov‘s fit function • Includingtheeffectoflonglivedresonancedecay

31. Azimuthal HBT radii for pions • Observed oscillation for Rside, Rout, Ros • Rout in 0-10% has oscillation • Different emission duration between in-plane and out-of-plane? out-of-plane in-plane

32. Model predictions Blast-wave model AMPT Out n=2 n=3 Side Out Side Out-Side S.Voloshin at QM11 T=100[MeV], ρ=r’ρmax(1+cos(nφ)) S.Voloshin at QM11 Both models predict weak oscillation will be seen in Rside and Rout.