Measurement of Quantum Interference of Two Identical Particles with respect to the Event Plane in Relativistic Heavy Ion Collisions at RHIC-PHENIX

Transcription

1 Measurement of Quantum Interference of Two Identical Particles with respect to the Event Plane in Relativistic Heavy Ion Collisions at RHIC-PHENIX Takafumi Niida High Energy Nuclear Physics Group TAC seminar, Dec th /1

2 outline n Introduction ² HBT Interferometry ² Motivation n Analysis ² PHENIX Detectors ² Analysis Method n Results & Discussion ² HBT measurement with respect to nd -/3 rd -order event plane ² Blast-wave model n Summary Takafumi Niida, TAC seminar, Dec., 1

3 Introduction 3 Takafumi Niida, TAC seminar, Dec., 1

4 Quark Gluon Plasma (QGP) n State at a few µ-seconds after Big Bang n Quarks and gluons are reconfined from hadrons Introduction probably here from BNL web site Takafumi Niida, TAC seminar, Dec., 1 n QGP will be created at extreme temperature and energy density 4

5 Relativistic Heavy Ion Collisions Introduction Species/Energy Au+Au 13GeV Au+Au, p+p GeV d+au GeV, p+p GeV Au+Au, 6.4GeV Cu+Cu, 6.4,.4GeV p+p, 6.4GeV Au+Au GeV d+au, p+p GeV p+p, 5GeV Au+Au, 6.4, 39, 7.7GeV Au+Au, 7, 19.6GeV U+U 193GeV, Cu+Au GeV Energy density Lattice QCD calculation Tc ~ 17 MeV εc ~ 1 GeV/fm3 Au+Au εbj ~ 5 GeV/fm3 > εc Takafumi Niida, Year ² Brookhaven National Laboratory in U.S.A ² Two circular rings (3.8 km in circumstance) ² Various energies: 19.6, 7, 39, 6.4, GeV ² Various species: p+p, d+au, Cu+Cu, Cu+Au, Au+Au, U+U TAC seminar, Dec., 1 n Relativistic Heavy Ion Collider is an unique tool to create QGP.

6 Space-Time Evolution Introduction ω, ρ, φ γ jet π, K, p 5. Thermal freeze-out 4. Chemical freeze-out 3. Phase transition Hadronization. Partonic thermarization QGP state 1. Collision occurs Takafumi Niida, TAC seminar, Dec., 1 How fast the system thermalizes and evolves? How much the system size? What is the nature of phase transition? 6

7 HBT Interferometry Introduction n HBT effect is quantum interference between two identical particles. n R. Hanbury Brown and R. Twiss ² In 1956, they measured the angular diameter of Sirius. n Goldhaber et al. ² In 196, they observed the correlations among identical pions in p+anti-p collision independent of HBT. C = 1(p 1,p ) 1(p 1 ) (p ) G. Goldhaber, Proc. Int. Workshop on Correlations and Multiparticle production(1991) 1+ (q) =1 + exp( r q ) detector Takafumi Niida, TAC seminar, Dec., 1 1/Δr detector q=p 1 -p [GeV/c] 7

8 What does HBT radii depend on? Introduction n Centrality ² HBT radii depends on the size of collision area. n Average pair momentum k T ² Case of static source : measuring the whole size ² Case of expanding source : measuring homogeneity region ~ kt = 1 (~p T 1 + ~p T ) ~q out k ~ k T,~q side? ~ k T central collision pheripheral collision ~p T 1 ~p T 1 Takafumi Niida, TAC seminar, Dec., 1 low k T high k T ~p T ~p T 8

9 Comparison of models and the past HBT results PRL., 331(9) Introduction STAR, Au+Au GeV First-order phase transition with no prethermal flow, no viscosity Including initial flow Using stiffer equation of state Adding viscosity Including all features Takafumi Niida, TAC seminar, Dec., 1 Hydrodynamic model can reproduce the past HBT result! HBT can provide constraints on the model! 9

10 Introduction HBT with respect to Reaction Plane n Azimuthal HBT can give us the source shape at freeze-out. n Final eccentricity is determined by initial eccentricity, pressure gradient(velocity profile) and expansion time etc. Reaction Plane central STAR, PRL 93, 131 Takafumi Niida, TAC seminar, Dec., 1 /π π /π π φ - R.P [rad] peripheral

