Detailed HBT measurementwith respect to the Event planein Au+Au 200 GeV collisions at PHENIX	

Takafumi Niida for the PHENIX Collaboration
University of Tsukuba
日本物理学会第６８回年次大会	

HBT Interferometry	n HBT effect is quantum interference between two identical particles.
n R. Hanbury Brown and R. Twiss

JPS spring, Mar.29, 2013	

²In 1956, they measured the angular diameter of Sirius.
n Goldhaber et al.
²In 1960, they observed the correlations among identical pions inp+anti-p collision independent of HBT.
G. Goldhaber, Proc. Int. Workshop on Correlations
and Multiparticle production(1991)	
|(p , p )|212|

1 2221 (p1 )| | 2 (p2 )|2⇡1 + |˜⇢(q)|=1 + exp(r2 q 2 )〜1/Δr	

T . Niida

C2 =detector

q=p1-p2 [GeV/c]	

2	detector

HBT with respect to Reaction Plane	n Azimuthal HBT can give us the source shape at freeze-out.

n Very useful tool to investigate space-time evolution in HI !	

T . Niida

central	JPS spring, Mar.29, 2013	n Final eccentricity is determined by initial eccentricity, velocity
profile and expansion time.

Reaction Plane	

peripheral	

3	

Reaction Plane	Azimuthal HBT w.r.t 3rd-order event plane	n Higher-order flow vn and Event plane ΨndN
/ 1+2v2 cos2(d+2v3 cos3(Ψ2	Ψ4	+2v4 cos4(vn = hcosn(JPS spring, Mar.29, 2013	

Ψ3	2)
3)
4)

n )iCollective
Ψ 3 expansion	What is final shape ?	

?	
4	

Initial spatial fluctuation	

T . Niidan Is the deformation due to initial fluctuations is preserved until
freeze-out?

Measurement by PHENIX Detectors	
Event plane resolution	

✰ PID by EMC-PbSc➫ select charged π

CNT: |η|<0.35✰ Ψn by forward detector RXN✰ Correlation function C2dN/dη	

MPC: 3.1<|η|<3.7	
BBC: 3.0<|η|<3.9-505

ηR(q)C2 =M (q)R(q),M(q): relative momentum dist.
for real and mixed pairs	

5	

RXN in: 1.5<|η|<2.8& out: 1.0<|η|<1.5

T . Niida

centrality (%)

JPS spring, Mar.29, 2013	

n=2 RXN
n=3 RXN
n=4 RXN
n=2 MPC
n=3 MPCEMC	

3-dimensional HBT analysis	
n “Out-Side-Long” system

Rlongbeam	ü Longitudinally Co-Moving System (LCMS)

RsideRout

JPS spring, Mar.29, 2013	

² Bertsch-Pratt parameterizationn Core-halo model² To deal with Coulomb interaction

22	 =exp( RsideG
qsideλRside
RoutRosRlong]
22
Routqout22Rlongqlong: chaoticity: transverse size
: transverse size + emission duration: cross term between “out” and “side”: longtudinal size

T . Niida=N [ (1 + G)F ] + [122Ros
qside qout )Rside	
Rout	observer	

6	

C2 =C2core + C2halo~kT = 1 (~pT 1 + p~T 2 )2~qout k ~kT , ~qside ? ~kTComparison of 2nd and 3rd order component	n In 0-10%, Rout have stronger oscillation for Ψ2 and Ψ3 than Rside 105500


Au+Au 200GeV 0-10%π+π++π-πw.r.t Ψ2w.r.t Ψ3Rout	-3-2-1

0

12

3

φ - Ψn [rad]φpair	
Ψ2-3-2-1

0

12

3

φ - Ψn [rad]φpair	
Ψ3T . Niida

10Rside	7	

R2o [fm2]

R2s [fm2]

Average of radii is set to “10” or “5” for w.r.t Ψ2 and w.r.t Ψ3	JPS spring, Mar.29, 2013	

² Does the emission duration depend on azimuthal angle ?
² Different sensitivity for possible sources to make the oscillation ?

