Azimuthal angle dependence of HBT radiiin Au+Au collisions at RHIC-PHENIX	

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The 12th Asia Pacific Physics Conference	Quark Gluon Plasma (QGP)	

http://www.scientificamerican.com/	n State at a few µ-seconds after Big Bang

now	n Quarks and gluons are reconfined from hadrons
probably here	
from BNL web site	n QGP will be created at extreme
temperature and energy densityn Relativistic heavy ion collisionsis a unique way to study the QGP	2	Space-Time evolution in HI collisions	arXiv:1201.4264 [nucl-ex]	

n Space-time extent at freeze-out reflects the properties ofsystem evolution, such as the phase transition, hydrodynamic
expansion and hadron rescattering etc.
n HBT interferometry is a powerful tool to study the space-time
evolution in Heavy Ion collisions.	

3	

HBT Interferometry	n R. Hanbury Brown and R. Twiss²In 1956, the angular diameter of Sirius was measured.
n Goldhaber et al.
_	²In 1960, correlation among identical pions in p+p collision was observed.
n Quantum interference between two identical particles
wave function for2 bosons(fermions) :	

1p=[ (x1 , p1 ) (x2 , p2 ) ±122(x2 , p1 ) (x1 , p2 )]P (p1 , p2 )C2 =⇡ 1 + |˜⇢(q)|2 = 1 + exp( R2 q 2 )P (p1 )P (p2 )R(HBT radius)

spatial distribution ρ	

p1	
detector〜1/R	r2⇢(r) ⇠ exp()
2R2detectorp2	

q=p1-p2 [GeV/c]	

4	

Azimuthal angle dependence	n HBT w.r.t Reaction Plane give us source shape at freeze-out.
² R.P defined by beam axis and vector between centers of colliding nuclein Final eccentricity is determined by initial eccentricity, velocity
profile and expansion time etc.
² Initial anisotropy causes momentum anisotropy

Reaction
Plane	

out-of-plane	Reaction
Plane	

in-plane	beam	

Rout-of-plane	elliptical shapespherical shape

Rin-plane	: Rin-plane > Rout-of-plane: Rin-plane = Rout-of-plane	5	

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(+2v4 cos4(2)3)4)

vn = hcosn(n )ivn : strength of higher harmonic flowΨn : higher harmonic Event plane
φ : azimuthal angle of emitted particles	

fluctuating picture	What is final shape ?	

Ψ3	
Ψ2	Ψ4	?	

6	

3D HBT radii	

Rsiden “Out-Side-Long” frame

Rlong

beam	

² Bertsch-Pratt parameterization² Longitudinal Center of Mass System (pz1=pz2)

C2 =1 + G
G = exp( R2 q2 )22=exp( RsideqsideLCMS	22⇡exp( Rsideqside⇤2 2RoutqoutλRsideRoutRlong
Ros~kT = 1 (~pT 1 + p~T 2 )2~qout k ~kT , ~qside ? ~kT

22Rlongqlong⇤22 2(Rout + T ⌧ )qout__________

2
2
G =exp( RsideqsideRout⌧ 2 q02 )22Rlongqlong)=Rout2	
22
Rout
qout

22Rlongqlong

22Rosqside qout ): chaoticity: transverse HBT radius: transverse HBT radius + Δτ (emission duration): longitudinal HBT radius: cross term for φ-dependent analysis	

7	

HBT radii w.r.t 2nd-order event plane	

151515101010PHENIX Preliminary

0.4

200.3425RoutRos0150.1
10-210Rlong

25
Au+Au200GeV π+π++π-π-

220150.2

0 0.5 1 1.5 2 2.53Δφ [rad]Rlong2 [fm2]

Rside2 [fm2]

Rside
λ3D

0.5
25

0 0.5 1 1.5 2 2.5
3
Δφ [rad]
22Ros
Rout 2[fm[fm]2]

0 0.5 1 1.5 2 2.5
3Δφ [rad]20

150-10%10-20%

PRC70, 044907 (2004)	

20-30%
1030-60%00

0.5 1 1.5 2 2.53
Δφ [rad]
0 0.5 1 1.5 2 2.53Δφ [rad]0.50.4in 	 in Rosout
4PHENIX Preliminary

Rside
0.3______	

in 	

0 0.5 1 1.5 2 2.53
Δφ [rad]εfinalλ3Dout0.5 1 1.5 2 2.53Δφ [rad]0 0.5 1 1.5 2 2.53
Δφ [rad]Ros2 [fm2]in-4 02Rout