11 Higher Harmonic Flow and Event Plane Introduction Ψ 3 n Initial density fluctuations cause higher harmonic flow v n n Azimuthal distribution of emitted particles: dn d / 1+v cos( ) +v 3 cos3( 3) +v 4 cos4( 4) v n = hcosn( n)i Takafumi Niida, TAC seminar, Dec., 1 Ψ 4 Ψ v n : Strength of higher harmonic flow Ψ n : Higher harmonic event plane φ : Azimuthal angle of emitted particles 11

12 HBT vs Higher Harmonic Event Plane Introduction n The idea is to expand azimuthal HBT to higher harmonic event planes. ² may show the fluctuation of the shape at freeze-out. ² provide more constraints on theoretical models about the system evolution. Ψ 3 Hydrodynamic model calculation Takafumi Niida, TAC seminar, Dec., 1 S.Voloshin at QM11 T=[MeV], ρ=r ρ max (1+cos(nφ)) 1

13 Motivation Introduction n Study the properties of time-space evolution of the heavy ion collision via azimuthal HBT measurement. ² Measurement of charged pion/kaon HBT radii with respect to nd - order event plane, and Comparison of the particle species ² Measurement of HBT radii with respect to 3 rd -order event plane to reveal the detail of final state and system evolution. 13 Takafumi Niida, TAC seminar, Dec., 1

14 My Activity Introduction 6(M1) 7(M) 3 years later (D1) MRPC construction 11(D) Talk WPCF11 RXNP construction Installed MRPC&RXNP Azimuthal HBT analysis using Run4 data Talk JPS fall Summer Shift taking & Detector Expert for preliminary result Centrality dependence of π/k HBT w.r.t Ψ Talk JPS spring Talk HIC in LHC era Di-jet Calorimeter construction Summer 1(D3) Talk QM1 Shift Start azimuthal HBT analysis using Run7 data Summer Shift taking & Detector Expert for Poster Radon Workshop preliminary result Centrality dependence of π HBT w.r.t Ψ 3 Takafumi Niida, TAC seminar, Dec., 1 preliminary result m T dependence of π HBT w.r.t Ψ 14

15 Analysis 15 Takafumi Niida, TAC seminar, Dec., 1

16 PHENIX Experiment Analysis Beam line Takafumi Niida, TAC seminar, Dec., 1 16

17 PHENIX Detectors Beam-Beam Counter ( η =3~4) Quartz radiator+64pmts Zero Degree Calorimeter Spectator neutron energy Reaction Plane Detector ( η =1~.8) rings of 4 scintillators Central arms ( η <.35) DC, PCs, TOF, EMCAL South Analysis Minimum Bias Trigger Start time Collision z-position Centrality Event Planes Tracking, Momentum Paticle Identification beam line North Takafumi Niida, TAC seminar, Dec., 1 collision point 17

18 Centrality Analysis n Centrality is used to classify events instead of impact parameter. ² % to % central to peripheral collision n BBC measures charged particles coming from participant. peripheral central Participant Spectator Takafumi Niida, TAC seminar, Dec., 1 BBC charge sum Spectator 18

19 Event Plane Analysis <cos((ψ -Ψ r ))> 1.8 Resolution of Event Plane North+South North or South Centrality [%] beam axis n = 1 n arctan wi cos(n i ) w i sin(n i ) n Event plane was determined by Reaction Plane Detector φ i Ψ 3 ² Resolution: <cos(n(ψ n -Ψ real ))> n= : ~.75 n=3 : ~.34 Ψ Ψ 4 Takafumi Niida, TAC seminar, Dec., 1 19

20 Track Reconstruction Analysis Central Arms n Drift Chamber EMC α ² Momentum determination p T ' K n Pad Chamber (PC1) K: field integral α: incident angle ² Associate DC tracks with hit positions on PC1 n Outer detectors (PC3,TOF,EMCal) ² Extend the tracks to outer detectors Takafumi Niida, TAC seminar, Dec., 1 Drift Chamber Pad Chamber

