Detailed HBT measurementwith respect to Event plane andcollision energy in Au+Au collisions	Takafumi Niida for the PHENIX Collaboration
University of Tsukuba
Quark Matter 2012	

outline	n Low energy at PHENIXn Summary

T . Niidan Azimuthal HBT w.r.t v3 plane2	n Azimuthal HBT w.r.t v2 plane

Quark Matter 2012, Aug.14, 2012	n Introduction of HBTWhat is HBT ?	

n Hadron HBT can measure the source size at freeze-out(not whole size but homogeneity region in expanding source)	

12inv inv

assuming gaussian source	C2	  
q = p1 − p2
p1 + p 2
kT =2
q side ⊥ k T , q out // k T
p1detector〜1/R	p2q [GeV/c]	

T . Niida1detector3	 P( p1 , p2 )P(p ) : Probability of detecting a particle
C2 = 
P(p ,p ) : Probability of detecting pair particles
P( p1 ) ⋅ P( p2 )2= 1 + ρ~(q) = 1 + exp(− R 2 q 2 )Quark Matter 2012, Aug.14, 2012	n Quantum interference between two identical particles

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

Sliced view

Rside

= N[ λ (1+ G)F]+[1− λ ]22G = exp(−Rinvqinv)
22222
2= exp(−Rsideqside− Routqout− Rlong
qlong− 2Ros2 qside qout )Rlong: Longtudinal size
Rside: Transverse size
Rout: Transverse size + emission duration
Ros: Cross term between Out and Side

detector

Rout

T . Niida² Particles in core are affected bycoulomb interactionC	
2 = C2core + C2halop24	² Bertsch-Pratt parameterizationn Core-halo model

Quark Matter 2012, Aug.14, 2012	

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

Measurement by PHENIX Detectors	

centrality (%)

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

5	

RXN in: 1.5<|η|<2.8& out: 1.0<|η|<1.5

R(q)C2 =M (q)Quark Matter 2012, Aug.14, 2012	

TOF	

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

T . NiidaEMC	

Azimuthal HBT w.r.t v2 plane	

What is thefinal eccentricity ?	
Δφ	v2 Plane

T . Niida

Momentum anisotropy v2	

Quark Matter 2012, Aug.14, 2012	

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

6	n Final eccentricity can be measured by azimuthal HBTEccentricity at freeze-out	Rs,02	2Rs,2ε final = 2 20	 Rπ/2	π	s,0φpair- Ψ2	in-plane	n εfinal ≈ εinitial/2 for pion

Quark Matter 2012, Aug.14, 2012	

@WPCF2011	

T . Niida

Rs2	 PRC70, 044907 (2004)	
Rs,22	2
2Rs,n = Rs,n (Δφ )cos(nΔφ )² Kaon may freeze-out sooner than pion because of less cross section² Need to check the difference of mT between π/K? 	

7	

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

mT dependence of εfinal	εfinalmT = kT2 + m 2
PHENIX Preliminary

Quark Matter 2012, Aug.14, 2012	 
0.3Au+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%

0.1

00

0.2

0.4

0.6

0.8

1

<mT> [GeV/c]

T . Niida0.4n εfinal of pions increases with mT in most/mid-central collisions²Indicates sooner freeze-out time of K than π ?

8	n There is still difference between π/K for mid-central collisions
even in same mT

mT dependence of relative amplitude	
0.3

0.3
0.3 Temporal+Geom.	
Geometric info.	

0.40.4

0.2

0.2

0.2

0.1

0.1

0.1

00000.4

0.2 0.4 0.6 0.8

1 022<m > [GeV/c]
T-2Ro,2 / Rs,00.4

0.2

0.4

0.6

0.8

100.1

000.4

0.6

0.8

 
Au+Au 200GeV

0.2

0.1

0.2

π+π++π-π- 0-20%
π+π++π-π- 20-60%----

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

00.2

0.4

0.6

0.8

10<mT> [GeV/c]

1<mT > [GeV/c]
2R2os,2 / R2s,0 <mT > [GeV/c] PHENIX Preliminary

0.3
0.3 Temporal+Geom.	

in-plane	
0.2-2R2l,2 / R2l,00.2

0.4

0.60.8Quark Matter 2012, Aug.14, 2012	

2R2s,2 / R2s,0T . Niida

out-of-plane	-2R2o,2 / R2o,00.4

1<mT > [GeV/c]²Does it indicate emission duration between in-plane and out-ofplane is different at low mT?	

