Azimuthal HBT measurementsof charged pions and kaons in Au+Au
200GeV collisions at RHIC-PHENIX
Takafumi Niida from Univ. of Tsukuba
for the PHENIX Collaborations

JPS Fall 2011 @ Hirosaki UniversityOutline
 Introduction
 Physics Motivation

 Analysis flow Results
 Summary2

JPS Fall 2011

IntroductionWhat is HBT ?
Quantum interference between identical two particles
Powerful tool to explore space-time evolution in HI collisions
Correlation function c2 is defined as :P(p1) : Probability of detecting a particle
P(p1,p2) : Probability of detecting pair particles P( p1 , p2 )C2 P( p1 )  P( p2 )2
 1  ~ (q)  1  exp(  R 2 q 2 )  q  p1  p2

p1  p 2kT 2q side  kT , q out // kTp1
detector

inv inv(If assuming gaussian source)p2

detector

Bertsch-Pratt parameterization at LCMS frame
22
C 2  1   exp(  Rinvqinv)
2222221   exp(  Rsideq side Routqout Rlongqlong
 2 Ros2 q sideqout )

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

3

Rside : transverse size of source
Rout : transverse size of source + emission duration
Rlong : longitudinal size of souce
Ros : cross term between side and out

RsideRoutJPS Fall 2011

Physics Motivation
Azimuthal HBT analysis

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Sensitive to “system lifetime”

Related to momentum anistropy

HBT Results for charged pion and kaon

4

Measures the source shape w.r.t Reaction Plane
Source shape at freeze-out isCentrality and mT dependence were measured for pion and kaon
→no significant difference between both species
How about azimuthal dependence?

JPS Fall 2011

Analysis flow5Measure the experimantal C2

Correct Event Plane resolution
 Finite resolution reduce the oscillation
amplitude of HBT radii
 U.Heinz et al, PRC66, 044903 (2002)

Fitting C2
 Sinyukov fitting method(includes coulomb correction and effect of long lived decay)

Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
JPS Fall 2011

Analysis flowMeasure the experimantal C2C2 

6R(q)
M (q)

R(q): relative momentum dist. of Real pairs
M(q): that of mixed pairs

Correct Event Plane resolution
 Finite resolution reduce the oscillation
amplitude of HBT radii
 U.Heinz et al, PRC66, 044903 (2002)

Fitting C2
 Sinyukov fitting method(includes coulomb correction and effect of long lived decay)

Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
JPS Fall 2011

Analysis flowMeasure the experimantal C2

C2 

7R(q)
M (q)

R(q): relative momentum dist. of Real pairs
M(q): that of mixed pairs

Correct Event Plane resolution
 Finite resolution reduce the oscillation
amplitude of HBT radii
 U.Heinz et al, PRC66, 044903 (2002)

Fitting C2
 Sinyukov fitting method(includes coulomb correction and effect of long lived decay)

Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
JPS Fall 2011

Analysis flowMeasure the experimantal C2C2 R(q)M (q)R(q): relative momentum dist. of Real pairs
M(q): that of mixed pairs

Correct Event Plane resolution
 Finite resolution reduce the oscillation
amplitude of HBT radii
 U.Heinz et al, PRC66, 044903 (2002)

Fitting C2
 Sinyukov fitting method(includes coulomb correction and effect of long lived decay)
C 2  C 2core  C 2halo [ (1  G ) F ]  [1   ]
22
2
2
2
2
G  exp(  Rsideq side
 Routqout
 Rlongqlong
 2 Ros2 q sideqout )
8Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
JPS Fall 2011

Analysis flowMeasure the experimantal C2C2 R(q)M (q)R(q): relative momentum dist. of Real pairs
M(q): that of mixed pairsCorrect Event Plane resolution
 Finite resolution reduce the oscillation
amplitude of HBT radii
 U.Heinz et al, PRC66, 044903 (2002)

Fitting C2
 Sinyukov fitting method(includes coulomb correction and effect of long lived decay)
C 2  C 2core  C 2halo [ (1  G ) F ]  [1   ]22
2
2
22G  exp(  Rsideq side
 Routqout
 Rlongqlong
 2 Ros2 q sideqout )9Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
JPS Fall 2011

Correlation function for pion
Raw c2With sinyukov’ fitting functionCentrality:30-60%

10JPS Fall 2011

Correlation function
Raw c2With sinyukov’ fitting function R.PCentrality:30-60%

1DInv

3D
Side

OutLong

R.P

R.P

R.P

11

JPS Fall 2011

Azimuthal dependence of HBT radii for pion

Observed the oscillation for Rside, Rout, Ros

Different emission duration between in-plane and out-of-plane at 0-10%?

