Detailed HBT measurement with respect to Event plane and collision energy in Au+Au collisions

Takafumi Niida for the PHENIX CollaborationUniversity of Tsukuba

Quark Matter 2012 in Washington,DC

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outline

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Introduction of HBT Azimuthal HBT w.r.t v2 plane Azimuthal HBT w.r.t v3 plane Low energy at PHENIX Summary

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What is HBT ?

Quantum interference between two identical particles Hadron HBT can measure the source size at freeze-out

(not whole size but homogeneity region in expanding source)

21 ppq

detector

detector

1p

2p

ToutTside

T

kqkq

ppk

//,2

21

)exp(1)(~1

)()(),(

222

21

212

invinvqRq

pPpPppPC

P(p1) : Probability of detecting a particleP(p1,p2) : Probability of detecting pair particles

3

assuming gaussian source

〜 1/R

C2

q [GeV/c]

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3D HBT radii “Out-Side-Long” system

Bertsch-Pratt parameterization Core-halo model

Particles in core are affected by coulomb interaction

4

Rlong: Longtudinal sizeRside: Transverse sizeRout: Transverse size + emission durationRos: Cross term between Out and Side

detector

detector

1p

2p

R long

Rside

Rout

Sliced view

Beam

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centrality (%)

n =

<co

s n(

n(

mea

s.) -

n(

true))>

Measurement by PHENIX Detectors

50 5-5

ZDC/SMD

dN/d

RXN in: 1.5<||<2.8 & out: 1.0<||<1.5

MPC: 3.1<||<3.7

BBC: 3.0<||<3.9

CNT: ||<0.35

✰ PID by EMC&TOF➫ charged π/K are selected

✰ Ψn by forward detector RXN

EMCTOF

n=2 RXNn=3 RXNn=4 RXNn=2 MPCn=3 MPC

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

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Azimuthal HBT w.r.t v2 plane

Final eccentricity can be measured by azimuthal HBTIt depends on initial eccentricity, pressure gradient, expansion time,

and velocity profile, etc.Good probe to investigate system evolution 6

Momentum anisotropy v2

Initial spatial eccentricity

v2 Plane

Δφ

What is thefinal eccentricity ?

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Eccentricity at freeze-out

εfinal ≈ εinitial/2 for pion Indicates that source expands to in-plane direction, and still elliptical shape PHENIX and STAR results are consistent

εfinal ≈ εinitial for kaon Kaon may freeze-out sooner than pion because of less cross section Need to check the difference of mT between π/K? 7

ε final = ε initial

@WPCF2011Rs2

φpair- Ψ2

0 π/2 π

Rs,22

Rs,02

PRC70, 044907 (2004)

in-plane

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mT dependence of εfinal

εfinal of pions increases with mT in most/mid-central collisions There is still difference between π/K for mid-central collisions even

in same mT

Indicates sooner freeze-out time of K than π ? 8

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mT dependence of relative amplitude

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

Does it indicate emission duration between in-plane and out-of-plane is different at low mT? 9

Geometric info. Temporal+Geom.

Temporal+Geom.in-plane

out-of-plane

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Azimuthal HBT w.r.t v3 plane

Final triangularity could be observed by azimuthal HBT w.r.t v3 plane(Ψ3) if it exists at freeze-outRelated to initial triangularity, v3, and expansion time, etc.Detailed information on space-time evolution can be obtained

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Initial spatial fluctuation(triangularity)

Momentum anisotropytriangular flow v3

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Centrality dependence of v3 and ε3

Weak centrality dependence of v3

Initial ε3 has centrality dependence

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v3

@ pT=1.1GeV/c

PRL.107.252301

ε3ε2

v3v2

Npart

🍙 Final ε3 has any centrality dependence?