9	n Relative amplitude of Rout in 0-20% doesn’t depend on mT

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

Quark Matter 2012, Aug.14, 2012	

Momentum anisotropy
triangular flow v3	

T . Niida

Initial spatial fluctuation(triangularity)	

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

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	11	n Weak centrality dependence of v3

T . Niida

S.Esumi	  @WPCF2011	

Quark Matter 2012, Aug.14, 2012	

PRL.107.252301	

2515151010105 00.5

11.5

φ - Ψ 3 [rad] 

0.45 02λΨ32015R2os [fm2]φpair	200.5

11.52

φ - Ψ 3 [rad]25 00.5

11.5

PHENIX Preliminary

1Au+Au 200GeV π+π+ & π-π0-10%

00.2

10-20%-120-30%
0 00.511.52

φ - Ψ 3 [rad]-22φ - Ψ 3 [rad]

00.5

11.52

φ - Ψ 3 [rad]Quark Matter 2012, Aug.14, 2012	

2025T . Niida

25R2l [fm2]R2o [fm2]

R2s [fm2]

Azimuthal HBT radii w.r.t Ψ3	30-60%n Rout have a oscillation in most central collisions	12	n Rside is almost flat

Comparison of 2nd and 3rd order component	10 105
Au+Au 200GeV 0-10%
π+π++π-πw.r.t Ψ25w.r.t Ψ3
0Rout	-3-2-1

01

2

3

φ - Ψn [rad]φpair	
Ψ20-3-2-1

0

1

23

φ - Ψn [rad]φpair	
Ψ3

Rside	T . Niida

R2o [fm2]

R2s [fm2]

Average of radii is set to “10” or “5” for w.r.t Ψ2 and w.r.t Ψ3	13	²Its oscillation indicates different emission duration between 0°/60°
w.r.t Ψ3

Quark Matter 2012, Aug.14, 2012	n In 0-10%, Rout have stronger oscillation for Ψ2 and Ψ3 than RsideTriangularity at freeze-out	Rs,02	
0	π/3	 2π/3	φpair- Ψ3	Au+Au 200GeV
0.2

ε2
ε30.1

 

00T . Niida

2Rs,3ε3, final = 2 2Rs,0Quark Matter 2012, Aug.14, 2012	

Rs,32	

0.1

0.2

0.3

0.4

εn,initial✰Triangular component at freeze-out seems to vanish
for all centralities within systematic error

14	Rs2	

εn,finaln Relative amplitude is used to represent “triangularity” at freeze-outSpatial anisotropy by Blast wave model	
Poster, Board #195
Sanshiro Mizuno	Tf : temperature at freeze-out
ρ0 : average velocity
ρn : anisotropic velocity	
sn : spatial anisotropy	

104

spectra+v2
20 - 30%

310104spectra+v3

3

10104

spectra+v4

3

10102

102

102

102

10

10

10

101

1

1

1

10-1

10-1

10-1

10-2

10-2

10-2-3-3

10-1
10-2-3π ++π K ++K p+p

10 00.5

0.3

surface BW

11.5

10 02.52v2	

0.5

10.15

0.2 χ2 =2952

0.1

1.5

2

10 02.5v3	

0.5

10.15

χ2=456

1.5

spectra+v4(Ψ2)

310-3

10 0
2.50.08

2v4	

0.5

10.06

0.1

χ2=2821.5

2

2.5v4(Ψ4)	

χ2=3300.04

0.1

ü s2 and s3 correspond to final
eccentricity and triangularity

0.05

00

1

2

0.05

00

1

2

0.02

00

1

002

12

Initial vs Final spatial anisotropy	

²s2 increase with goingto peripheral collisions²s3 is almost zero

0.30.2s2

s3

Quark Matter 2012, Aug.14, 2012	

²Parameters used in the model

104s4
radius integrated

T . Niidan Blast wave fit for spectra & vn

surface0.10☞ Similar results with HBT	

0.1

0.2

0.3

ε200.1

0.2

0.3

ε30

0.1

0.2

0.3

ε4

15	0

16	T . Niida

Quark Matter 2012, Aug.14, 2012	

Image of initial/final source shape 	Low energy at PHENIX	
R out

Rside

Rout

4552

 

Quark Matter 2012, Aug.14, 2012	

00-30 % 6out

462GeV	39GeV	

100.2< kT <2.0 GeV/cAu+Au π(++)(- -)Systematic Uncertainity
RRsideR (fm)Rlong
Rlong

452 004005

6
0.3

0.4

7
0.5

4

0.6

050.7

T . Niida06N1/3
part

0.3

0.4

7

0.5

40.6

50.7

0.3

67

0.4

0.5

0.6

0.7

mT (GeV/c)n No significant change beyond systematic error in 200GeV,
62GeV and 39GeV for centrality and mT dependence	

