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)

F.M., 12.10.2005 – p. 6/38

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

F.M., 12.10.2005 – p. 7/38

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

F.M., 12.10.2005 – p. 15/38

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

F.M., 12.10.2005 – p. 31/38

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