Transverse Asymmetries in Elastic Electron Nucleon ... Asymmetries in Elastic Electron Nucleon...
Transcript of Transverse Asymmetries in Elastic Electron Nucleon ... Asymmetries in Elastic Electron Nucleon...
Transverse Asymmetries in Elastic ElectronNucleon Scattering and the Imaginary Part of the
Two-Photon Amplitude
Frank E.Maas
Institut de Physique Nucleaire de Orsay
Institut fur KernphysikMAINZER MIKROTRON
Workshop on Nucleon Form Factors
Frascati, October 12-14, 2005
F.M., 12.10.2005 – p. 1/38
Imaginary Part of Two-Photon-Exchange
Beam Spin Normal Asymmetries in elastic~e pscattering
- SAMPLE@MIT-Bates: backward
- HAPPEX@JLab: forward
- G0@JLab: forward
- E158@SLAC: forward
- A4@MAMI: forward
Beam Spin Normal Asymmetries in Møller scattering
- E158@SLAC: forward
Future Measurements
F.M., 12.10.2005 – p. 2/38
Beam Spin Normal Asymmetries in Elastic Scattering
- Single-Spin-Asymmetries: e− Spin longitudinal,
Parity Violating, φ-symmetric
APV = 10−6
e
e´
p´
p
p
e
γ
p'
e' e
p
Z0
p'
e'
- Single-Spin-Asymmetries: e− Spin transverse,
Dependence on Azimuth Angle φ: sin(φ),
Abeam⊥ = 10−5,Atarget
⊥ = 10−2
e
e´
p´
p e
e´
p´
p
p
e
γ
p'
e'
p
e
γ
p'
e'
γ
F.M., 12.10.2005 – p. 3/38
2-γ-Exchange
e e'
p p'
γ
e e'
p p'
γ γ
e''
X:p,∆,...
Tnonflip Tflip
Helicity Amplitudes
u(k2) γ ·P u(k1) · u(p2) γ ·K u(p1) u(k2)u(k1) · u(p2)u(p1)
u(k2) γ ·P u(k1) · u(p2)u(p1) u(k2)u(k1) · u(p2) γ ·K u(p1)
u(k2) γ5γ ·P u(k1) · u(p2) γ5γ ·K u(p1) u(k2) γ5 u(k1) · u(p2) γ5 u(p1)
Generalized Form Factors
GM(s,Q2), GE(s,Q2), F3(s,Q2) F4(s,Q2), F5(s,Q2), F6(s,Q2)
F.M., 12.10.2005 – p. 4/38
Two-Photon Exchange
Mnon−flip =e2
Q2 u(k2) γµ u(k1) u(p2) [GM(s,Q2) γµ −
F2(s,Q2)
Pµ
M+ F3(s,Q
2)γ ·KPµ
M2 ]u(p1)
Mflip =me
Me2
Q2 [u(k2)u(k1) u(p2) [F4(s,Q2)
+F5(s,Q2)
γ ·KM
]u(p1)
+F6(s,Q2)u(k2) γ5 u(k1) u(p2) γ5 u(p1)]
F.M., 12.10.2005 – p. 5/38
Observables
- 1-Photon forbidden Transitions in Nuclear States
- Elastic Cross Section Measurement (Real Part, Correction to
1-Photon)
- σe−p - σe+p (Real Part, Correction to 1-Photon)
- ε-Dependence (at fixed Q2) (Real Part, Correction to 1-Photon)
- Recoil Polarization Px,Py,Pz (Real Part,Imaginary Part)
- Transverse Target Spin Asymmetry (Imaginary Part, forbidden in
1-Photon)
- Transverse Beam Spin Asymmetry (Imaginary Part, only in
2-Photon)
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Single Spin Asymmetry in Elast. Scattering
e
e´
P
Sn
1
2
3
4 5
6
7
8
φe,φP
θe
θP
~P −~P
~Sn = (~k1×~k2)/|~k1×~k2|
A⊥ =σ↑↑−σ↓↑σ↑↑ +σ↓↑
A(φe,θe) = A⊥(θe)~Sn ·~P
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Single Spin Asymmetry in Elast. Scattering
A⊥ =σ↑↑−σ↓↑σ↑↑ +σ↓↑
A⊥ = −me
M
√
2ε(1− ε)√
1+ ττ
(1+ετ|GE|2|GM|2)−1
× (−τ I (F3
GM)− |GE|
|GM| I (F4
GM)− 1
1+ τ(τ+
|GE||GM|)I (
νF5
M2| ˜GM|))
F.M., 12.10.2005 – p. 8/38
Imaginary Part: Study of Intermediate State Spectrum
e e'
p p'
γ
Q1
γ
Q2
e''
X:p,∆,...
