k T Dependence of Pion HBT Radii with respect to 3 rd -order Event Plane

162 APPENDIX B. SYSTEMATIC STUDY OF HBT RADII

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Ros

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[rad]

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Figure B.2: HBT parameters of charged pions in 0.2< k_T <2.0 GeV/c as a function of azimuthal pair angle with respect to 2^nd-order event plane in six kT and two centrality bins with different PID cut.

B.4 k_T DEPENDENCE OF PION HBT RADII WITH RESPECT TO Ψ₃ 163

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Figure B.3: HBT parameters of charged pions in 0.2< k_T <2.0 GeV/cas a function of azimuthal pair angle with respect to 2^nd-order event plane in four kT and two centrality bins with different event planes.

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default Coulomb +1fm Coulomb -1fm

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Figure B.4: HBT parameters of charged pions in 0.2< k_T <2.0 GeV/cas a function of azimuthal pair angle with respect to 2^nd-order event plane in four k_T and two centrality bins with different input source size for the calculation of the Coulomb interaction.

164 APPENDIX B. SYSTEMATIC STUDY OF HBT RADII

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Figure B.5: HBT parameters of charged kaons in 0.3< kT <2.0 GeV/c as a function of azimuthal pair angle with respect to 2^nd-order event plane in two centrality bins with different matching cut.

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Figure B.6: HBT parameters of charged kaons in 0.3< k_T <2.0 GeV/c as a function of azimuthal pair angle with respect to 2^nd-order event plane in two centrality bins with different PID cut.

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Figure B.7: HBT parameters of charged kaons in 0.3< k_T <2.0 GeV/c as a function of azimuthal pair angle with respect to 2^nd-order event plane in two centrality bins with different event planes.

B.4 k_T DEPENDENCE OF PION HBT RADII WITH RESPECT TO Ψ₃ 165

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Figure B.8: HBT parameters of charged kaons in 0.3< kT <2.0 GeV/cas a function of azimuthal pair angle with respect to 2^nd-order event plane in two centrality bins with different input source size for the calculation of the Coulomb interaction.

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Figure B.9: HBT parameters of charged pions in 0.2< k_T <2.0 GeV/cas a function of azimuthal pair angle with respect to 3^rd-order event plane in four centrality bins with different matching cuts.

166 APPENDIX B. SYSTEMATIC STUDY OF HBT RADII

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Figure B.10: HBT parameters of charged pions in 0.2< k_T <2.0 GeV/cas a function of azimuthal pair angle with respect to 3^rd-order event plane in four centrality bins with different PID cut.

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Figure B.11: HBT parameters of charged pions in 0.2< kT <2.0 GeV/cas a function of azimuthal pair angle with respect to 3^rd-order event plane in four centrality bins with different event planes.

B.4 k_T DEPENDENCE OF PION HBT RADII WITH RESPECT TO Ψ₃ 167

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0 1 2

0 10 20 30

0 1 2

0 10 20 30

[rad]

φ

0 1 ∆2

0 10 20 30

default Coulomb +1fm Coulomb -1fm

0 1 2

-2 0

os 2

R

0 1 2

-2 0 2

0 1 2

-2 0 2

[rad]

φ

0 1 ∆2

-2 0 2

Figure B.12: HBT parameters of charged pions in 0.2< k_T <2.0 GeV/cas a function of azimuthal pair angle with respect to 3^rd-order event plane in four centrality bins with different input source size for the calculation of the Coulomb interaction.

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

λ1D

kt:0.2-0.35[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.35-0.46[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.46-0.58[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.58-0.75[GeV/c]

[rad]

φ

0 0.5 1 1.5 ∆2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.75-1.5[GeV/c]

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

Rinv

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

λ3D

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

[rad]

φ

0 0.5 1 1.5 ∆2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 5 10 15 20 25 30

Rside

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

Rout

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

Rlong

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30 35

default matching 1.5 matching 2.5

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

Ros

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

[rad]

φ

0 0.5 1 1.5∆2

-3 -2 -1 0 1 2 3

Figure B.13: HBT parameters of charged pions in 0.2< k_T <2.0 GeV/cas a function of azimuthal pair angle with respect to 3^rd-order event plane in five kT and two centrality bins with different matching cuts.

