Azimuthal angle dependence of HBT radiiwith respect to the Event Planein Au+Au collisions at PHENIX	

TTaakkaaffuummii  NNiiiiddaa  ffoorr  tthhee  PPHHEENNIIXX  CCoollllaabboorraattiioonn  
UUnniivveerrssiittyy  ooff  TTssuukkuubbaa  

WWND2014 @Galveston, USA	Space-Time evolution in HI collisions	arXiv:1201.4264 [nucl-ex]	

n Final emitting particles carry information on the properties of
the QGP and its space-time evolutionn Space-time picture of the system evolution is emerging fromrecent studies at RHIC and the LHC

2	Momentum anisotropy at final state	
Ψ3	
Ψ2	
Ψ4	

beam	

n Initial source eccentricity with fluctuations leads to momentum anisotropy
at final state, known as higher harmonic flow vn
PHENIX	  PRL.107.252301	

²Sensitive to η/s (PRL107.252301)

dN/ 1+2⌃vn cos[n(dvn = hcos[n(

n )]

n )]i

Ψn : higher harmonic event plane
φ : azimuthal angle of emitted particles	

v2

v3

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 viscosity² 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+pn By quantum interference between two identical particles
wave function for
2 bosons(fermions) :	

C2 =

1
p
=
[ (x1 , p1 ) (x2 , p2 ) ±12
2(x2 , p1 ) (x1 , p2 )]P (p1 , p2 )⇡ 1 + |˜⇢(q)|2 = 1 + exp( R2 q 2 )P (p1 )P (p2 )spatial distribution ρ	

p1	
detector〜1/R	r2⇢(r) ⇠ exp()
2
2R

detectorp2	

q=p1-p2 [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+pn By quantum interference between two identical particles
wave function for
2 bosons(fermions) :	

C2 =R(HBT radius)1p=[ (x1 , p1 ) (x2 , p2 ) ±12
2(x2 , p1 ) (x1 , p2 )]P (p1 , p2 )⇡ 1 + |˜⇢(q)|2 = 1 + exp( R2 q 2 )P (p1 )P (p2 )spatial distribution ρ	

p1	
detector〜1/R	r2⇢(r) ⇠ exp()
2
2R

detectorp2	

q=p1-p2 [GeV/c]	

6	

to the HBT radii from an azimuthally integrated analysis
Strong 2nd-order oscillations are observed for R2o , R2s
2
and Rndos , and the signs of the oscillations are qualitatively
self-consistent [10,24], though the amplitude for mostcentral events is small. Similar oscillations were observed
STAR, PRL93, 012301	

Azimuthal sensitive HBT w.r.t 2 -order event plane	central	Rout-of-plane	

10-20%

40-80%

2

30

20
15

20

10
10

peripheral	

2

2

30

2
Rs,2
ε final = 2 2
Rs,0

20

0.15<kT<0.6 GeV/c	

2

PRC70, 044907 (2004), Blast-wave model	

0

R2os (fm )R2l (fm )Rin-plane	Reaction plane ≈ 2nd-order event plane(v2 plane)

2
2
Rs,n
= Rs,n(Δφ )cos(nΔφ )2Ro2 (fm )25

Rs2 (fm )in-plane	

0-5%

-2
0

π/2

π

0

Φ (radians)

π/2

πFIG. 1 (color online). Squared HBT radii using Eq. (1) rela-n Rs,2 istivesensitive
to final
to the reaction planeangle foreccentricity
three centrality classes. The

solid lines show allowed [24] fits to the individual oscillations²Oscillation indicates elliptical shape012301-4to out-of-plane direction.
extended

Results of HBT w.r.t 2nd- and 3rd-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	BBC (3.0<|η|<3.9)- centrality, zvertex- minimum bias trigger	
RXNP (1.0<|η|<2.8)- Event plane

Beam line	

BBC

R
X
N
P

R
X
N BBC
P

10	

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

EMC
al
PC
DC

Beam line	

BBC

R
X
N
P

R
X
N BBC
P

RXNP (1.0<|η|<2.8)- Event plane
DC,PC,EMCal (|η|<0.35)- Tracking- Particle Identification