0 ______	

0-10%+ +Au+Au 200GeV π π +π- π+

0 0.5 1 1.5 2 2.53
Δφ [rad]+-Au+Au 200GeV K K +K K

0.4-STAR (PRL,93,12301)
εinitial = εfinal

10-20%20-30%30-60%0)i

0.50.3-2) cos(n22"f inal = 2Rs,2/Rs,0Au+Au 200GeV π+π++π-π-

0.2
0.1

2Rs,n= hRs2 (PHENIX Preliminary

0.2-4

0 0.5 1 1.5 2 2.5
3Δφ [rad]n εfinal ≈ εinitial/2 for pion

0.1

000.050.1²expansion to in-plane, but still elliptical at freeze-out²consistent with STAR experimentn εfinal ≈ εinitial for kaon
²emission region we’re looking at is different?

0.15

0.2

0.25

0.3

0.35

0.4

εinitial

8	mT dependence	n HBT does not measure the whole size but the emission region forexpanding
source 2222220.4
0.4

2 / R22R2Rs,2s,2 / Rs,0s,00.4
0.4

2 / R2-2R-2Ro,2o,2 / Ro,0o,0

0.4
0.4

2 / R2-2R-2Rl,2l,2 / Rl,0l,0²HBT radii depend on pair transverse momentum mass mT
0.3
0.3
0.3
0.3
0.3 m than pion
0.3 ²Kaon has higher
T
0.2
0.2
0.2
0.2 difference even0.2at the same m in 20-60%0.2n Rs,22/Rs,02 shows
T0.1
0.10.1000.2
0.8 11 00
0.222 0.4
0.4 20.6
0.6
2<m 0.8> [GeV/c]

0.1

0.1
0.1
²mT scaling works
well for averageradius of π/K (PRL103.142301(2009))
000
00²Different freeze-out
dynamics for 0both species ?
0.2
0.2

0.4
0.4

0.6
0.6

0.8
0.8

1100

0.4
0.4
0.3
0.3

0.3
0.3

0.3

0.2
0.2
0.2

0.2
0.2

0.2

0.1
0.1

0.1
0.1

00

00

00

0.2
0.4
0.6
0.8
11 0
0.2 0.4
0.4 0.6
0.6 0.8
0.2
0<m 0.8> [GeV/c]

0.4

0.20.20.4
0.40.60.6

110.10 Au+Au
Au+Au 200GeV200GeV
ππ++ππ++++ππ--ππ-- 0-20%
0-20%ππ++ππ++++ππ--ππ-- 20-60%
20-60%- K++K+++K -K - 0-20%

K K +K K 0-20%-<m<mTTT>> [GeV/c][GeV/c]-2R2o,2 / R2s,00.4

0.80.822 222 <m22 <mPreliminary<mTT>> [GeV/c][GeV/c]2R/ RR2s,0<mTT>> [GeV/c][GeV/c] PHENIX
PHENIX
Preliminary-2R-2R/Ros,22Ro,2 //R
0.4l,2os,2o,0l,0s,02 / R 2<mT > [GeV/c]-2R2Rs,2/ Rs,0s,0T
0.4-2Ro,20.4o,2 / R
s,00.2
0.2

0.4
0.4

0.6
0.6

0.80.8110<m > [GeV/c]
2R2os,2 / R2s,0 <mTT > [GeV/c]-+ +- - 20-60%
KK+KK++K+K K
K 20-60%
0.2 0.4 0.6 0.8
1

mT =q

kT2 + m2

<mT > [GeV/c]
PHENIX Preliminary 9	HBT radii w.r.t 3rd-order event plane	
R2o [fm2]

R2s [fm2]

Average of radii is set to “10” or “5” for w.r.t Ψ2 and w.r.t Ψ3	10 105
Au+Au 200GeV 0-10%π+π++π-πw.r.t Ψ25w.r.t Ψ3
0-3-2-10

1

2

3φ - Ψn [rad]0-3-2-1

0

1

2

3

φ - Ψn [rad]n Rout clearly shows a finite oscillation w.r.t Ψ3 in most central event²Strength w.r.t Ψ3 is comparable to w.r.t Ψ2n What make this Ro oscillation?