Oscillation of Rs	n Relative amplitude of Rs for 2nd-order is used to represent“Eccentricity” at freeze-out

0	π/n	 2π/n	φpair- Ψn	2
Rs,n"n,f inal = 2 2
Rs,0JPS spring, Mar.29, 2013	

Rs,02	

Au+Au 200GeV
0.2

ε2
ε30.1

 0T . Niida

Rs,n2	?	
00.10.2✰ Relative amplitudes for 3rd-order show zero~negative.
What does it indicate? Zero triangularity?

0.3

0.4

εn,initial8	Rs2	εn,final² Strong expansion to in-plane direction, but still elliptical shape !

Simulation for Triangular shape	n Main possible sources to make Ψ3 dependence of HBT radii

Rxy = R(1e3 cos(35Ψ3,sim	))
0T = tanh(⇢)⇢ = tanh 1 [ 0 +e3=0.1

3 cos(3)](rxy)Rxy² HBT correlation: 1+cos(Δr×Δp)² pT spectra with Tf = 160 MeV² No Coulomb interaction, no opacity

T . Niidaü β0 for radial flow is fixed as 0.8.

10-5-10-10-50510x [fm]9	² Assuming Woods-Saxon distribution² Triangular shape controlled by “e3”² Triangular flow controlled by “β3”y [fm]n Setup of Monte-Carlo Simulation

JPS spring, Mar.29, 2013	

² Spatial triangular shape in expanding source² Triangular flow v3

Simulation Results	

20

Expanding	

15

20

15

10

staticflow β =0.8, β =00
3flow β =0.8, β =0.1

10ü Oscillation appears !
e3=0.1	

1.5

20Δ φ [rad]Static	25

20

1Expanding	

150.5

311.5

2

Δ φ [rad]25

T . Niida

0.5

Ro2 [fm2]

ü β3 makes oscillation !

0Rs2 [fm2]²Spherical shape0201510staticflow β =0.8, β =003
flow β =0.8, β =0.1

10

000.5

11.52Δ φ [rad]

00.5

3

11.5

2

Δ φ [rad]10	²Triangular shape

25

JPS spring, Mar.29, 2013	

25

Ro2 [fm2]² No oscillation
for triangular shapen Expanding source

Rs2 [fm2]n Static source

e3=0	

Simulation Results	
202015151010

β =03
β =0.063
β =0.1430.5

11.52Δ φ [rad]

00.5

11.52

Δ φ [rad]n Oscillation is determined by triangular shape and β3

T . Niida

0JPS spring, Mar.29, 2013	

Ψ3Ro2 [fm2]e3 < 0	 e3 > 0	Rs2 [fm2]e3=-0.04	

² Data is close to the situation with e3<0 and finite β3² Negative e3 may indicate that initial triangular deformation ismodified by triangular flow

11	n Zero oscillation does not necessarily indicate the sphericalsourceSummary	n Monte-Carlo simulation of HBT for triangular source²Ψ3 dependence of HBT radii will be determined by the balance oftriangular flow and spatial triangularity.
²Data in 0-10% is close to the source with negative e3 and finite β3.
Initial triangular deformation may be modified by triangular flow.

T . Niida☛ Different emission duration for azimuthal angle ?

12	²First measurement of Ψ3 dependent HBT radii have been presented.
²Oscillation of Rs is very weak, almost zero or slightly negative sign.
²Ro clearly has finite oscillation in most central collisions.

JPS spring, Mar.29, 2013	n Azimuthal HBT radii w.r.t v3 plane13	T . Niida

JPS spring, Mar.29, 2013	

Back up	Model Calculations	
Blast-wave model	

n=2n=3	

Side	Out	Side	Out-Side	S.Voloshin at QM11
T=100[MeV], ρ=r’ρmax(1+cos(nφ)) 	

S.Voloshin at QM11T . Niida

Out	JPS spring, Mar.29, 2013	

AMPT	BW ▷▶ Opposite sign of Rside and RoutAMPT ▷▶ Same sign of Rside and Rout	

14	

Both models predict weak oscillation will be seen in Rside and Rout.

Centrality dependence of v3 and ε3	v3@ pT=1.1GeV/c	n Initial ε3 has centrality dependence	🍙 Final ε3 has any centrality dependence?	

