Azimuthal angle dependence of HBT radii with respect to the Event Plane in Au+Au collisions at PHENIX

Azimuthal angle dependence of HBT radii with respect to the Event Plane in Au+Au collisions at PHENIX TTaakkaaffuummii NNiiiiddaa ffoorr tthhee PPHHEENNIIXX CCoollllaabboorraattiioonn UUnniivveerrssiittyy ooff TTssuukkuubbaa WWND014 @Galveston, USA

Space-Time evolution in HI collisions arxiv:101.464 [nucl-ex] n Final emitting particles carry information on the properties of the QGP and its space-time evolution n Space-time picture of the system evolution is emerging from recent studies at RHIC and the LHC

Momentum anisotropy at final state Ψ 3 Ψ beam Ψ 4 n Initial source eccentricity with fluctuations leads to momentum anisotropy at final state, known as higher harmonic flow v n ² Sensitive to η/s (PRL107.5301) dn / 1+ v n cos[n( n)] d v n = hcos[n( n)]i Ψ n : higher harmonic event plane φ : azimuthal angle of emitted particles PHENIX PRL.107.5301 v v 3 3

Spatial anisotropy at final state in-plane in-plane beam n What is the final source shape? ² Spatial-extent at final state depends on the magnitude of initial eccentricity with fluctuation, the strength of flow, expansion time, and viscosity ² Does the initial fluctuation also remain at final state? n HBT interferometry relative to different event plane could probe them. 4

HBT Interferometry n 1956, H. Brown and R. Twiss, measured angular diameter of Sirius _ n 1960, Goldhaber et al., correlation among identical pions in p+p n By quantum interference between two identical particles wave function for bosons(fermions) : 1 = 1 p [ (x 1,p 1 ) (x,p ) ± (x,p 1 ) (x 1,p )] C = P (p 1,p ) P (p 1 )P (p ) 1+ (q) =1+exp( R q ) p 1 detector detector 1/R spatial distribution ρ (r) exp( r R ) p q=p 1 -p [GeV/c] 5

HBT Interferometry n 1956, H. Brown and R. Twiss, measured angular diameter of Sirius _ n 1960, Goldhaber et al., correlation among identical pions in p+p n By quantum interference between two identical particles wave function for bosons(fermions) : 1 = 1 p [ (x 1,p 1 ) (x,p ) ± (x,p 1 ) (x 1,p )] C = P (p 1,p ) P (p 1 )P (p ) 1+ (q) =1+exp( R q ) R (HBT radius) p 1 detector detector 1/R spatial distribution ρ (r) exp( r R ) p q=p 1 -p [GeV/c] 6

(fm ) (fm ) Azimuthal sensitive HBT w.r.t nd -order event plane R out-of-plane central STAR, PRL93, 01301 0-5% 10-0% 40-80% 5 ) (fm R o 30 0 0 15 Rs in-plane R in-plane Reaction plane nd -order event plane(v plane) ) (fm R l 10 peripheral 30 0 0.15<k T <0.6 GeV/c 10 0 - Ros PRC70, 044907 (004), Blast-wave model R s,n = R s,n (Δφ)cos(nΔφ) ε final = R s, R s,0 0 π/ π 0 π/ Φ (radians) n R s, is sensitive to final eccentricity ² Oscillation indicates elliptical shape extended to out-of-plane direction. π Results of HBT w.r.t nd - and 3 rd -order event planes are presented today! 7

PHENIX Experiment Beam line 8

PHENIX Experiment BBC (3.0< η <3.9) - centrality, zvertex - minimum bias trigger Beam line BBC BBC 9

PHENIX Experiment Beam line BBC (3.0< η <3.9) - centrality, zvertex - minimum bias trigger RXNP (1.0< η <.8) - Event plane BBC R X N P R X N P BBC 10

PHENIX Experiment Beam line BBC R X N P EMCal PC DC R X N P BBC BBC (3.0< η <3.9) - centrality, zvertex - minimum bias trigger RXNP (1.0< η <.8) - Event plane DC,PC,EMCal ( η <0.35) - Tracking - Particle Identification 11

Event Plane Determination 1< η <.8 4 scintillator segments beam pipe φ i Ψ 3 Ψ Ψ 4 <cos(n[ Ψ n - Ψ r ])> 1 0.8 0.6 0.4 Resolution of Event planes Event Plane Resolution n=, North+South n=, North or South n=3, North+South n=3, North or South beam axis n Determined by anisotropic flow itself using Reaction Plane Detector n = 1 n tan 1 wi cos(n i ) w i sin(n i ) 0. 0 0 10 0 30 40 50 60 70 Centrality [%] n EP resolutions <cos[n(ψ n -Ψ real )]> ² Res{Ψ } ~ 0.75, Res{Ψ 3 } ~ 0.34 1

