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

WPCF2011 @ Tokyo University

Outline
Introduction
 Physics Motivation
 Analysis
 PHENIX Detector
 Analysis flow Results
 PionAzimuthal dependence of HBT radii Fourier components


Kaon


Azimuthal dependence of HBT radii

Eccentricity at freeze-out comparing between pion and kaon
 Summary & Outlook
2WPCF2011

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
p1detectorinv inv(If assuming gaussian source)p2

detector

Bertsch-Pratt parameterization at LCMS frame2
2C 2  1   exp(  Rinvqinv)

Sliced view

2222221   exp(  Rsideq side Routqout
 Rlongqlong
 2 Ros2 q sideqout )




3

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

Rside

RoutWPCF2011

Physics Motivation
Azimuthal HBT analysis






Sensitive to “system lifetime”

Related to momentum anisotropy

HBT Results for charged pion and kaon

4Measures the source shape w.r.t Reaction PlaneSource shape at freeze-out isCentrality and mT dependence were measured for pion and kaon
→No significant difference between both species
How about azimuthal dependence?

WPCF2011

PHENIX DetectorBBC, ZDC

Event planeReaction Plane Detector(RxNP)

1<|η|<2.8

Trackingwest-EMC

Vertex, Centrality

Drift Chamber, Pad Chamber

PID


EMCal (all sectors in west arm)

mass square|η|<0.35, ⊿φ=90°

K-K+π-π+RxNP

charge x momentum
5WPCF2011

Analysis flow

6Measure the experimental 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 resonancedecay)

Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
WPCF2011

Analysis flow
Measure the experimental C2C2 

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 resonancedecay)

Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
WPCF2011

Analysis flowMeasure the experimental C2

C2 

8R(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 resonancedecay)

Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
WPCF2011

Analysis flowMeasure the experimental 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 resonancedecay)
C 2  C 2core  C 2halo [ (1  G ) F ]  [1   ]222
2
2
2G  exp(  Rsideq side
 Routqout
 Rlongqlong
 2 Ros2 q sideqout )
9Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
WPCF2011

Analysis flowMeasure the experimental 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 resonancedecay)
C 2  C 2core  C 2halo [ (1  G ) F ]  [1   ]
2
2
2
2
2
2G  exp(  Rsideq side
 Routqout
 Rlongqlong
 2 Ros2 q sideqout )10

Get HBT radii(Rside,Rout,Rlong,…) as a fitting result
WPCF2011

Correlation function for pion

11Raw c2With sinyukov’ fitting functionCentrality:30-60%

WPCF2011

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

1DInv

3DSideOutLong

R.PR.P

R.P

12WPCF2011

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, l
R  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

13WPCF2011

Fourier components of azimuthal HBT radiiFourier component for Rside is calculated by the following fit
22
2R  Rside2
Rcos(2)
2R,0side, 2side, 4 cos(4 )R2s,4 < 0R2s,4 > 0

Relative 4th order radius seems to have negative value,
But it’s zero within systematic error
14WPCF2011

Correlation function for kaon

Raw c2with sinyukov’ fitting function

Centrality: 20-60%

1DInv

3DSideOutLong

R.P

R.P

R.P

R.P
15

WPCF2011

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 plane

16

WPCF2011

Eccentricity at freeze-outR2s ,2Final eccentricity is defined as ε final= 2 2Rs ,0if εfinal= εinitial

by 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 consistent 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?
17WPCF2011Summary & Outlook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 consistent with STAR result Final eccentricity of kaon is larger than that of pion

Outlook

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 plane⑧⑦⑥⑤Analysis using 3rd order event plane is in progress Provides information about relation
between v3 and source shape?
18

④③
②
①Psi3

WPCF2011

Thank you!

19

WPCF2011

Back up20

WPCF2011

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>2σ

Event mixing21

quality: 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


Run7 Au+Au 200GeV

Zvertex: 30[bins]
Centrality: 20[bins] (10[bins] for kaon)
Reaction plane by RxP: 30[bins] (20[bins] for kaon)
WPCF2011