ε2	v2	ε3	v3	Npart	15	n Weak centrality dependence of v3

T . Niida

S.Esumi	  @WPCF2011	JPS spring, Mar.29, 2013	

PRL.107.252301	

Azimuthal HBT w.r.t v2 plane	

What is thefinal eccentricity ?	
Δφ	v2 Plane

T . Niida

Momentum anisotropy v2	

JPS spring, Mar.29, 2013	

Initial spatial eccentricity	²It depends on initial eccentricity, pressure gradient, expansion time,and velocity profile, etc.
²Good probe to investigate system evolution

16	n Final eccentricity can be measured by azimuthal HBT

Azimuthal HBT w.r.t v3 plane	Ψ3Ψ3n Final triangularity could be observed by azimuthal
HBT w.r.t v3 plane(Ψ3) if it exists at freeze-out

JPS spring, Mar.29, 2013	

Momentum anisotropy
triangular flow v3	

T . Niida

Initial spatial fluctuation(triangularity)	

17	

²Related to initial triangularity, v3, and expansion time, etc.
²Detailed information on space-time evolution can be obtained

3D HBT radii	p1n “Out-Side-Long” system

detector

Rside

22
22
2
2
= exp(−Rsideqside− Routqout− Rlongqlong− 2Ros2 qside qout )Rlong: Longtudinal size
Rside: Transverse size
Rout: Transverse size + emission duration
Ros: Cross term between Out and SideRout

JPS spring, Mar.29, 2013	

Sliced view= N[ λ (1+ G)F]+[1− λ ]22
G = exp(−Rinvqinv)

detector

T . Niida² Particles in core are affected bycoulomb interactionC	
2 = C2core + C2halo


p2

18	

² Bertsch-Pratt parameterizationn Core-halo modelAnalysis method for HBT	² Ratio of real and mixed q-distribution of pairs
q: relative momentumn Correction of event plane resolution² U.Heinz et al, PRC66, 044903 (2002)n Coulomb correction and Fitting² By Sinyukov‘s fit function² Including the effect of long lived resonance decay	
C2 = C2core + C2halo

T . Niida

R(q)C2 =M (q)JPS spring, Mar.29, 2013	n Correlation function

222222G = exp(−Rsideqside− Routqout− Rlong
qlong− 2Ros2 qside qout )19	= N[ λ (1+ G)F]+[1− λ ]Eccentricity at freeze-out	
Rs2	 PRC70, 044907 (2004)	
Rs,22	
22Rs,n = Rs,n (Δφ )cos(nΔφ )@WPCF2011	

in-plane	n εfinal ≈ εinitial/2 for pion

T . Niida

2Rs,2ε final = 2 20	 Rπ/2	π	s,0φpair- Ψ2	JPS spring, Mar.29, 2013	

Rs,02	² Kaon may freeze-out sooner than pion because of less cross section² Need to check the difference of mT between π/K? 	

20	

² Indicates that source expands to in-plane direction, and still elliptical shape² PHENIX and STAR results are consistentn εfinal ≈ εinitial for kaon

251515

1010105 00.5

11.5φ - Ψ 3 [rad] 0.45 02λΨ32015

R2os [fm2]φpair	

20

0.5

11.5

2

φ - Ψ 3 [rad]25 00.5

11.5

2

φ - Ψ 3 [rad]PHENIX Preliminary

1Au+Au 200GeV π+π+ & π-π0-10%

00.2

10-20%-1

JPS spring, Mar.29, 2013	

20

25

T . Niida

25

R2l [fm2]

R2o [fm2]

R2s [fm2]

Azimuthal HBT radii w.r.t Ψ3	

20-30%
0 00.511.5

2

φ - Ψ 3 [rad]-200.511.5

2

φ - Ψ 3 [rad]30-60%n Rout have a oscillation in most central collisions	21	n Rside is almost flat

Relative amplitude of HBT radii	n Similar definition with “final eccentricity”

0	0.1

Rµ,32	

Geometric info.	