Particle IDentification EMC here! n EMC-PbSc is used. ² timing resolution ~ 600 ps n Time-Of-Flight method ct m = p 1! L p: momentum L: flight path length t: time of flight n Charged π within σ Mass square 1.5 1 0.5 0-0.5 Particle Identification by PbSc-EMC K - K + π - π + 10 4 3 10 10 10 ² π/k separation up to ~1 GeV/c -1-3 - -1 0 1 3 Momentum charge 1 13

3D-HBT Analysis n Core-Halo picture with Out-Side-Long frame ² Longitudinal center of mass system (p z1 =p z ) ² taking into account long lived decay particles R s ~ kt = 1 (~p T 1 + ~p T ) ~q o k ~ k T, ~q s? ~ k T C =C core + C halo =[ (1 + G)F coul ]+[1 ] beam R o R l G =exp( R sq s R oq o R l q l R osq s q o ) F coul : Coulomb correction factor λ : fraction of pairs in the core R l = Longitudinal Gaussian source size R s = Transverse Gaussian source size R o = Transverse Gaussian source size + Δτ R os = Cross term b/w side- and outward drections 14

RESULTS 15

HBT radii w.r.t nd - and 3 rd -order event planes nd -order n=3 [fm ] n= Rµ 3 rd -order 5 0 15 10 Au+Au 00GeV - - + + + (a) 5 0-10% 0-30% 0 15 10 (e) sys. error R s R o R l R os µ=s 0.<k T <.0 GeV/c - 0 n Oscillation w.r.t Ψ could be intuitively explained by out-of-plane extended elliptical source ² Opposite sign of R s and R o n For Ψ 3, weak but finite oscillations can be seen, especially in R o ² Same sign of R s and R o in 0-30% centrality n R o oscillation > R s oscillation for both orders (b) (f) - 0 µ=o - n [rad] (c) (g) - 0 µ=l (d) R os =0 (h) - 0 µ=os arxiv:1401.7680 16

Initial ε n vs oscillation amplitudes R µ,n /R,0 n nd -order 0. 0 0 0. 0.4 central n= n=3 STAR µ=s, =s 0 0. 0.4 ² R s, /R s,0 ~ final source eccentricity under the BW model, and consistent with STAR result ² ε final ε inital /, source eccentricity is reduced, but still retain initial shape extended out-of-plane n 3 rd -order (a) ² Weaker oscillation and no significant centrality(ε n ) dependence ² R s,3 0 and R o,3 0 are seen in all centralities. n Does this result indicate non spatial triangularity at final state? 17 0 n n peripheral = R /R µ,n,0 0. < k T <.0 GeV/c µ=o, =o (c) 0 n

Triangular deformation can be observed via HBT? n HBT radii w.r.t Ψ 3 don t almost show oscillation in a static source, but it appears in a expanding source. (S. Voloshin, J. Phys. G38, 14097) n Initial triangularity is weaker than initial eccentricity (Glauber MC) ² Effect of triangular flow may be dominant for the emission region static source : emission region w/ radial flow w/ radial + triangular flow flow geometry R s (Δφ=0) 18

Gaussian toy model fm 5 0 15 R o R s PRC88, 044914 (013) deformed flow Thick blue: deformed flow field Thin red: deformed deformed geometry n Gaussian source including 3 rd -order modulation for flow and geometry ² ² 3 v 3 : triangular spatial deformation : triangular flow deformation R s, o 10 5 K 0.5 GeV Π Π 3 Π 3 0 Π 3 Π 3 Π 3 Emission function(s) and transverse flow rapidity η t : r S(x, K) / exp[ R r (1 + 3 cos[3( t = f R (1 + v 3 cos[3( 3)]) 3)])] deformed flow 3 =0, v 3 6=0 3 6=0, v 3 =0 Δφ=π/3 Δφ=0 deformed geometry n Two extreme case was tested ² Spherical source with triangular flow(+radial flow) ² Triangularly deformed source with radial flow n Deformed flow shows qualitative agreement with data 1