S.Esumi @WPCF2011

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Azimuthal HBT radii w.r.t Ψ3

Rside is almost flat

Rout have a oscillation in most central collisions 12

Ψ3

φpair

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Comparison of 2nd and 3rd order component In 0-10%, Rout have stronger oscillation for Ψ2 and Ψ3 than Rside

Its oscillation indicates different emission duration between 0°/60°　 w.r.t Ψ3

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Average of radii is set to “10” or “5”　 for w.r.t Ψ2 and w.r.t Ψ3

Ψ2

φpair

Ψ3

φpair

Ψ2

φpair

Ψ3

φpair

Ψ2

φpair

Ψ3

φpairRside

Rout

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Triangularity at freeze-out Relative amplitude is used to represent “triangularity” at freeze-out

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Rs2

φpair- Ψ3

0 π/3 2π/3

Rs,32

Rs,02

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

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v2 v3 v4 v4(Ψ4)

Spatial anisotropy by Blast wave model

15☞ Similar results with HBT

Blast wave fit for spectra & vn

Parameters used in the model

s2 and s3 correspond to final eccentricity and triangularity

s2 increase with going to peripheral collisions s3 is almost zero

Tf : temperature at freeze-outρ0 : average velocityρn : anisotropic velocitysn : spatial anisotropy

Initial vs Final spatial anisotropy

Poster, Board #195 Sanshiro Mizuno

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Image of initial/final source shape

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Low energy at PHENIX

No significant change beyond systematic error in 200GeV, 62GeV and 39GeV for centrality and mT dependence 17

200GeV62GeV39GeV

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Volume vs Multiplicity Product of 3D HBT radii shows the volume of homogeneity

regions Consistent with global trends

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Poster, Board #246Alex Mwai

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Summary Azimuthal HBT radii w.r.t v2 plane

Final eccentricity increases with increasing mT, but not enough to explain the difference between π/K☛ Difference may indicate faster freeze-out of K due to less cross section

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

☛ It may indicate the difference of emission duration between in-plane and out-of-plane

Azimuthal HBT radii w.r.t v3 planeFirst measurement of final triangularity have been presented.

It seems to vanish at freeze-out by expansion.while Rout clearly has finite oscillation in most central collisions

☛ It may indicate the difference of emission duration between Δφ=0°/60° direction

Low energy in Au+Au collisionsNo significant change between 200, 62 and 39 [GeV]Volume is consistent with global trends

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Japanese rice ball has just “triangular shape” !!

Elliptical shape is minor …

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Back up

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Relative amplitude of HBT radii Relative amplitude is used to represent “triangularity” at freeze-out Relative amplitude of Rout increases with increasing Npart

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Rμ2

φpair- Ψ3

0 π/3 2π/3

Rμ,32

Rμ,02

✰ Triangular component at freeze-out seems to vanish for all centralities(within systematic error)

Geometric info. Temporal+Geom.

Temporal+Geom.

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Higher harmonic event plane Initial density fluctuations cause higher harmonic flow vn

Azimuthal distribution of emitted particles:

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Ψ2

Ψ3

Ψ4

Ψn : Higher harmonic event planeφ : Azimuthal angle of emitted particles

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Charged hadron vn at PHENIX

v2 increases with increasing centrality, but v3 doesn’t

v3 is comparable to v2 in 0-10%

v4 has similar dependence to v2 24

PRL.107.252301

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v3 breaks degeneracy

v3 provides new constraint on hydro-model parameters Glauber & 4πη/s=1 : works better KLN & 4πη/s=2 : fails

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V2

V3

PRL.107.252301

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Azimuthal HBT radii for kaons Observed oscillation for Rside, Rout, Ros

Final eccentricity is defined as εfinal = 2Rs,2 / Rs,0

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in-plane

out-of-plane

PRC70, 044907 (2004)

@WPCF2011

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kT dependence of azimuthal pion HBT radii in 20-60%

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

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kT dependence of azimuthal pion HBT radiiin 0-20%

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Centrality / mT dependence have been measured for pions and kaons No significant difference between both species

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The past HBT Results for charged pions and kaons

mT dependencecentrality dependence

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Analysis method for HBT Correlation function

Ratio of real and mixed q-distribution of pairs q: relative momentum

Correction of event plane resolution U.Heinz et al, PRC66, 044903 (2002)

Coulomb correction and Fitting By Sinyukov‘s fit function Including the effect of long lived resonance decay

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Azimuthal HBT radii for pions Observed oscillation for Rside, Rout, Ros

Rout in 0-10% has oscillation Different emission duration between in-plane and out-of-plane?

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out-of-plane

in-plane

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Model predictions

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S.Voloshin at QM11T=100[MeV], ρ=r’ρmax(1+cos(nφ))

Blast-wave model AMPT

Out

Side

S.Voloshin at QM11

Side

Out

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

n=2n=3

Out-Side