11	

Event Plane Determination	
1<|η|<2.8	

24 scintillator segments	

beam pipe	
φi	
 Ψ3	
Ψ2	
Ψ4	

<cos(n[ Ψn - Ψr ])>Resolution of Event planes

1

Event Plane Resolution	
n=2, North+Southn=2, North or Southn=3, North+Southn=3, North or South

0.8

n Determined by anisotropic flow itself
using Reaction Plane Detector

1
1
=
tan
n
n

0.6

0.4

✓

⌃wi cos(n i )⌃wi sin(n i )◆n EP resolutions <cos[n(Ψn-Ψreal)]>

0.2²Res{Ψ2} ~ 0.75, Res{Ψ3} ~ 0.34

00beam axis	

10

20

30

40

50

60
70
Centrality [%]12	Particle IDentification	
EMC here!	
n EMC-PbSc is used.
² timing resolution ~ 600 psn Time-Of-Flight method

m =p

2

ct
L

◆2

Particle Identification by PbSc-EMC
2
104

1

p: momentum L: flight path length
t: time of flight	

n Charged π within 2σ

1.5

Mass square	

2

✓

!

103

1

0.5

K-

K+	

102

π-

π+	

10

0

-0.5

-1

²π/K separation up to ~1 GeV/c -3

-2

-1

0

1

2

3

1

Momentum × charge	

13	

3D-HBT Analysis	
n Core-Halo picture with “Out-Side-Long” frame²Longitudinal center of mass system (pz1=pz2)²taking into account long lived decay particles=[ (1 + G)Fcoul ] + [1Ro2 qo2

Rs

Rl

beam	

C2 =C2core + C2halo
G =exp( Rs2 qs2~kT = 1 (~pT 1 + p~T 2 )2~qo k ~kT , ~qs ? ~kTRo]
Rl2 ql22
2Ros
qs qo )

Fcoul: Coulomb correction factor
λ : fraction of pairs in the core

Rl = Longitudinal Gaussian source size	Rs = Transverse Gaussian source size	Ro = Transverse Gaussian source size + Δτ	
Ros= Cross term b/w side- and outward drections	

14	RESULTS	

15	

HBT radii w.r.t 2nd- and 3rd-order event planes	
Rs	

Ro	
µ=s

Au+Au- 200GeV-

2nd-order	
25 / / +/ /
n=2

+ +

Ros	

Rl	

µ=o

µ=l

µ=os

20

n=3

R2µ [fm2]

15
10 (a)

25
20

(b)

0-10%

(d)

20-30%

sys. error

R2os=015

0.2<kT<2.0 GeV/c	

3rd-order	

10 (e)

(c)

(f)
-2

0

2

(g)
-2

0

2

q - ^n [rad]

(h)
-2

0

2

-2

0

2

arXiv:1401.7680	

n Oscillation w.r.t Ψ2 could be intuitively explained by out-of-plane
extended elliptical source²Opposite sign of Rs and Ron For Ψ3, weak but finite oscillations can be seen, especially in Ro²Same sign of Rs and Ro in 20-30% centralityn Ro oscillation > Rs oscillation for both orders16	2R2µ,

2R2µ,

Initial εn vs oscillation amplitudes	
0

(a)

n=3
0.2

STAR

0
0

0.2

-2R2µ,n/R2i ,0

n

(b)
(a)

2
2
¡ n = |2R/R
| µ=o, i =s
Au+Au
200GeVµ,n i ,0 µµ=os,=s=o, ii=o+ +/ / +/ /0.2 < kT< 2.0 GeV/c	
0.2

(a)
(c)

¡ n = |2R2µ,n/R2i ,0|central	

2nd-order=s,ii=o=sµµ=o,-2R2µ,n/R2i ,0-2R
2R2µ,n/R2i ,0

2
2
¡n=2
n = |2Rµ,n/Ri ,0|

0

0.4

0
00

¡n
µ=o, i =o

(b)
(d)
(c)
0.2
0.2

peripheral	

0.4
0.4

0

¡n
µ=os, i =s

0.