168 APPENDIX B. SYSTEMATIC STUDY OF HBT RADII

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

λ1D

kt:0.2-0.35[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.35-0.46[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.46-0.58[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.58-0.75[GeV/c]

[rad]

φ

0 0.5 1 1.5 ∆2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.75-1.5[GeV/c]

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

Rinv

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

λ3D

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

[rad]

φ

0 0.5 1 1.5 ∆2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 5 10 15 20 25 30

Rside

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

Rout

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

Rlong

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

35 default

PID cut pair cut

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

Ros

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

[rad]

φ

0 0.5 1 1.5 ∆2

-3 -2 -1 0 1 2 3

Figure B.14: HBT parameters of charged pions in 0.2< kT <2.0 GeV/cas a function of azimuthal pair angle with respect to 3^rd-order event plane in five k_T and two centrality bins with different PID cut.

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

λ1D

kt:0.2-0.35[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.35-0.46[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.46-0.58[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.58-0.75[GeV/c]

[rad]

φ

0 0.5 1 1.5 ∆2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.75-1.5[GeV/c]

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

Rinv

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

λ3D

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

[rad]

φ

0 0.5 1 1.5 ∆2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 5 10 15 20 25 30

Rside

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

Rout

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

Rlong

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

35 default -north Ψ3

-south Ψ3

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

Ros

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

[rad]

φ

0 0.5 1 1.5 ∆2

-3 -2 -1 0 1 2 3

Figure B.15: HBT parameters of charged pions in 0.2< kT <2.0 GeV/cas a function of azimuthal pair angle with respect to 3^rd-order event plane in five k_T and two centrality bins with different event planes.

B.4 k_T DEPENDENCE OF PION HBT RADII WITH RESPECT TO Ψ₃ 169

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

λ1D

kt:0.2-0.35[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.35-0.46[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.46-0.58[GeV/c]

0 0.5 1 1.5 2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.58-0.75[GeV/c]

[rad]

φ

0 0.5 1 1.5 ∆2

1Dλ

0 0.1 0.2 0.3 0.4 0.5 0.6

kt:0.75-1.5[GeV/c]

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

Rinv

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35 40

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30 35 40

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

λ3D

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 0.1 0.2 0.3 0.4 0.5 0.6

[rad]

φ

0 0.5 1 1.5 ∆2

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.5 1 1.5 2

0 5 10 15 20 25 30

Rside

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

Rout

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

Rlong

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

0 0.5 1 1.5 2

0 5 10 15 20 25 30 35

[rad]

φ

0 0.5 1 1.5 ∆2

0 5 10 15 20 25 30 35

default Coulomb +1fm Coulomb -1fm

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

Ros

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

0 0.5 1 1.5 2

-3 -2 -1 0 1 2 3

[rad]

φ

0 0.5 1 1.5∆2

-3 -2 -1 0 1 2 3

Figure B.16: HBT parameters of charged pions in 0.2< k_T <2.0 GeV/cas a function of azimuthal pair angle with respect to 3^rd-order event plane in five k_T and two centrality bins with different input source size for the calculation of the Coulomb interaction.

Appendix C

Galuber Model

C.1 Spatial Eccentricity

Participant eccentricity is defined as:

ε_part= {y^′2} − {x^′2}

{y^′2}+{x^′2} (C.1)

wherex^′ and y^′ are the coordinates with respect to participant plane angle Ψ and given by

x^′ = rcos(ϕ−Ψ), (C.2)

y^′ = rsin(ϕ−Ψ). (C.3)

Participant eccentricity is rewritten by using Eq. (C.2), (C.3), ε_part =

∑r_i²sin²(ϕ_i−Ψ)−∑

r_i²cos²(ϕ_i−Ψ)

∑r²_i ,

=

∑r_i²(

sin²(ϕi−Ψ)−cos²(ϕi−Ψ))

∑r²_i ,

= −∑

r²_i cos[2(ϕi−Ψ)]

∑r_i² ,

= −⟨r²cos[2(ϕ−Ψ)]⟩

⟨r²⟩ . (C.4)

The participant plane angle Ψ of a give event is chosen to maximize the eccentricity, therefore we require the following condition:

dεpart

dΨ = 0. (C.5)

The Ψ is determined by solving Eq. (C.5), d

dΨ

(∑r_i²cos[2(ϕi−Ψ)]

)

= d

dΨ

(∑ [r_i²cos(2ϕi) cos(2Ψ) +r²_i sin(2ϕi) sin(2Ψ)]) ,

= ∑ [

−2r²_i cos(2ϕi) sin(2Ψ) + 2r²_i sin(2ϕi) cos(2Ψ)] ,

= 0.

170

ドキュメント内 RHIC-PHENIX 実験200GeV 金+金衝突における同種2粒子を用いた量子力学的干渉効果の反応平面依存性の測定 (ページ 185-194)