PRL.107.252301	

²Triangular spatial shape?
²Triangular flow?
ü v3 is comparable to v2 in most central²Emission duration?

10	

Centrality dependence of relative amplitudes	
22n Oscillation of Rs2Rshows
is almost zero
systematic-2R2o,3within/ R2o,0-2R2l,3error/ R2l,0s,3 / R s,00.1
0.1² Slightly negativevalue in peripheral?
n Ro has finite oscillation except peripheral event	
0Rµ2	Rµ,32	0-0.1
0100

Rµ,02	0	200300

Npart

-0.1
0100

22R2 2s,3 / R
2 s,0-2Ro,3 / Rs,00100
100200200

Npart100200300

Npart 0Au+Au200GeV100100200200

2R 2os,3 / R2s,00.1-0.1
00.1

0-0.1-0.1 0300
300Npart
00-2R2l,3Preliminary/ R2l,0PHENIX

0-2R2o,3 / R2s,00.1

Npart

0.1
0.1

0-0.1-0.1 00300

22-2R2 o,3 / 2R o,02R os,3 / Rs,00.1
π/3	 2π/3	0.1

φpair- Ψ3	2000.1300
300Npart-0.1
0π+π++π-π100200300

NpNpartPHENIX Preliminary

11	Possible explanation of Ro oscillation	n HBT w.r.t Ψ3 with toy model have been reported
in arXiv:1306.1485[nucl-ex] (2013)²assuming Gaussian source with triangular geometric deformationand triangular flow	
triangular source
spherical source
without flow anisotropy	 with flow anisotropy	

β0	β3	ª Close to “flow dominated” case ?
ª Need to check the kT dependence
to constraint ε3/β3	12	Summary	n Azimuthal angle dependence of HBT radii with respect to2nd- and 3rd-order event plane have been presented.
²Final eccentricity of kaons shows higher value that of pion even at
the same mT²Oscillation of Ro w.r.t Ψ3 have been observed in most central event,while Rs doesn’t show any signal beyond systematic errorü Ro oscillation may be explained by triangular flown Outlook²kT dependence of oscillation amplitudes w.r.t Ψ3 will be measured,
which will provides us information on the relative magnitude ofgeometrical and flow anisotropy

13	

Back up	14	

PHENIX Detectors	
EMCal	

24 scintillator segments	

Reaction Plane Detector(RxNP)	

φi	

beam axis	
✓1
tan 1n =n✰ Particle Identification by EMCalª π/K separation up to ~1GeV✰ Centrality by Beam-Beam Counter⌃wi cos(n i )⌃wi sin(n i )◆Res(Ψn)= <cos n(Ψn(meas) - Ψn(true))>
n=2 RXN
n=3 RXN
n=4 RXN
n=2 MPC
n=3 MPCª measure charge sum from participants✰ Event plane Ψn determined by RxNPª Res(Ψ2) ~0.75, Res(Ψ3) ~0.32

centrality (%)

15	σn = <cos n(Φn(meas.) - Φn(true))>

PHENIX Detectors	
EMC	
TOF	

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

centrality (%)

RXN in: 1.5<|η|<2.8& out: 1.0<|η|<1.5R(q)C2 =M (q)CNT: |η|<0.35
dN/dη	

MPC: 3.1<|η|<3.7✰ PID by EMC&TOF➫ charged π/K are selected

BBC: 3.0<|η|<3.9✰ Ψn by forward detector RXN	ZDC/SMD-5

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

05

η

16	

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 hitpositions on PC1
ü pz is determinedn Outer detectors (PC3,TOF,EMCal)²Extend the tracks to outer detectors 	
Drift Chamber	

Pad Chamber	

17	Particle IDentification	
n EMC-PbSc is used.
² timing resolution ~ 600 psn Time-Of-Flight methodm =p2ct
L◆2!

1

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

104
1.5

Mass square	

2✓Particle Identification by PbSc-EMC
2103

10.5

K-

K+	

102

π-π+	100-0.5n Charged π/K within 2σ-1-3²π/K separation up to ~1 GeV/c²K/p separation up to ~1.6 GeV/c-2-101231Momentum × charge	

18	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 andCoulomb effects.	

relative momentum dist.	
107

R(q)	

106

M(q)	

510

104

00.05

0.1

0.15

0.2

0.25

0.3

C2=R/M	

1.2

HBT effect	

1.11Coulomb repulsion	
0.9
00.05

0.1

0.15

0.2

0.25

qinv	 19	0.3
qinv[GeV/c]

mT dependence of εfinal	εfinal

mT = kT2 + m 2
PHENIX Preliminary
0.4

 
0.3

Au+Au 200GeV
π+π++π-π- 0-20%
π+π++π-π- 20-60%

0.2++--++--K K +K K 0-20%
K K +K K 20-60%

0.100

0.2

0.4

0.6

0.8

1

<mT> [GeV/c]n εfinal of pions increases with mT in most/mid-central collisionsn There is still difference between π/K for mid-central collisions
even in same mT²Indicates sooner freeze-out time of K than π ?