Monte-Carlo simulation n n Similar to Blast-wave model but Monte-Carlo approach ² thermal motion + transverse boost (PRC70.044907) ² introduced spatial anisotropy and triangular flow at freeze-out Setup ² Woods-saxon particle distribution: =1/(1 + exp[(r R)/a]), R = R 0 (1 e 3 cos[3( )]) ² transverse flow: ² HBT correlation: T = 0 (1 + 3 cos[3( )]) 1 + cos( x p) y [fm] 10 e 3 =0.06 R 0 =5 (fm) 5 0-5 -10 Ψ 3,sim -10-5 0 5 10 x [fm] ² parameters like T f (temperature), β 0, R 0 were tuned by spectra and mean HBT radii Assuming the spatial and momentum dist. at freeze-out ] [fm Rs 5 0 15 e 3 =0 ] [fm Ro 5 0 15 n Oscillations of R s and R o are controlled by e 3 and β 3 10 0 0.5 1 1.5 Δφ [rad] 10 static flow β =0.8, β =0 0 3 flow β =0.8, β =0.1 0 3 0 0.5 1 1.5 Δφ [rad]

k T dependence of 3 rd -order oscillation amplitude /R s,0 0.05 - - Au+Au 00GeV + + + 0-0% Rs 0-60% Ro n MC simulation qualitatively agrees with Gaussian toy model R s,3 0 /R o,0 R o,3-0.05 0.05 0-0.05-0.1 MC e =0, =0.1 3 3 (a) 0.5 1 [GeV/c] k T (c) (b) PRC88,044914 3 =0, v 3 =0.5 3 =0.5, v 3 =0 0.5 1 [GeV/c] k T (d) deformed flow flow geometry n R o,3 seems to be explained by deformed flow in both centralities. ² Note that model curves are scaled by 0.3 for the comparison with the data n R s,3 seems to show a slight opposite trend to deformed flow. deformed geometry ² Zero~negative value at low m T, and goes up to positive value at higher m T 3

k T dependence of 3 rd -order oscillation amplitude /R s,0 R s,3 /R o,0 R o,3 0.05 0-0.05 0.05 0-0.05-0.1 - - Au+Au 00GeV + + + 0-0% MC e =0, =0.1 3 3 (a) 0.5 1 [GeV/c] k T (c) Rs 0-60% Ro (b) PRC88,044914 3 =0, v 3 =0.5 3 =0.5, v 3 =0 0.5 1 [GeV/c] k T n MC simulation qualitatively agrees with Gaussian toy model C. Plumberg@WPCF013 deformed flow flow n R o,3 seems to be explained by deformed flow in both centralities. ² Note that model curves are scaled by 0.3 for the comparison with the data n R s,3 seems to show a slight opposite trend to deformed flow. deformed geometry geometry (d) Behavior of R s,3 at higher k T may be reproduced by a full hydrodynamic calculation. ² Zero~negative value at low k T, and goes up to positive value at higher k T 4

Constrain spatial(e 3 ) and flow( 3 ) anisotropy n MC simulation are compared to data varying e 3 and β 3 n χ minimization: =(([Rµ,3/R µ,0] exp [Rµ,3/R µ,0] sim )/E) where E is experimental uncert.. Shaded areas show χ <1. β 3 0.15 0-10% 0.1 R s R o 0-30% 0.05 0-0.05 0 0.05.05 0 0.05 e 3 Ø e 3 is well constrained by R s, less sensitivity to β 3 Ø Overlap of R s and R o shows positive β 3 and zero e 3 in 0-10% Ø R s seems to favor negative e 3 in 0-30% Ø Triangular deformation is reversed at freeze-out? 5

Time evolution of spatial anisotropy 0.8 0.6 0.4 0. n MC-KLN + e-b-e Hydrodynamics 1 0 ² 15-0%, Parameters are not tuned. C. Nonaka@Correlation013 n eps1 eps eps3 eps4 eps5 0 1 3 4 5 6 7 8 9 time (fm) n IC with cumulant expansion + ideal Hydrodynamics ε nx (τ) / ε nx (τ o ) 1. 1 0.8 0.6 0.4 0. 0-0. -0.4 b=7.6 fm (a) Dipole ε 1x Triangular ε 3x Elliptic ε x 3 4 5 6 7 8 9 10 τ(fm) PRC83.064904 ε (τ) / ε (τ ) Ø The time that ε 3 turns over is faster than ε in the hydrodynamic models. Ø Comparison with (e-b-e) full hydrodynamics may constrain the space-time picture of the system. 6

Summary n Azimuthal angle dependence of HBT radii w.r.t nd - and 3 rd -order event planes was measured at PHENIX ² Finite oscillation of R o is seen for 3 rd -order event plane as well as nd -order. ² Gaussian toy model and MC simulation were compared with data. They suggest that R o oscillation comes from triangular flow. ² χ minimization by MC simulation shows finite β 3 and zero ~ slightly negative e 3, which may imply that initial triangular shape is significantly diluted, and possibly reversed by the medium expansion 7

THANK YOU! 8

Higher Harmonic Flow and Event Plane n Initial density fluctuations cause higher harmonic flow v n n Azimuthal distribution of emitted particles: smooth picture fluctuating picture Ψ 3 Reaction Plane dn d / 1+v cos( ) +v 3 cos3( 3) +v 4 cos4( 4) v n = hcosn( n)i Ψ 4 Ψ v n : strength of higher harmonic flow Ψ n : higher harmonic event plane φ : azimuthal angle of emitted particles 9