21 Particle IDentification Analysis n EMC-PbSc is used. ² timing resolution ~ 6 ps n Time-Of-Flight method ct m = p 1! L p: momentum L: flight path length t: time of flight n Charged π/k within σ Mass square ² π/k separation up to ~1 GeV/c ² K/p separation up to ~1.6 GeV/c Particle Identification by PbSc-EMC K - K + π - π Momentum charge Takafumi Niida, TAC seminar, Dec., 1

22 Correlation Function Analysis n Experimental Correlation Function C is defined as: ² R(q): Real pairs at the same event. ² M(q): Mixed pairs selected from two different/similar events. C = R(q) M(q) q = p 1 p ² R(q) includes HBT effects, Coulomb interaction and detector inefficient effect, while M(q) doesn t include HBT, Coulomb R(q) M(q) Correlation function Takafumi Niida, TAC seminar, Dec., q inv qinv[gev/c]

23 3D HBT radii R side Analysis n Out-Side-Long system ² Bertsch-Pratt parameterization ² LCMS(Longitudinal Center of Mass System) frame is used. ~ kt = 1 (~p T 1 + ~p T ) C =1 + G =exp( G R invq inv) beam ~q out k ~ k T,~q side? ~ k T =exp( R sideq side R outq out R longq long R osq side q out ) λ : chaoticity R side : transverse size R out : transverse size + emission duration R os : cross term between out and side R long : longtudinal size R out R long Takafumi Niida, TAC seminar, Dec., 1 R out includes temporal information on emission duration of particles! 3

24 Pair Selection Analysis dφ[rad] n Ghost Tracks ² A single particle is reconstructed as two tracks n Merged Tracks ² Two particles is reconstructed as a single track Distance of pion pairs at DC 1 Real / Mixed Distance Ratio of of real pion and mixed pairs at EMC at EMC Removed Takafumi Niida, TAC seminar, Dec., 1 Removed dz[cm] dr[cm] dr[cm] 4

25 Coulomb Interaction Analysis n Coulomb repulsion for like-sign pairs reduces pairs at low-q. ² Estimated by Coulomb wave function apple ~ r µ + Z 1Z e (r) =E (r) r n The correction was applied in fit function for C ² Core-Halo model C =C core + C halo =N[ (1 + G)F coul ]+[1 ] F coul : Coulomb term G : Gaussian term 1. 1 = me ~ q Z 1Z C Fit function Coulomb strength Takafumi Niida, TAC seminar, Dec., q inv [GeV/c] 5

26 Analysis Correction of Event Plane Resolution n Smearing effect by finite resolution of the event plane Reaction Plane Event Plane Reaction Plane n Resolution correction ² correction for q-distribution PRC.66, 4493() A crr (q, j) =A uncrr (q, j) n,m = + n,m [A c cos(n j )+A s sin(n j )] n / sin(n /)hcos(n( m real))i event plane resolution ] [fm Rs true size measured size φ [rad] φ [rad] ] [fm Ro ] Ros [fm simulation φ [rad] φ [rad] ] [fm Rl φ [rad] original uncorrected corrected Takafumi Niida, TAC seminar, Dec., 1 6

27 Results & Discussion 7 Takafumi Niida, TAC seminar, Dec., 1

28 Results & Discussion Azimuthal HBT w.r.t nd order event plane Initial spatial eccentricity Momentum anisotropy v What is the final eccentricity? v Plane Δφ Takafumi Niida, TAC seminar, Dec., 1 8

29 Results & Discussion Centrality dependence of pion HBT radii w.r.t Ψ n Oscillation are seen for R side, R out, R os. n R out has strong oscillation in all centrality. ] [fm R s λ φ - Ψ [rad] ] [fm R o ] [fm R os φ - Ψ [rad] ] [fm R l φ - Ψ [rad] - - Au+Au GeV π + π + & π π < k T < [GeV/c] Takafumi Niida, TAC seminar, Dec., 1 -%. -% - -3% φ - Ψ [rad] φ - Ψ [rad] 3-6% 9

30 Results & Discussion Takafumi Niida, TAC seminar, Dec., 1 Centrality dependence of kaon HBT radii w.r.t Ψ n charged kaons also have similar trends! 3