0.2

²2Rs,22/Rs,02 ~ final source eccentricity under the BW model, and consistent withSTAR result²εfinal ≈ εinital/2, source eccentricity is reduced, but still retain initial shape extended
out-of-plane0n 3rd-order

(c)

0

0.2

0.4

(d)

0

0.2

¡n n) dependence²Weaker oscillation and no significant centrality(ε0.4²Rs,32 ≤ 0 and Ro,32 ≥ 0 are seen in all centralities.
n Does this result indicate non spatial triangularity at final state?

¡n

17	

Triangular deformation can be observed via HBT?	
n HBT radii w.r.t Ψ3 don’t almost show oscillation in a static source,
but it appears in a expanding source. (S. Voloshin, J. Phys. G38, 124097)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	Rs（Δφ=0）	

18	

Triangular deformation can be observed via HBT?	
n HBT radii w.r.t Ψ3 don’t almost show oscillation in a static source,
but it appears in a expanding source. (S. Voloshin, J. Phys. G38, 124097)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	Rs（Δφ=0） = Rs（Δφ=π/3）	

19	

Triangular deformation can be observed via HBT?	
n HBT radii w.r.t Ψ3 don’t almost show oscillation in a static source,
but it appears in a expanding source. (S. Voloshin, J. Phys. G38, 124097)n Initial triangularity is weaker than initial eccentricity (Glauber MC)² Effect of triangular flow may be dominant for the emission region	
static source	

w/ radial flow	

: emission region	

w/ radial+ triangular flow	
flow	

geometry	Rs（Δφ=0） = Rs（Δφ=π/3）	
n HBT w.r.t Ψ3 (also Ψ2) results from combination of spatial and flow anisotropy²Need to disentangle both contributions!!

20	

As already discussed at the end of Sec. II, the observed
2
small triangular oscillation amplitude Rs,3of Rs2 cannot[14] be directly interpreted as evidence for a small geometric triangularity of the source at freeze-out. What,then, is the correct interpretation of the experimental
observations?
PRC88, 044914 (2013)	

Gaussian toy model	

25

R2o

R2s, o "fm 2 #20

Thick blue: deformed flow field
deformedflow
Thin red : deformed geometry
deformed geometry	

R2sn Gaussian source including 3rd-ordermodulation for flow and geometry¯3 : triangular spatial deformation²✏²v̄3 : triangular flow deformation

15

Emission function(S) and transverse flow rapidity ηt :	

10

5
%Π

K! !0.5 GeV
%2Π!3

%Π!3

0

Π!3

2Π!3

Π

r2
S̃(x, K) / exp[
(1 + 2¯✏3 cos[3(2R2r¯3 )])⌘t = ⌘f (1 + 2v̄3 cos[3(R¯3 )])]'%$3

deformedgeometry	
deformed
FIG. 3: (Color
online) flow	Triangular oscillationsof Rs2 (dashed)2
and Ro (solid) for pion pairs with momentum K⊥ = 0.5 GeV,
3
3 angle Φ relative to3the triangular3
as a functionof emission
flow direction Ψ3 . Shown are results for two model scenarΔφ=π/3
ios: A deformed flow field(v̄3 = 0.25) in a spatially isotropic(ϵ̄3 = 0) density distribution (thick blue lines), and a sourcewith triangular geometric deformation (ϵ̄3 = 0.25) expanding
with radially symmetric (v̄3 = 0) flow (thin red lines). For theΔφ=0
two scenarios the oscillations of both Rs2 and Ro2 are seen to
be out of phase by π/3.

✏¯ = 0, v̄ 6= 0✏¯ 6= 0, v̄ = 0

In Fig. 3 we show triangular oscillations relative tothe triangular flow plane of Rs2 and Ro2 for pion pairsn Two extreme case was tested²Spherical source with triangularflow(+radial flow)²Triangularly deformed sourcewith radial flow	n “Deformed flow” shows
qualitative agreement with data21	Monte-Carlo simulation	
n Similar to Blast-wave model but Monte-Carlo approach
10²Woods-saxon particle distribution:⌦ = 1/(1 + exp[(r R)/a]), R = R0 (12e3 cos[3()])²transverse flow:
T = 0 (1 + 2 3 cos[3(²HBT correlation: 1 + cos( x · p))])e3=0.06 R0=5 (fm)5y [fm]²thermal motion + transverse boost (PRC70.044907)²introduced spatial anisotropy and triangular flow at freeze-outn Setup