F.M., 12.10.2005 – p. 9/38
Doubly Virtual Compton Scattering
integration over kinematics
0
0.5
1
0 0.5 1
Q2 2 (
GeV
2 )
Ee = 0.855 GeV
W = M30o
90o
150o
0
2
4
6
0 2 4 6
Ee = 3 GeV
W = M30o
90o
150o
0
0.5
1
0 0.5 1
Q1 2 (GeV2)
Q2 2 (
GeV
2 )
30o
90o
150o
W = 1.232 GeV
0
2
4
6
0 2 4 6
Q1 2 (GeV2)
30o
90o
150o
W = 1.232 GeV
F.M., 12.10.2005 – p. 10/38
Transverse Asymmetry in Elastic Scattering
- Systematic Studies of the 2-Photon-Amplitude at low Energies
- A⊥ proportional to Imaginary Part (Connect to Real Part via
Dispersion Relations)
- “known”πN Amplitudes from π-Electro-Production for Calculation
of A⊥ (B.Pasquini MAID)
- Complementary Access to π-Electro-Production
- Electroweak Precision Experiments depend on
γ Z0 and W+ W− Box Graphs
Parity Violating Electron Scattering (A4, G0, Happex,
SAMPLE, Qweak)
Parity Violation in Atomic Physics
Vud
- Generalized Parton Distributions
F.M., 12.10.2005 – p. 11/38
PV Experiments
A4 Measurement Principle
Longitudinally or transversely polarized electrons
Target: unpolarized protons
Detector: scattering angle
Counting experiment: A = N+−N−N++N−
F.M., 12.10.2005 – p. 12/38
Experimental Conditions for PV Experiments
SAMPLE: e−,Air-Cherenkov(MIT-Bates) %37~
MeV200
e
e
P
E =
o
scatt 170130 −=θ
HAPPEX: e−,magnetic Spectr., Integrating Det.
A4: e−,EM-Calorimeter
G0:p+,Time of Flight, Toroidal Magnetic field
22 (GeV/c)0.11.0~
,
-Q
GGGe
A
s
M
s
E
rangeover
separatedand
F.M., 12.10.2005 – p. 13/38
SAMPLE at MIT/Bates
F.M., 12.10.2005 – p. 14/38
Two Photon Physics: SAMPLE measurements
SAMPLE transverse beam asymmetry
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Two Photon Physics: SAMPLE measurements
Mottar
Xiv
:nuc
l-ex/
0002
010
v1
22 F
eb 2
000
F.M., 12.10.2005 – p. 16/38
Two Photon Physics: SAMPLE measurements
Afanasev
F.M., 12.10.2005 – p. 17/38
Two Photon Physics: SAMPLE measurements
Pasquini
F.M., 12.10.2005 – p. 18/38
Two Photon Physics: HAPPEX
θe=6◦, Q2 = 0.1(GeV/c)2, Ee = 3 GeV A⊥ = - 6.6 ppm± 1.5 ppm (stat) ± 0.2 ppm (syst) (Kent Paschke)Afanasev: A⊥ = - 7.2 ppm (no cut in W of inelastic
state)
F.M., 12.10.2005 – p. 19/38
G0 at JLab
22 (GeV/c)0.11.0~
,
-Q
GGGe
A
s
M
s
E
rangeover
separatedand
F.M., 12.10.2005 – p. 20/38
G0 at JLab
F.M., 12.10.2005 – p. 21/38
G0 at JLab
F.M., 12.10.2005 – p. 22/38
G0 at JLab
F.M., 12.10.2005 – p. 23/38
E158 at SLAC: Møller Scattering
F.M., 12.10.2005 – p. 24/38
E158 at SLAC:~ep Scattering
F.M., 12.10.2005 – p. 25/38
E158 at SLAC:~ep Scattering
Gorchtein
F.M., 12.10.2005 – p. 26/38
A4 at MAMI/Mainz
F.M., 12.10.2005 – p. 27/38
A4 fast PbF2 Calorimeter
Calorimeter:1022 PbF2 Crystal in 146FramesΘ = 30◦..40◦, Φ = 0..2πLuminosity Monitors:8 Integrating Water-Cherenkov DetectorsΘ = 4.4◦..10◦, Φ = 0..2πFull Coverage of theAzimuthal Angle φ
F.M., 12.10.2005 – p. 28/38
Strangeness Contribution
-1.5 -1 -0.5 0 0.5 1 1.5
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
EsG
