Polarised Compton Scattering and Annihilation inFlight
Pavel Starovoitov
NC PHEP, Minsk
August 3, 2006
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 1 / 18
Outline
1 Total Cross SectionAnnihilationCompton
2 Differential Cross SectionAnnihilation
AsymmetriesCross SectionPolarisation Transfer
ComptonAsymmetriesCross SectionPolarisation Transfer
3 Simulations
4 Next steps
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 2 / 18
Total Cross Section
σComptonpol = σCompton
0
[1 + zcz−ACompton
]~Sγ = (xl , yl , zc) ~Sele = (x−, y−, z−)
σAnnihpol = σAnnih
0
[1 + z+z−AAnnih
L + (x+x− + y+y−) AAnnihT
]~Spos = (x+, y+, z+) ~Sele = (x−, y−, z−)
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 3 / 18
Total Cross Section Asymmerties (Compton)
2 4 6 8 10En0me
-0.05
0.05
0.1
0.15
0.2
0.25
ACompton Compton total XS asymmetry
2000 4000 6000 8000 10000En0me
0.4
0.5
0.6
0.7
ACompton Compton total XS asymmetry
limEn0→0
ACompton = 0
limEn0→∞
ACompton = 1
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 4 / 18
Total Cross Section Asymmerties (Annihilation)
2 4 6 8 10
En0me
-0.2
0.2
0.4
0.6
0.8
1
AAnnih Annihilation total XS asymmetry
2000 4000 6000 8000 10000
En0me
-0.3
-0.2
-0.1
0.1
AAnnih Annihilation total XS asymmetry
longitudinal transverselim
En0→me
AAnnihT = 1
limEn0→∞
AAnnihT = −1
2
limEn0→me
AAnnihL = 1
limEn0→∞
AAnnihL = 0
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 5 / 18
Differential Cross Section (Annihilation)
dσAnnih(ξin1 , ξin
2 , ξout1 , ξout
2 )
dΩ=
dσAnnih0
dΩ
[1 + ξin
1 Aξin2
T]×[ (
C3
(ξin1 (1) + ξin
2 (1))
+ C2ξin2 (3) + C1ξ
in1 (3)
)ξout1 (3)
−(C3
(ξin1 (1) + ξin
2 (1))
+ C1ξin2 (3) + C2ξ
in1 (3)
)ξout2 (3)
+(ξout1 (1) + ξout
2 (1))L0
+ξout1 (1)
(ξin1 Lγ1
1 ξin2
T)
+ ξout1 (2)
(ξin1 Lγ1
2 ξin2
T)
+ξout2 (1)
(ξin1 Lγ2
1 ξin2
T)
+ ξout2 (2)
(ξin1 Lγ2
2 ξin2
T)
+ξout1 Correlation(ξin
1 , ξin2 )ξout
2T
]
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 6 / 18
Annihilation Differential Cross Section Asymmetries
A =
Axx 0 Axz
0 Ayy 0Axz 0 Azz
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 7 / 18
Annihilation Differential Cross Section Asymmetries
0.3 0.4 0.5 0.6 0.7Ε
-1
-0.8
-0.6
-0.4
-0.2
A Ein = 1 MeV
0.2 0.4 0.6 0.8Ε
-1
-0.75
-0.5
-0.25
0.25
0.5
0.75
A Ein = 10 MeV
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
1A Ein = 100 MeV
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
1A Ein = 1000 MeV
Azz Axx Axz AyyPavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 8 / 18
Annihilation Differential Cross Section
0.2 0.4 0.6 0.8Ε
1
2
3
4
5
d2 ΣdΕdΦ Ein = 10 MeV
100% Longitudinal - 100%Longitudinal Unpolarised
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 9 / 18
Polarisation Transfer in Annihilation
0.2 0.4 0.6 0.8Ε
-1
-0.5
0.5
1Circ POS: Long=+1, ELE: Long+1
0.2 0.4 0.6 0.8Ε
-1
-0.5
0.5
1Circ POS: Long=-1, ELE: Long-1
0.2 0.4 0.6 0.8Ε
-1
-0.75
-0.5
-0.25
0.25
0.5
Pol POS: Long=-1, ELE: Long=+1
0.2 0.4 0.6 0.8Ε
0.2
0.4
0.6
0.8
1Pol POS: Long=+1, ELE: Long=-1