Data points are fitted by cosine series function
R  R2 ,0  2 R2 , 2 cos2   2 R2 , 4 cos4    s, o, lR  R2 ,0  2 R2 , 2 sin 2   2 R2 , 4 sin 4   osside
Out-of-plane(⊿φ=π/2)

out⊿φIn-plane (⊿φ=0)
Reaction plane

12JPS Fall 2011

Fourier components of azimuthal HBT radiiFourier component for Rside is caluculated by the following fit
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2R  Rside
2Rcos(2)
2R,0side, 2side, 4 cos(4 )R2s,4 < 0

R2s,4 > 0・4th order Fourier component seems to have negative value,
But it’s zero within systematic error
13JPS Fall 2011

Correlation function for kaon

Raw c2with sinyukov’ fitting functionCentrality: 20-60%

1DInv

3DSideOutLong

R.PR.P

R.PR.P
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JPS Fall 2011

Azimuthal dependence of HBT radii for kaon

Observed the oscillation for Rside, Rout, Ros as well as pionData points are fitted by cosine series function
R  R2 ,0  2 R2 , 2 cos 2    s, o, l
R  R2 ,0  2 R2 , 2 sin 2   osside
Out-of-plane(⊿φ=π/2)

out⊿φIn-plane (⊿φ=0)
Reaction plane15

JPS Fall 2011

Eccentricity at freeze-out

Final eccentricity is difined asif εfinal= εinitialR2s ,2ε final= 2 2Rs ,0by Blast-wave model

εinitial: initial eccentricity calculated by Glauber model
εfinal : final eccentricity calculated by above

Same source shape between
Initial state and freeze-out

if εfinal< εinitial
Source expands to In-plane direction

・PHENIX result is consitent with STAR result for pion・εfinal of kaon is larger than that of pion and close to ε initial Due to different average mT? or different cross section?
16JPS Fall 2011

Summary & Next to doMeasurements of azimuthal dependence of HBT radii for pion andkaon in Au+Au 200GeV collisions
 Observed the oscillation of Rside and Rout for kaon as well as for pion
 4th order in oscillation of Rside for pion is zero within systematic error Final eccentricity of pion is consitent with STAR result Final eccentricity of kaon is larger than that of pionNext to doNeed to check mT dependence of final eccentricity
Possible to understand the difference of pion and kaon?

Comparison with model (ex.blast wave model) Azimuthal HBT w.r.t higher order event planeAnalysis using 3rd order event plane is in progress Privides information about relation
between v3 and source shape?
17⑧⑦⑥
⑤④
③
②
①Psi3

JPS Fall 2011

Back up18

JPS Fall 2011

Data selection
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Data

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Track Cut
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pion: Pi<2σ && K>2σ && P>2σkaon: Pi>2σ && K<2σ && P>2σEvent mixing

19quality: 63 or 31
pion : pt > 0.2[GeV/c] && mom<2.0[GeV/c]kaon : pt > 0.3[GeV/c] && mom<2.0[GeV/c]
temc < 50[nsec]
3σ matching cut @ PC3
3σ matching cut @ EMC
ecent > 0.1[GeV]
EMC-west(all sectors)

PID
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Run7 Au+Au 200GeV

Zvertex: 30[bins]
Centrality: 20[bins] (10[bins] for kaon)
Reaction plane by RxP: 30[bins] (20[bins] for kaon)
JPS Fall 2011

PHENIX Detector
Vertex, Centrality
 BBC, ZDC
 Event plane Reaction Plane Detector(RxNP) Tracking
 Drift Chamber, Pad Chamber20

PID by EMCal Used all sectors in west arm

JPS Fall 2011