Correlation Function n Experimental Correlation Function C is defined as: ² R(q): Real pairs at the same event. ² M(q): Mixed pairs selected from different events. Event mixing was performed using events with similar z-vertex, centrality, E.P. relative momentum dist. C = R(q) M(q) 7 10 6 10 5 10 R(q) M(q) q = p 1 p 10 4 ² Real pairs include HBT effects, Coulomb interaction and detector inefficient effect. Mixed pairs doesn t include HBT and Coulomb effects. 1. 1.1 1 HBT effect C =R/M Coulomb repulsion q inv 0.9 0 0.05 0.1 0.15 0. 0.5 0.3 qinv[gev/c] 30

Spatial anisotropy at final state n Angle dependence of HBT radii relative to Reaction Plane reflects the source shape at kinetic freeze-out. n Initial spatial anisotropy causes momentum anisotropy (flow anisotropy) ² One may expect in-plane extended source at freeze-out n Final source eccentricity will depend on initial eccentricity, flow profile, expansion time, and viscosity etc. out-of-plane aafftteerr eexxppaannssiioonn R out-of-plane in-plane in-plane R in-plane beam 31

Correction of Event Plane Resolution n Smearing effect by finite resolution of the event plane Reaction Plane Event Plane Reaction Plane true size measured size n Correction for q-distribution ² PRC.66, 044903(00) ü model-independent correction ² Checked by MC-simulation Smeared Corrected! [fm Rs 30 ] 5 0 15 10 0 0.5 1 1.5.5 3 Δφ [rad] [fm Ro A crr (q, j) =A uncrr (q, j) ] 30 5 0 15 10 + n,m [A c cos(n j )+A s sin(n j )] n / n,m = sin(n /)hcos(n( m real))i 0 0.5 1 1.5.5 3 Δφ [rad] event plane resolution w.r.t RP w.r.t RP Uncorrected w.r.t EP Uncorrected w.r.t EP Corrected w.r.t EP 3

Centrality dependence of v n and initial ε n Higher harmonic flow v n PHENIX PRL.107.5301 Initial source anisotropy ε n v (a) 1 PHOBOS Glauber MC Au+Au 00GeV PRC.81.054905 (b) 1 PHOBOS Glauber MC Au+Au 00GeV ε 0.5 ε ε 3 ε 3 0.5 0 100 00 300 N part 0 100 00 300 N part v 3 (p T =1.1GeV/c) FIG.. Distribution of (a) eccentricity, ε, and (b) triangularity, ε 3,asafunctionofnumberofparticipatingnucleons, 00 GeV Au + Au collisions. consistent with the expected fluctuations in the initial state geometry with the new definition of eccentricity [46]. In this article, we use this method of quantifying the initial anisotropy exclusively. Mathematically, the participant eccentricity is given as n Weak centrality dependence of (σ v 3 ) unlike v + 4(σxy ) σy n Initial ε 3 has finite values and weaker + σ x centrality where σx dependence than ε in Glauber, σ y,andσ xy, aretheevent-by-event(co-)variances of the participant nucleon distributions along the transverse MC simulation ε = " Triangular component equivalent in source to shape exists at final state? y σ x, (3) directions x and y [8]. If the coordinate system is shifted to the center of mass of the participating nucleons such that x = y = 0, it can be shown that the definition of eccentricity is r cos(φ part ) + r sin(φ part ) Measurement of HBT radii ε = relative to Ψ (4) r 3 33 in this shifted frame, where r and φ part are the polar coordinate where ψ 3 is the minor axis of participant triang ψ 3 = atan( r sin(3φ part ), r cos(3φ pa 3 It is important to note that the minor axis is found to be uncorrelated with the react and the minor axis of eccentricity in Glaub calculations. This implies that the avera calculated with respect to the reaction plane zero. The participant triangularity defined in E is calculated with respect to ψ 3 and is always The distributions of eccentricity and triangu with the PHOBOS Glauber Monte Carlo imp for Au + Au events at s NN = 00 GeV are The value of triangularity is observed to flu event and have an average magnitude of th eccentricity. Transverse distribution of nucleo

Track Reconstruction EMC (PbSc) Central Arms α n Drift Chamber ² Momentum determination p T ' K K: field integral α: incident angle n Pad Chamber (PC1) ² Associate DC tracks with hit positions on PC1 ü p z is determined n Outer detectors (PC3,TOF,EMCal) ² Extend the tracks to outer detectors Drift Chamber Pad Chamber 34