Ψ3,sim	

0
-5

-10
-10

-5

0

x [fm]

5

10²parameters like Tf(temperature), β0, R0 were tuned by spectra and mean HBT radii25

Ro2 [fm2]

Rs2 [fm2]※Assuming the spatial and momentum dist. at freeze-out	
e3=0	
20

25

n Oscillations of Rs2 and Ro2 arecontrolled by e3 and β3

20

15

15

10

10

staticflow β =0.8, β =003flow β =0.8, β =0.1
0

0

0.5

1

1.5

2

Δ φ [rad]

0

0.5

3

1

1.5

2

Δ φ [rad]22	R2s,3/R2s,0kT dependence of 3rd-order oscillation amplitude	

0.05

Au+Au 200GeV /+/++/-/0-20%

Ron MC simulation qualitatively
agrees with Gaussian toy model

0

(a)

-0.05

(b)
PRC88,044914
D3=0, v 3=0.25

0.05

R2o,3/R2o,0

Rs

20-60%-0.1

deformed geometry	flow	

D3=0.25, v 3=0

0
-0.05

deformed flow	MC

e3=0, `3=0.12
0.5

(c)
1

kT [GeV/c]

(d)
0.5

geometry	

1

kT [GeV/c]n Ro,32 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 datan Rs,32 seems to show a slight opposite trend to “deformed flow”.
²Zero~negative value at low mT, and goes up to positive value at higher mT23	R2s,3/R2s,0kT dependence of 3rd-order oscillation amplitude	

0.05

Au+Au 200GeV /+/++/-/0-20%

20-60%Ron MC simulation qualitatively
agrees with Gaussian toy model

0

(a)

-0.05

-0.1

flow	

D3=0.25, v 3=0

0
-0.05

C. Plumberg@WPCF2013	(b)
deformed geometry	
deformed flow	
PRC88,044914
D3=0, v 3=0.25

0.05

R2o,3/R2o,0RsMC

e3=0, `3=0.12
0.5

(c)

2(d)
BehaviorofRat higher kT
s,3
0.5
1

geometry	

may be reproduced bykT [GeV/c] a full hydrodynamickT [GeV/c] calculation.	
1n Ro,32 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 datan Rs,32 seems to show a slight opposite trend to “deformed flow”.
²Zero~negative value at low kT, and goes up to positive value at higher kT

24	

6

spatial(e) and[39]flow(βtudes,Constrain
the values
measuredby mT 3spectra
and the averages
of HBT3) anisotropy	
se for 2nd -order.
radii shown in Fig. 1. For this analysis ⌧ was set to 3.5
fm/c (2.7 fm/c) for 0%–10% (20%–30%) to achieve betteri are influenced
MC simulation
e3 andβ3
agreement arewithcompared
the averagetoofdata
Ro2 . varying
A simulation
resultns betweenn mo2 shown
2 inexp
2
2 asimwith e3 = 0 and 23 == 0.12
displaying
e time of freezen χ2 minimization:(([Risµ,3/Rµ,0] Fig. 3,[R)/E)2µ,3 /Rµ,0 ]
trend that is qualitatively consistent with Ref. [32].
pair momentum
where E is experimental uncert.. Shaded areas show χ2<1.	
ows these results
2
2
The Ro,3
/Ro,0
0-10%
20-30%
0.15
0.15
does not show a
β

3

R

s
otropy in Fig. 3
0.1
0.1
Ro
on at freeze-out,
influence of dy0.05
0.05
ar flow [32]. To
these e↵ects wer a source with
0
0
-0.05
0
0.05
-0.05
0
0.05
(¯
✏3 =0, v̄3 =0.25)
e3tion and radialØ e3 is well constrained byRs, less sensitivity to β3
curves are taken
FIG. 4: (Color online) 2 contours representing the di↵erence
0.3 to fit within22Ø Overlapof data
Rs andβ3(µ=s,and o),
zero
e3 in 0-10%
betweenand R
simulation
2Rµ,2
/Rµ,0
as funco showsinpositive2
he deformed flow
tions of e3 and 3 . Shaded areas represent
less than unityØ Rs seems
to favorbynegative
e3 in 20-30%
ormed flow only
and constrained
the experimental
uncertainty.