photon #1 photon #2 linear polarisation Initial energy 10 MeVPavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 10 / 18
Polarisation Transfer in Annihilation
0.2 0.4 0.6 0.8Ε
-0.4
-0.2
0.2
0.4
0.6
0.8
1Pol POS: Long=+1, ELE: Long=0
0.2 0.4 0.6 0.8Ε
-1
-0.8
-0.6
-0.4
-0.2
0.2
0.4
Pol POS: Long=-1, ELE: Long=0
photon #1 photon #2 linear polarisation Initial energy 10 MeV
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 11 / 18
Differential Cross Section (Compton)
dσCompton(ξin1 , ξin
2 , ξout1 , ξout
2 )
dΩ=
dσCompton0
dΩ
[1 + ξin
1 (1)A0 + ξin1 Aξin
2T
]×[
ξout1 (1)
(Lγ
0 + ξin1 (1)Lγ
1 + ξin1 (3)Lγ
2ξin2 (1)
)ξout1 (2)
(ξin1 (2)Mγ
1 + ξin1 (3)Mγ
2 ξin2 (2)
)ξout1 (3)
(ξin1 (3)Nγ
1 + ξin2 (1)Nγ
2 + ξin2 (3)Nγ
3 + ξin1 Nγ
4 ξin2
T)
ξout2 (1)
(ξin1 (3)Le
1 + ξin2 (1)Le
2 + ξin2 (3)Le
3 + ξin1 Le
4ξin2
T)
ξout2 (2)
(ξin2 (2)Me
1 + ξin1 Me
2ξin2
T)
ξout2 (3)
(ξin1 (3)Ne
1 + ξin2 (1)Ne
2 + ξin2 (3)Ne
3 + ξin1 Ne
4ξin2
T)
+ξout1 Correlation(ξin
1 , ξin2 )ξout
2T
]Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 12 / 18
Compton Differential Cross Section Asymmetries
0.2 0.4 0.6 0.8Ε
-0.8
-0.6
-0.4
-0.2
0.2
0.4
AsymmetryEin = 1 MeV
0.2 0.4 0.6 0.8 1Ε
-1
-0.75
-0.5
-0.25
0.25
0.5
0.75
Asymmetry Ein = 10 MeV
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
Asymmetry Ein = 100 MeV
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
1Asymmetry Ein = 1000 MeV
Circular - Longitudinal Linear Circular - In-planePavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 13 / 18
Compton Differential Cross Section
0.2 0.4 0.6 0.8 1Ε
5
10
15
20
d2 ΣdΕdΦ Ein = 10 MeV
100% Circular - 100%Longitudinal Unpolarised
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 14 / 18
Polarisation Transfer in Compton Scattering
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
1Γ: Circ=+1, e-: Long=+1
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
1Γ: Circ=-1, e-: Long=+1
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
1Γ: Circ=-1, e-: Long=-1
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
1Γ: Circ=1, e-: Long=-1
photon electron Initial energy 10 MeVPavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 15 / 18
Polarisation Transfer in Compton Scattering
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
1Γ: Circ=1, e-: POL=0
0.2 0.4 0.6 0.8 1Ε
-1
-0.5
0.5
1Γ: Circ=-1, e-: POL=0
photon electron Initial energy 10 MeV
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 16 / 18
Simulations. E166 Analyzing Power (Karim)
3 6 9 120
2
4
6
8
10
12
14
16
18
20
Peter/Vahagn layout 5a Positron. E166_G4_SIM./Annihilation (Vahagn's aproach) Positron. E166_G4_SIM./Annihilation (Calculated x-section and pol-transfer Pavel/Andreas) Positron. E166_G4_SIM. Updated release. 02.08.2006
Ana
lyzi
ng p
ower
[%]
Positron Energy [MeV]
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 17 / 18
Next steps
Check everything
GEANT4 version 4.8.1
Think on Polarimeter design
Prepare publications
Pavel Starovoitov (NC PHEP, Minsk) Polarised Compton Scattering and Annihilation in Flight LC Group seminar 18 / 18