17	R (fm)

810Rlong

10 GeV 2010
62200 GeV 2007
39 GeV 2010
62 GeV 2010
Systematic Uncertainity
39 GeV 2010 662Au+Au π

8(++)(- -)Rlong [fm]8200GeV	

R out [fm]200 GeV 2007

400

E895 2.7, 3.3, 3.8, 4.3 GeV

NA49 8.7, 12.5, 17.3 GeV

CERES 17.3 GeVSTAR 62.4, 200 GeV

PHOBOS 62.4, 200 GeV

ALICE 2760 GeV

300
PHENIX Run-10 39 GeV Au+Au,
Run-10 62.4 GeV Au+Au,
Run-7 200 GeV Au+Au

200

0-5 % Centrality<kT> = 0.3 GeV/c

100

T . Niida

RoutRsideRlong [fm3]n Product of 3D HBT radii shows the volume of homogeneity
regions
Poster, Board #246n Consistent with global trends	
Alex Mwai	

Quark Matter 2012, Aug.14, 2012	

Volume vs Multiplicity	0 5001000

1500

dNch/dη

18	

PHENIX PreliminarySummary	n Azimuthal HBT radii w.r.t v2 plane²Relative amplitude of Rout in 0-20% doesn’t depend on mT☛ It may indicate the difference of emission duration between in-planeand out-of-planen Azimuthal HBT radii w.r.t v3 plane²First measurement of final triangularity have been presented.
It seems to vanish at freeze-out by expansion.
²while Rout clearly has finite oscillation in most central collisions☛ It may indicate the difference of emission duration between Δφ=0°/60°direction

T . Niida☛ Difference may indicate faster freeze-out of K due to less cross section

Quark Matter 2012, Aug.14, 2012	

²Final eccentricity increases with increasing mT, but not enough toexplain the difference between π/K²No significant change between 200, 62 and 39 [GeV]²Volume is consistent with global trends

19	n Low energy in Au+Au collisions

	Quark Matter 2012, Aug.14, 2012	

T . Niida

Japanese rice ballhas just “triangular shape” !!	

20	

Thank you for your attention!

21	

T . Niida

Quark Matter 2012, Aug.14, 2012	

Back up	Relative amplitude of HBT radii	n Relative amplitude is used to represent “triangularity” at freeze-out

0	0.1

Rµ,32	

Geometric info.	

0π/3	 2π/3	φ-0.1pair- Ψ3	0100

200300

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

Temporal+Geom.	

0.1
0.1

0.1
0.1

00

0
0-0.1
-0.10
0100
100

200200300
Npart300

Npart✰ Triangular component at freeze0.1
Temporal+Geom.	
out seems to vanish
for all
0.1
0.1
centralities(within systematic error)

0-0.1-0.10
0-2R22o,3 / R2s,02R os,3 / R2s,0-2R2o,3 / R2s,00.1-0.1
0-0.1-0.10
0-0.1
0100
100200200300
Npart
300300Npart
300

Npart-0.100300

200200 00200

100
100

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

0100

0.1

T . Niida

Rµ,02	2R 2s,32 / R2s,02-2Ro,3 / Ro,02R 2s,3 / R2s,0Au+Au 200GeV
π+π++π-π100

200

300

22	Rµ2	Quark Matter 2012, Aug.14, 2012	n Relative amplitude of Rout increases with increasing Npart	

NpartHigher harmonic event plane	n Initial density fluctuations cause higher harmonic flow vn+2v4 cos 2 (φ − Ψ 4 )Ψ3	Ψ2	Ψ4	vn = cosn (φ − Ψ n )Ψn : Higher harmonic event planeφ : Azimuthal angle of emitted particles	

T . Niida+2v3 cos 2 (φ − Ψ 3 )23	dN∝1+ 2v2 cos 2 (φ − Ψ 2 )dφQuark Matter 2012, Aug.14, 2012	n Azimuthal distribution of emitted particles:	Charged hadron vn at PHENIX	

T . Niida

Quark Matter 2012, Aug.14, 2012	

PRL.107.252301	

n v2 increases with increasing centrality, but v3 doesn’tn v4 has similar dependence to v2	24	n v3 is comparable to v2 in 0-10%

needed with MC-KLN calculations to match v2 , leads toa much lower v3 than obtained with Glauber MC calculations. Consequently, our measurement of v3 f!3 g helps tov breaks degeneracy	