31 Eccentricity at freeze-out Results & Discussion pion R s, kaon R s,n R s R s, π/ π φ pair - Ψ = R s,n (Δφ)cos(nΔφ) ε final = R s, R s, in-plane PRC7, 4497 (4) in-plane n ε final ε initial / for pion ² This Indicates that source expands to in-plane direction, and still elliptical shape. ² PHENIX and STAR results are consistent. n ε final ε initial for kaon ² Kaon may freeze-out sooner than pion because of less cross section. ² Due to the difference of m T between Takafumi Niida, TAC seminar, Dec., 1 31

32 m T dependence of ε final Results & Discussion m T = k T + m ε final PHENIX Preliminary Au+Au GeV π π +π π -% π π +π π -6% K + K + +K + + K K +K - K K -% -6% <m T > [GeV/c] n ε final of pions increases with m T in most/mid-central collisions Takafumi Niida, TAC seminar, Dec., 1 n Still difference between π/k in -6% even at the same m T ² Indicates sooner freeze-out time of K than π? 3

33 Results & Discussion m T dependence of relative amplitude.4 Rs, / Rs, -Ro, / Ro,.4 -Rl, / Rl, out-of-plane in-plane Ro, / Rs,.3..1 Geometric info. Temporal+Geom..3 Temporal+Geom. R os, / Rs, <m T > [GeV/c] <m T > [GeV/c] <m T > [GeV/c] PHENIX Preliminary Au+Au GeV - - π + π + +π π - - π + π + +π π K K +K K K K +K K -% -6% -% -6% Takafumi Niida, TAC seminar, Dec., 1 n Relative amplitude of R out in -% doesn t depend on m T ² Does it indicate the difference of emission duration between in-plane and out-of-plane at low m T? 33

34 Results & Discussion Azimuthal HBT w.r.t 3 rd order event plane Initial spatial fluctuation What is final shape? Ψ 3 expansion n Note that no anisotropy is observed by HBT in static source.? Takafumi Niida, TAC seminar, Dec., 1 34

35 Azimuthal HBT radii w.r.t Ψ 3 Results & Discussion ] [fm R s 5 ] [fm R o 5 ] [fm R l 5 φ pair Ψ 3 λ φ - Ψ φ - Ψ 3 n R side is almost flat [rad] [rad] ] [fm R os φ - Ψ φ - Ψ 3 [rad] [rad] n R out have a oscillation in most central collisions φ - Ψ 3 [rad] PHENIX Preliminary - - Au+Au GeV π + π + & π π -% -% -3% 3-6% Takafumi Niida, TAC seminar, Dec., 1 35

36 Results & Discussion Comparison of nd and 3 rd order component n In -%, R out have stronger oscillation for Ψ and Ψ 3 than R side ² This oscillation indicates different emission duration between /6 w.r.t Ψ 3? or depth of the triangular shape? Rout ] [fm R s φ - Ψ [rad] n φ pair Average of radii is set to or 5 for w.r.t Ψ and w.r.t Ψ 3 ] [fm R o φ - Ψ [rad] n φ pair Au+Au GeV -% - - π + π + +π π w.r.t Ψ w.r.t Ψ 3 Rside Takafumi Niida, TAC seminar, Dec., 1 Ψ Ψ 3 36

37 Relative amplitude of R side Results & Discussion n Relative amplitude of R side w.r.t Ψ 3 is zero within systematic error. R s, R s R s,3 π/3 π/3 φ pair - Ψ 3 ε n,final. ε 3.1 Au+Au GeV ε ε 3, final = R s,3 R s, ε n,initial Takafumi Niida, TAC seminar, Dec., 1 The width of the homogeneity seems to be the same between /6 w.r.t Ψ 3 unlike the depth(+emission duration). 37

38 Blast wave model Results & Discussion n Hydrodynamic model assuming radial flow ² Well described at low p T for spectra & elliptic flow ² Expand to HBT : PRC 7, 4497 (4) ² Physical parameters are treated as free parameters. 7 free parameters T f : temperature at freeze-out ρ, ρ : transverse rapidity (r, )= r[ + cos( )] R x, R y : transverse sizes (shape) τ, Δτ : system lifetime and emission duration dn ( d exp ) PRC 7, 4497 (4) Takafumi Niida, TAC seminar, Dec., 1 Assuming a Gaussian distribution peaked at τ and with a width Δτ,$ and source size doesn t change with τ. 38