ØTriangular deformation is reversed at freeze-out?

ns of spatial andTo understand how the data may constrain these val-

25	

Eccentrici5es'vs'higher'harmonics
Time
evolution of spatial anisotropy	
• RHIC)(one)event)

n IC with cumulant expansion
PHYSICAL RE+ ideal Hydrodynamics

1

0.6

0.8

(b)

0.4

0.2

0.2

0.1
0

5

0

1

2

vn

vn(pT)

0.6

40

ε
n
C. Nonaka@Correlation2013	

eps1
eps2 0.5
eps3
eps4 0.4
eps5
0.3

¡n

er
an
nt

²15-20%, Parameters are not tuned.

vn

PRC83.064904	

1.

0.25 1.2v1 b=7.6 fm	
 Dipole ε1x1v2
Triangular ε3x
0.2 0.8
v3
Elliptic ε2xv4
0.6
0.15 v51.
εnp(τ) / εnx(τo)

ND DIPOLE ASYMMETRY IN . . .

εnx(τ) / εnx(τo)

n MC-KLN + e-b-e Hydrodynamics

0.4

0.1 0.2
Glauber
Gaussianwith 4th cumulant

0

1
4

2
3
3
5
6
7
pT (GeV)time (fm)00.05 -0.2
4
8

5
9

0

0

1

2

0.

0.

0.

(a)

-0.4

0.

2

3

4

3

5 6 7 8
4 5 6
τ(fm)

time (fm)

9 10

7

8

9

ne) (a) Spectra
the smooth(optical)GlauberØ Theintime
that ε3 turns
overis faster than εFIG.
hydrodynamic
models.
8. (Color
online) (a)The spat2 in thecumulant
expansion. The
coefficientstheØ Comparison
with(e-b-e) fullofhydrodynamics
may constrain
the ϵ3x (see tex
distribution
ϵ1x , ϵ2x , andspace-timeof thesystem.	
der cumulant
expansionspicture
have beenadjustedtob = 7.6 fm. (b) The momentum aniso
C.)NONAKA)
442φ⟩ and ⟨r cos 2φ⟩, ⟨r cos 4φ⟩, respectively.
26	text) as a function of time. The timesc

Summary	n Azimuthal angle dependence of HBT radii w.r.t 2nd- and 3rd-order
event planes was measured at PHENIX²Finite oscillation of Ro2 is seen for 3rd-order event plane as well as
2nd-order.
²Gaussian toy model and MC simulation were compared with data.
They suggest that Ro oscillation comes from triangular flow.
²χ2 minimization by MC simulation shows finite β3 and zero ~ slightly
negative e3, which may imply that initial triangular shape issignificantly diluted, and possibly reversed by the medium expansion

27	

THANK YOU!	

28	

Higher Harmonic Flow and Event Plane	n Initial density fluctuations cause higher harmonic flow vnn Azimuthal distribution of emitted particles:	smooth picture	

Reaction Plane	dN/ 1+2v2 cos2(d+2v3 cos3(

2)3)+2v4 cos4(

fluctuating picture	

vn = hcosn(

Ψ3	
Ψ2	
Ψ4	

4)

n )i

vn : strength of higher harmonic flowΨn : higher harmonic event plane
φ : azimuthal angle of emitted particles	

29	Correlation Function	
n Experimental Correlation Function C2 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 eventswith similar z-vertex, centrality, E.P.

R(q)
C2 =
M (q)
q = p1p2² Real pairs include HBT effects, Coulombinteraction and detector inefficient effect.
Mixed pairs doesn’t include HBT and
Coulomb effects.
	relative momentum dist.	
107

R(q)	

106

M(q)	

5

10

104

0

0.05

0.1

0.15

0.2

0.25

0.3

C2=R/M	

1.2

HBT effect	1.1

1Coulomb repulsion	
0.9
0

0.05

0.1

0.15

0.2

0.25

qinv	
 30	
0.3
qinv[GeV/c]

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-outn Final source eccentricity will depend on initial eccentricity,
flow profile, expansion time, and viscosity etc.