PRL.107.252301	
PHENIX
KLN + 4πη/s = 2
Glauber + 4πη/s = 1 (1)

v2

0.2

V2	

0.1
00.1

0100

200(c) pT = 0.75-1.0 GeV/c300

UrQMD + 4πη/s = 0Glauber + 4πη/s = 1 (2)0.0500100

2003000100200300

100200300(d) pT = 1.75-2.0 GeV/c

V3	0Npart
Npartof v2 f!2 gs, demon-n vFIG.
constrainton ofhydro-model
3 provides
3 (color newonline).
Comparison[(a) and (b)] vparameters
2 f!2 g vse and alsoand (d)] :vworks
vs Npart measurements andpart and [(c)3 f!3 g better²NGlauber& 4πη/s=1
f different
theoretical predictions (see text): ‘‘MC-KLN þ 4!"=s ¼ 2’’²KLN & 4πη/s=2: fails	
et al. [27]and ‘‘Glauber þ 4!"=s ¼ 1 (1)’’ [27]; ‘‘Glauber þ 4!"=s ¼ 1
1 dimen(2)’’ [32]; and ‘‘UrQMD’’ [29]. Shaded areas (magenta) around

Quark Matter 2012, Aug.14, 2012	(b) pT = 1.75-2.0 GeV/c

T . Niida(a) pT = 0.75-1.0 GeV/c

25	

0.3

v3

with pT forore central
3om central
pected in,28]. The
ance, also
dependent,
ost central
er calculazed ‘‘trian(b) and (d)sults fromlity trends
nt with thepT below

Azimuthal HBT radii for kaons	n Observed oscillation for R , R , Rsideoutos

PRC70, 044907 (2004)	

in-plane	

out-ofplane	@WPCF2011	

T . Niida

226	2² Rs,n = Rs,n (Δφ )cos(nΔφ )Quark Matter 2012, Aug.14, 2012	n Final eccentricity is defined as εfinal = 2Rs,2 / Rs,0kT dependence of azimuthal pion HBT radiiin 20-60%	

1510105

50 0

0.5

11.5

2

2.50 03

Δ φ [rad]λR2os [fm2]

0.8
0.6
0.4

0.5

1

1.5

2

2.5

3

Δ φ [rad]0 00.5

11.5

22.5

3

Δ φ [rad]PHENIX Preliminary
Au+Au 200GeV π+π+ & π-πcentrality: 20-60%

200.2

kt 0.2-0.3

kt 0.5-0.6

kt 0.3-0.4

kt 0.6-0.8

kt 0.4-0.5

kt 0.8-1.5-2
0 00.5

11.5

22.5

3

Δ φ [rad]

00.5

11.5

22.5

Quark Matter 2012, Aug.14, 2012	

1020

T . Niida

15

R2l [fm2]

R2o [fm2]20

R2s [fm2]

20

3

Δ φ [rad]27	

n Oscillation can be seen in Rs, Ro, and Ros for each kT regions	

30

20
20

100 0100.5

11.5

22.50 03

Δ φ [rad]λR2os [fm2]0.80.60.4

100.5

11.5

22.5

3Δ φ [rad]0 00.5

11.5

22.5

3

Δ φ [rad]PHENIX Preliminary
Au+Au 200GeV π+π+ & π-πcentrality: 0-20%

200.2

kt 0.2-0.3

kt 0.5-0.6

kt 0.3-0.4

kt 0.6-0.8

kt 0.4-0.5

kt 0.8-1.5

T . Niida

20R2l [fm2]R2o [fm2]30

R2s [fm2]

30

Quark Matter 2012, Aug.14, 2012	

kT dependence of azimuthal pion HBT radiiin 0-20%	

0 00.511.5

22.5

3Δ φ [rad]00.5

11.522.5

3Δ φ [rad]28	-2The past HBT Results for charged pions and kaons 	n Centrality / mT dependence have been measured for pions and kaons

T . NiidamT dependence	

29	

centrality dependence	

Quark Matter 2012, Aug.14, 2012	² No significant difference between both species

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)Quark Matter 2012, Aug.14, 2012	n Correlation function

222222G = exp(−Rsideqside− Routqout− Rlongqlong− 2Ros2 qside qout )30	

= N[ λ (1+ G)F]+[1− λ ]Azimuthal HBT radii for pions	n Observed oscillation for R , R , R
sideoutosin-plane	31	

out-of-plane	

T . Niida² Different emission duration between in-plane and out-of-plane?	

Quark Matter 2012, Aug.14, 2012	n Rout in 0-10% has oscillation

Model predictions	
AMPT	

Quark Matter 2012, Aug.14, 2012	

Blast-wave model	Out	n=2n=3	Side	Out	S.Voloshin at QM11
T=100[MeV], ρ=r’ρmax(1+cos(nφ)) 	

T . NiidaSide	

Out-Side	S.Voloshin at QM11

32

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