39 Fit by Blast wave model 5 3 n Spectra and v are used to reduce parameters. 5 -% 3 5 -% 3 5 -% % Results & Discussion % -% % -3% pt[gev/c] 5 pt[gev/c] 5 pt[gev/c] 5 pt[gev/c] dphi[rad] 3-3% dphi[rad] 3 3-6% dphi[rad] dphi[rad] % dphi[rad] 3 dphi[rad] 3 dphi[rad] dphi[rad] 4. -%. -%. -% -% v & R side ρ, R x and R y R 1 out, R long, R os τ, Δτ R side %.5 3 R dphi[rad] 3 out %.5 3 R dphi[rad] 4 long %.5 3 R os R out and R os doesn t seem to be fitted well. 1 Need to plot 15 the systematic 15 error In this model, Δτ doesn t depend on azimuthal angle % dphi[rad] dphi[rad] 3-6% - -3 Specta T f and ρ dphi[rad] dphi[rad] dphi[rad] dphi[rad] 3-6% Takafumi Niida, TAC seminar, Dec., 1 39

40 Extracted freeze-out parameters Results & Discussion.3 Spectra fit Tf Rho.3 Rho v and Rs fit Rx <Npart> Ry/Rx <Npart> <Npart> Tau <Npart> <Npart> d_tau <Npart> <Npart> Ro, Rl, Ros fit Takafumi Niida, TAC seminar, Dec., 1 n Size(R x,r y ) and R y /R x seem to be valid. n τ and Δτ increases with going to centrality." 4

41 Summary n Azimuthal HBT radii w.r.t nd order event plane ² 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. ² Relative amplitude of R out in -% doesn t depend on m T. It may indicate the difference of emission duration between in-plane and out-of-plane. n Azimuthal HBT radii w.r.t 3 rd -order event plane ² R side doesn t seem to have azimuthal dependence. ² While R out clearly has finite oscillation in most central collisions. It may indicate the difference of emission duration between Δφ= /6 direction or depth of the triangular shape. n Balst wave model Takafumi Niida, TAC seminar, Dec., 1 ² System lifetime and emission duration seems to get longer in central collisions. 41

42 Back up 4 Takafumi Niida, TAC seminar, Dec., 1

43 Centrality dependence of v 3 and ε 3 PRL n Weak centrality dependence of v 3 n Initial ε 3 has centrality dependence ε ε 3 v p T =1.1GeV/c Takafumi Niida, TAC seminar, Dec., 1 Final ε 3 has any centrality dependence? v v 3 Npart 43

44 PHENIX Detectors Analysis EMC TOF RXN in: 1.5< η <.8 & out: 1.< η <1.5 MPC: 3.1< η <3.7 CNT: η <.35 dn/dη Takafumi Niida, TAC seminar, Dec., 1 BBC: 3.< η <3.9 ZDC/SMD -5 5 η 44

45 Takafumi Niida, TAC seminar, Dec., 1 Image of initial/final source shape 45

46 Spatial anisotropy by Blast wave model n Blast wave fit for spectra & v n ² Parameters used in the model T f : temperature at freeze-out ρ : average velocity ρ n : anisotropic velocity s n : spatial anisotropy ü s and s 3 correspond to final eccentricity and triangularity ² s increase with going to peripheral collisions ² s 3 is almost zero.3..1 s π + +π - - K + +K p+p.3 surface BW χ =95 spectra+v - 3% 1.5 spectra+v 3 1 spectra+v spectra+v ) 4 4 (Ψ v v 3.8 v 4 v 4 (Ψ 4 ).6.1 χ =456.1 χ =8 χ = Initial vs Final spatial anisotropy s 3 s 4. 1 radius integrated surface Takafumi Niida, TAC seminar, Dec., 1 Similar results with HBT.1..3 ε ε 3 ε 4 Poster, Board #195 Sanshiro Mizuno 46