Rout-of-plane	
out-of-plane	

aafftteerr  eexxppaannssiioonn  

in-plane	

in-plane	

Rin-plane	

beam	

31	

Correction of Event Plane Resolution	n Smearing effect by finite resolution of the event plane
Reaction Plane	true size	Event Plane	measured size	Reaction Plane	n Correction for q-distribution Acrr (q,Smeared	
Corrected!	

Ro2 [fm2 ]Rs2 [fm2 ]ü model-independent correction²Checked by MC-simulation25

j)+2⌃⇣n,m [Ac cos(n j ) + As sin(n j )]n /2⇣n,m =
sin(n /2)hcos(n( mreal ))i²PRC.66, 044903(2002)30j ) =Auncrr (q,event plane resolution	

30

w.r.t RP
w.r.t RP

25

20

20

15

15

10

10

Uncorrected w.r.t EP

0

0.5

1

1.5

2

2.5

3

Δφ [rad]Uncorrected w.r.t EP
Corrected w.r.t EP
0

0.5

1

1.5

2

2.5

3

Δφ [rad]32	

Centrality dependence of vn and initial εn	Higher harmonic flow vn	
Initial source anisotropy εn	
PHENIX	  PRL.107.252301	

PHYSICAL REVIEW C 8

COLLISION-GEOMETRY FLUCTUATIONS AND . . .

1(a)

PHOBOS Glauber MC

ε2

0.5

0

1

Au+Au 200GeV

100

200

ε3

ε2

v2

PRC.81.054905	
(b)

Npart

v3

Au+Au 200GeV

ε3

0.5

0

300

PHOBOS Glauber MC

100

200

300

Npart

FIG. 2. Distribution of (a) eccentricity, ε2 , and (b) triangularity, ε3 , as a function of number of participating nucleons,
200 GeV Au + Au collisions.

consistent with thefluctuations in the initial state(pexpected
T=1.1GeV/c)	
geometry with the new definition of eccentricity [46]. In thisarticle, we use this method of quantifying the initial anisotropy
exclusively.
Mathematically, the participant eccentricity is given as!"#2
2 2 + 4(σ )2σy2 − σ3
xy
x
,
(3)
ε2 =
σy2 + σx2

where ψ3 is the minor axis of participant triang

ψ3 =n Weak centrality dependence of v unlike v

atan2(⟨r 2 sin(3φpart )⟩, ⟨r 2 cos(3φpa
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 planezero. The participant triangularity defined in E
is calculated with respect to ψ3 and is always
The distributions of eccentricity and trianguwith the PHOBOS Glauber Monte Carlo imp√
for Au + Au events at sNN = 200 GeV are
The value of triangularity is observed to flu
event and have an average magnitude of th
eccentricity. Transverse distribution of nucleon Initial ε3 has finite values
and weaker centrality
where σ , σ , and σ , are the event-by-event (co-)variances
the participant nucleon distributions along the transverse
dependence than ε2 inofdirections
Glauber
MC simulation	
x and y [8]. If the coordinate system is shifted to the
2
x

"

2
y

xy

center of mass of the participating nucleons such that ⟨x⟩ =⟨y⟩ = 0, it can be shown that the definition of eccentricity isequivalent to$⟨r 2 cos(2φpart )⟩2 + ⟨r 2 sin(2φpart )⟩2
ε2 =(4)⟨r 2 ⟩
3

Triangular component in source shape exists at final state?
➡Measurement of HBT radii relative to Ψ 	
in this shifted frame, where r and φpart are the polar coordinate33	

Track Reconstruction	
n Drift Chamber
EMC(PbSc)	

Central Arms	

²Momentum determination
α	

pT '

K
↵

K: field integral
α: incident angle	

n Pad Chamber (PC1)²Associate DC tracks with hit
positions on PC1
ü pz is determinedn Outer detectors (PC3,TOF,EMCal)²Extend the tracks to outer detectors 	
Drift Chamber	

Pad Chamber	

34