polarised compton scattering and annihilation in flight · total cross section asymmerties...
TRANSCRIPT
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