0π/3	 2π/3	φ-0.1pair- Ψ3	0100200

300

Npart-2R2o,3/ R22o,02-2Rl,3 / Rl,0

Temporal+Geom.	

0.1
0.1

0.1
0.1

000
0-0.1
-0.10
0100
100

200
200

300
Npart300

Npart

0-0.1
-0.10
0-2R22o,3 / R2s,02R os,3 / R2s,0-2R2o,3 / R2s,00.1
0.1

0.1

0.1

0000-0.1
0-0.1
-0.10
0-0.1
0100200

300

100
100200200300
Npart
300

Npart

2R 2os,3 Preliminary/ R2s,0PHENIX

Temporal+Geom.	

0.1-0.1
0T . Niida

Rµ,02	

2R 2s,32 / R2s,02-2Ro,3 / Ro,02R 2s,3 / R2s,0 

100
100

200
200

300
Npart
300

Au+Au 200GeV
π+π++π-π100

200

300

22	Rµ2	

JPS spring, Mar.29, 2013	

n Relative amplitude of Rout increases with increasing Npart	Npart

Freeze-out parameters
extracted by Blast wave model	
²Parameters used in the model

104

104

spectra+v3310104

spectra+v4

310102102102101010111

110-1

10-110-110-210-2

10-2-3-3

10-2-3π ++π K ++K p+p

10 00.5

0.3

surface BW

11.5

10 02.5v2	
20.5

11.5

0.15

0.2 χ2 =2952

0.1

10 0
2.5v3	
20.5

1

1.5

0.15

χ2=456

spectra+v4(Ψ2)

31010-3

10 0
2.5
0.08

v4	
20.5

10.06

0.1

χ2=282v4(Ψ4)	
1.5

22.5

χ2=3300.04

0.1
00ü s2 and s3 correspond to final
eccentricity and triangularity

0.05

12000.05

10.02

002

1002

12

Initial vs Final spatial anisotropy	

T . Niida²s2 increase with goingto peripheral collisions²s3 is almost zero

104

102

10-1

Tf : temperature at freeze-out
ρ0 : average velocity
ρn : anisotropic velocity	
sn : spatial anisotropy	

spectra+v2
20 - 30%

3100.30.2

s2

s3

JPS spring, Mar.29, 2013	n Blast wave fit for spectra & vn

S. Mizuno, QM12	s4
radius integrated
surface0.1
0☞ Similar results with HBT	

0.1

0.2

0.3

ε200.10.2

0.3

ε300.10.2

0.3

ε423	0Contour plot ρn vs sn	24	T . Niida

JPS spring, Mar.29, 2013	

S. Mizuno, QM12	

Parameter Search of β3 vs e3	
n Difference between data and simulation are shown as contour plot

0.1

0.15

0.1

0.05

0.05

00.1

0e3

0.05

0.1

0e3

e3

T . Niida

3

ββ

0.05

00.1

0.15

0.1

-0.1

030-60%

0.1

0-0.1

20-30%

3n Overlap of v3 and Rs
0-0.1
indicates 0~negative e3,
where β3 shows similar values
in all centralities.
0.15

RsRov3

JPS spring, Mar.29, 2013	

0.15

-0.1

00.1✰ v3 flow may overcome the initial triangular deformation !

e325	

310-20%ββn The contours for Rµrepresents the systematic
error of the data.

30-10%

Summary	☛ Different emission duration for azimuthal angle ?

n Monte-Carlo simulation of HBT for triangular source²Ψ3 dependence of HBT radii will be determined by the balance oftriangular flow and spatial triangularity.
²Rs and v3 indicates that the parameter e3 has a zero to negative value.
Initial triangular deformation may be modified by triangular flow.
²Ro oscillation doesn’t seem to be explained only by e3 and β3.

T . Niida²First measurement of Ψ3 dependent HBT radii have been presented.
²Oscillation of Rs is very weak, almost zero or slightly negative sign.
²Ro clearly has finite oscillation in most central collisions.

JPS spring, Mar.29, 2013	n Azimuthal HBT radii w.r.t v3 planeü Related to different sensitivity to β3 between Rs and Ro ?

26	ü Different emission duration for azimuthal angle ?