47 Relative amplitude of HBT radii n Relative amplitude is used to represent triangularity at freeze-out n Relative amplitude of Rout increases with increasing Npart R µ, R µ R µ,3 π/3 π/3 φ pair - Ψ 3 Triangular component -R at o,3 / R freezes, out seems to vanish for all.1 centralities(within systematic error).1 Rs,3 / Rs, N part.1.1 Geometric info. -R R o,3 os,3 / R / R s, s, Temporal+Geom R -R o,3 / R / R o, l, N part.1 l,3 Temporal+Geom. s, PHENIX Ros,3 Preliminary / R Au+Au GeV Takafumi Niida, TAC seminar, Dec., N part - - π + π + +π π N part 47

48 Takafumi Niida, TAC seminar, Dec., 1 Charged hadron v n at PHENIX PRL n v increases with increasing centrality, but v3 doesn t n v 3 is comparable to v in -% n v 4 has similar dependence to v 48

49 v 3 breaks degeneracy f g.3 (a) p = GeV/c T (b) p T PRL = GeV/c v v PHENIX KLN + 4 πη/s = Glauber + 4πη/s = 1 (1) 3.1 (c) p = GeV/c T UrQMD + 4πη/s = Glauber + 4πη/s = 1 () 3 N part V V 3 3 (d) p = GeV/c T 3 N part Takafumi Niida, TAC seminar, Dec., 1 n v 3 provides new constraint on hydro-model parameters ² Glauber & 4πη/s=1 : works better ² KLN & 4πη/s= : fails 49

50 Azimuthal HBT radii for kaons n Observed oscillation for R side, R out, R os n Final eccentricity is defined as ε final = R s, / R s, ² R s,n = R s,n (Δφ)cos(nΔφ) PRC7, 4497 (4) in-plane out-ofplane Takafumi Niida, TAC seminar, Dec., 5

51 k T dependence of azimuthal pion HBT radii in -6% ] [fm ] [fm ] [fm R s 15 R o 15 R l λ φ [rad] φ [rad] ] [fm R os φ [rad] φ [rad] φ [rad] PHENIX Preliminary - - Au+Au GeV π + π + & π π centrality: -6% kt.-.3 kt.3-.4 kt.4-.5 kt.5-.6 kt.6-.8 kt Takafumi Niida, TAC seminar, Dec., 1 n Oscillation can be seen in R s, R o, and R os for each kt regions 51

52 k T dependence of azimuthal pion HBT radii in -% ] [fm R s λ φ [rad] ] [fm R o ] [fm R os φ [rad] ] [fm R l φ [rad] PHENIX Preliminary - - Au+Au GeV π + π + & π π centrality: -% Takafumi Niida, TAC seminar, Dec., 1 kt.-.3 kt φ [rad] φ [rad] kt.3-.4 kt.4-.5 kt.6-.8 kt

53 The past HBT Results for charged pions and kaons n Centrality / m T dependence have been measured for pions and kaons ² No significant difference between both species centrality dependence m T dependence 53 Takafumi Niida, TAC seminar, Dec., 1

54 Analysis method for HBT n Correlation function C = R(q) M(q) ² Ratio of real and mixed q-distribution of pairs q: relative momentum n Correction of event plane resolution ² U.Heinz et al, PRC66, 4493 () n Coulomb correction and Fitting ² By Sinyukov s fit function ² Including the effect of long lived resonance decay C = C core + C halo = N[λ(1+ G)F]+[1 λ] G = exp( R side q side R out q out R long q long R os q side q out ) Takafumi Niida, TAC seminar, Dec., 1 54

55 Azimuthal HBT radii for pions n Observed oscillation for R side, R out, R os n Rout in -% has oscillation ² Different emission duration between in-plane and out-of-plane? out-of-plane in-plane 55 Takafumi Niida, TAC seminar, Dec., 1

56 Model predictions Blast-wave model AMPT Side Out Out-Side S.Voloshin at QM11 T=[MeV], ρ=r ρ max (1+cos(nφ)) S.Voloshin at QM11 Out n= n=3 Side Takafumi Niida, TAC seminar, Dec., 1 Both models predict weak oscillation will be seen in R side and R out. 56