MsG
SAMPLE
Awith G
A4
He4HAPPEX-
HAPPEX-H
G0 (extrapolated)
2 = 0.1 GeV2
Q
PRL 94, (2005) 152001, PRL 93 (2004) 022002
F.M., 12.10.2005 – p. 29/38
Extraction of physics asymmetry
0 50 100 150 200 2500
500
1000
1500
2000
2500
2x10
pol1 raw
pol1 dnl
pol0 raw
pol0 dnl
peak
p0
D
Elastic Cut
Elastic Cut
N , N+ -
Energy (ADC)
1
2
3
45
6
7
8
Φ=0°
Φ=90°
Φ=180°
Φ=270°
Φ=45°
Φ=135° Φ=225°
Φ=315°
Extract elastic counts N+i , N−
i
from channel i = 1..1022
Combine the 1022 channels
to 8 sectors
N+Sec= ΣN+
i , N−Sec= ΣN−
i
Normalization to target den-
sity (L=luminosity, I=beam
current)
ASecexp ≡ Aexp(Φi) =
N+Sec
ρ− − N−Sec
ρ−
N+
ρ− + N−ρ−
, ρ± =L±
I±
F.M., 12.10.2005 – p. 30/38
Determination of A⊥
E = 855.2MeV, Q2 = 0.23(GeV/c)2, 50 h
Angle (deg)
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360
Asy
mm
etr
y (p
pm
)
-15
-10
-5
0
5
10
855 MeV T ransversal f(phi)= A*cos(phi)
Chisquare / NDF = 2.290 / 4 = 0.573
A = (7.44 + - 2.43) ppm
Weighted mean
Fit
A⊥ = (−7.62 ±2.34stat ±0.80syst) ppm
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Determination of A⊥
E = 569.3MeV, Q2 = 0.11(GeV/c)2, 50 h
Angle (deg)
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360
Asy
mm
etr
y (p
pm
)
-10
-5
0
5
10
570 MeV T ransversal f(phi)= A*cos(phi)
Chisquare / NDF = 16.980 / 7 = 2.426
A = (8.19 + - 0.99) ppm
Weighted mean
Fit
A⊥ = (−8.28 ±0.93stat ±0.49syst) ppm
F.M., 12.10.2005 – p. 32/38
Comparison of A⊥ with Model Calculations
p
e
γ
p'
e'
p
e
γ
p'
e'
γ
Intermediate State: Proton, πN States (MAID)(B. Pasquini)
0.2 0.4 0.6 0.8 1 1.2 1.4
-20
-15
-10
-5
0
Beam Energy [GeV]
Tra
nsv
erse
Asy
mm
etry
[1
0-6
]
PRL 94, 082001 (2005)F.M., 12.10.2005 – p. 33/38
Elastic Scattering at Forward Angles
F.M., 12.10.2005 – p. 34/38
Program at θ = 35◦
Hydrogen and Deuterium
200 400 600 800 1000 1200 1400 1600
-15
-10
-5
0
5A
n[1
0-6
]
Electron Beam Energy [MeV]
proton
deuteron
F.M., 12.10.2005 – p. 35/38
Program at θ = 145◦
Hydrogen and Deuterium
200 400 600 800 1000 1200 1400 1600
-100
-80
-60
-40
-20
0
20A
n[1
0-6
]
Electron Beam Energy [MeV]
proton
deuteron
F.M., 12.10.2005 – p. 36/38
A4 transverse Programm
Ee [MeV] θe [degrees] δAp⊥ [ppm] hours δAD
⊥ [ppm] hours δAn⊥ [ppm]
proton deuteron (extracted)
315 (35±5)◦ 0.5 20 0.5 20 20
420 (35±5)◦ 0.5 40 0.5 35 11
510 (35±5)◦ 0.5 90 0.5 70 7
570 (35±5)◦ 0.5 90 0.5 70 7
854 (35±5)◦ 0.5 300 0.5 220 4
1200 (35±5)◦ 1 260 1 180 6
1500 (35±5)◦ 2 180 2 120 11
315 (145±5)◦ 3 90 2 130 10
420 (145±5)◦ 3 (230) 2 (320) 10
510 (145±5)◦ 4 (300) 3 (390) 13
570 (145±5)◦ 4 (370) 3 (390) 13
854 (145±5)◦ 8 (490) 7 (380) 28
F.M., 12.10.2005 – p. 37/38
Summary
Transverse Single-Spin-Asymmetries SAMPLE, A4, G0,
HAPPEX, E158
Imaginary Part of the 2-Photon-Amplitude
precision tool → inelastic πN intermediate States
Intermediate Inelastic States Dominate
Systematic Study of 2-Photon-Amplitude
Experiments at Forward- and Backward angles
F.M., 12.10.2005 – p. 38/38