20	Centrality dependence of v3 and ε3	
PRL.107.252301	

v3@ pT=1.1GeV/c	S.Esumi	  @WPCF2011	

n Weak centrality dependence of v3n Initial ε3 has centrality dependence	🍙 Final ε3 has any centrality dependence?	

ε2	v2	ε3	v3	
Npart	21	

2525

20

20

1515

15

101010

5 0

0.5

11.5

φ - Ψ 3 [rad] 0.45 02λΨ325

20

R2os [fm2]φpair	

R2l [fm2]

R2o [fm2]

R2s [fm2]

Azimuthal HBT radii w.r.t Ψ3	0.5

11.52

φ - Ψ 3 [rad]25 00.5

11.52

φ - Ψ 3 [rad]PHENIX Preliminary

1Au+Au 200GeV π+π+ & π-π0-10%

00.2

10-20%-120-30%
0 00.511.52

φ - Ψ 3 [rad]

-2

00.5

11.52φ - Ψ 3 [rad]30-60%n Rside is almost flatn Rout have a oscillation in most central collisions	

22	Image of initial/final source shape 	

23	

Charged hadron vn at PHENIX	
PRL.107.252301	

n v2 increases with increasing centrality, but v3 doesn’tn v3 is comparable to v2 in 0-10%n v4 has similar dependence to v2	

24	

The past HBT Results for charged pions and kaons 	PRL103.142301(2009)	

h1.5
1++-

kaon - Hydro+UrQMD(f)(hep-ph/0202224)
kaon - Hydro+Cascade/BS fit)
(nucl-th/0811.3363)(a)

Au+Au 200GeV-K K +KK
Systematic error (kaon pair)/-/- (PRL 92 152302 (2004))
Systematic error (pion pair)

0.5

Rside [fm]086(b)

1/3

RALL = p1*Npartp1=0.51 ± 0.01
r2/DoF=14.6/8

4
2

Rout [fm]08

Rlong [fm]

(c)

(h)

(d)

(i)

(e)

(j)

6²higher transverse mass mT for kaons leads
to smaller radii compared to pions
ü pion <mT> ~ 0.47 GeV/c
ü kaon <mT> ~ 0.89 GeV/c²mT scaling works well

4208
6
4
20
1.5

Rout/Rside(g)n Centrality / mT dependence have beenmeasured for pions and kaons

10.5
002

4

N1/3
part600.5

1

mT [GeV/c2]

25	

Azimuthal HBT radii for pions	n Observed oscillation for R , R , R
sideoutosn Rout in 0-10% has oscillation

25

20

Rout2520

Rlong2 [fm2]

Rside

Rout 2 [fm2]

Rside2 [fm2]² Different emission duration between in-plane and out-of-plane?	
Rlong
25

20

15

15

15

10

10

10

0.5
0.4

λ3D
PHENIX Preliminary

0.3

0 0.5 1 1.5 2 2.5
3
Δφ [rad]Ros2 [fm2]

0 0.5 1 1.5 2 2.5
3
Δφ [rad]4

out-of-plane	

0 0.5 1 1.5 2 2.5
3
Δφ [rad]Ros
Au+Au 200GeV π+π++π-π-200-10%in-plane	

10-20%

0.20.1-220-30%
30-60%

00 0.5 1 1.5 2 2.5
3Δφ [rad]-40 0.5 1 1.5 2 2.5
3
Δφ [rad]26	

Azimuthal HBT radii for kaons	n Observed oscillation for R , R , R
sideoutosn Final eccentricity is defined as εfinal = 2Rs,2 / Rs,022² Rs,n = Rs,n (Δφ )cos(nΔφ )PRC70, 044907 (2004)	

in-plane	

out-ofplane	@WPCF2011	27