Developments in the measurement of

Gn

E, the neutron electric form factor

Donal DayUniversity of Virginia

July 17, 2003

0-0

Outline

Introduction: Formalism, Interpretation, Motivation

Models

Experimental Techniques

Traditional (unpolarized beams)

Modern (polarized beams, targets, polarimeters)

Experiments using polarized electrons at Jefferson Lab

– Recoil polarization

– Beam-target asymmetry

Outlook

Formalism

dσ

dΩ= σMott

E′

E0

n

(F1)2 + τ

h

2 (F1 + F2)2 tan2 (θe) + (F2)2

io

electron nucleon

E,

−→

k

E ′,

−→

k′

ER,

−→

PR

M

GE,M

γ

F p1 = 1 F n

1 = 0

F p2 = 1.79 F n

2 = −1.91

In Breit frame F1 and F2 related to

charge and spatial curent densities:

ρ = J0 = 2eM [F1 − τF2]

Ji = euγiu[F1 + F2]i=1,2,3

GE

`Q2

´= F1(Q2) − τF2

`Q2

´GM

`Q2

´= F1

`Q2

´+ F2

`Q2

´

For a point like probe GE and GM are the FT of the charge and magnetizations

distributions in the nucleon, with the following normalizations

Q2 = 0 limit: GpE = 1 Gn

E = 0 GpM = 2.79 Gn

M = −1.91

GnE Interpretation

In the NR limit (Breit Frame), GE is FT of the charge distribution ρ(r):

GnE

`q

2´

=1

(2π)3

Z

d3rρ(r)e(iq·r) = 0 −q

2

6

˙r2ne

¸+ ...

'

&

$

%

Experimental: Mean square charge radius˙r2ne

¸is negative.

Theory has intuitive explanation:

r (fm)0 0.5 1 1.5 2 2.5 3

(r)

ρ2 rπ4

-0.05

0

0.05

0.1

0.15

Charge Distribution

r (fm)0 0.5 1 1.5 2 2.5 3

(r)

ρ2 rπ4

-0.05

0

0.05

0.1

0.15

pion-nucleon theory: n = p + π− cloud

valence quark model: n = ddu & spin-spin force ⇒ d → periphery

Charge radius, Foldy term

˙

r2ne

¸

= −6dGn

E(0)

dQ2= −6

dF n1 (0)

dQ2+

3

2M2F n

2 (0)

=˙

r2in

¸

+˙

r2Foldy

¸

Foldy term, 3µn

2mn= (−0.126)fm2, has nothing to do with the rest frame charge

distribution.˙

r2ne

¸

is measured through neutron-electron scattering

˙

r2ne

¸

=3mea0

mnbne = −0.113 ± 0.003 ± 0.004 fm2.

˙

r2in

¸

= −0.113 + 0.126 ≈ 0 suggesting that the spatial charge extension seen in

F1 is about 0 or very small. Recent Work:

N. Isgur, Phys. Rev. Lett. 83, 272 (1999)

M. Bawin & A.A. Coon, Phys. Rev. C. 60,

025207 (1999)

GnE arises from the neutron’s rest frame

charge distribution.

A. Glozman & D. Riska, Phys. Lett. B 459

(1999) 49.

Pionic loop fluctuations make minute

contribution to˙r2in

¸.

Why measure GnE ?

FF are fundamental quantities

Test of QCD description of the nucleon

Symmetric quark model, with all valence quarks with same wf: GnE ≡ 0

GnE 6= 0 → details of the wavefunctions

0

0.025

0.05

0.075

0.1

0 0.25 0.5 0.75 1 1.25Q2(GeV/c)2

GEn

Galster

CI (valence)CI+DI (valence+sea)

Dong, Liu, Williams, PRD 58 074504

Sensitive to sea quark contri-

butions

Soliton model: ρ(r) at large r

due to sea quarks

Necessary for study of nuclear structure.

Few body structure functions

Proton Form Factor Data

Rosenbluth separation

dσ

dΩ=

σMott

(1 + τ)

E′

E0

"

G2E + τ(1 + (1 + τ)2 tan2(θ/2))G2

M| z

#

GpM well measured via Rosenbluth, but not Gp

E hence Recoil Polarization

Dipole Parametrization: Good description of early GpE,M data

GpE =

GpM

µp

= GD =

1 +Q2

0.71

!

−2

GD =“

1 + Q2

k2

”

−2

implies an exponential

charge distribution: ρ (r) ∝ e−kr

Q (GeV/c)

Q2(GeV/c)

2

GEp/G

D

Andivahis

Walker

Hohler

Price

JLAB

0.2

0.4

0.6

0.8

1

1.2

1.4

10-1

1 10

Q2(GeV/c)

2

GM

p/µ

pG

D

Andivahis

Walker

Sill

Hohler

Price

0.6

0.7

0.8

0.9

1

1.1

1.2

10-1

1 10

Neutron Form Factors without Polarization

No neutron target, GnM dominates Gn

E

Traditional techniques used to measure GnM and Gn

E have been:

Elastic scattering 2H(e, e′)2H

Inclusive quasielastic scattering: 2H(e, e′)X

Neutron in coincidence with electron: 2H(e, e′n)p

Neutron in anti-coincidence with electron: 2H(e, e′p)p

Ratio techniques d(e,e′n)pd(e,e′p)n minimizes roles of g.s. wavefunction and

FSI.

Measurements of the Neutron Form FactorsTarget Type Q2(GeV/c)2 Deduced quantities Reference

2H elastic 0.004-0.032 GEn F.A. Bumiller et al., PRL 25, 1774 (1970)

2H elastic 0.012-0.085 GEn Drickey & Hand, PRL 9, 1774 (1962)

2H elastic 0.002-0.16 GEn G.G. Simon, et al., NP A364, 285 (1981)

2H ratio 0.11 GMn H.A. Anklin et al., PL B336, 313 (1994)

2H quasielastic 0.11-0.16 GEn, GMn B. Grossette et al., PR 141, 1435 (1966)

2H elastic 0.116-0.195 GEn, GMn P. Benaksas et al., PRL 13, 1774 (1964)

2H coincidence 0.109-0.255 GMn P. Markowitz et al. PR C48, R5 (1993)

2H quasielastic 0.06-0.3 GEn, GMn E.B. Hughes et al. PR 146, 973 (1966)

2H elastic 0.116-0.195 GMn J.I. Friedman et al. PR 120, 992 (1960)

2H elastic 0.2-0.56 GEn S. Galster et al. NP B32, 221 (1971)

2H ratio 0.22-0.58 GEn, GMn P. Stein et al. PRl 16, 592 (1966)

2H ratio 0.125-0.605 GMn E.E. Bruins et al. PRL 75, 21 (1995)

2H ratio 0.2-0.9 GMn H.A. Anklin et al., PL B428, 248 (1998)

0.2-0.9 GMn G. Kubon et al., PL B524, 26 (2002)

2H elastic 0.04-0.72 GEn S. Platchov et al. NP A510, 740 (1990)

2H ratio 0.39-0.78 GEn, GMn W. Bartel et al. PL 30B, 285 (1969)

2H quasielastic 0.48-0.83 GMn A.S. Esaulov et al. Sov. J. NP 45, 258 (1987)

2H quasielastic 0.04-1.2 GEn, GMn E.B. Hughes et al. PR 139, B458 (1965)

2H quasielastic 0.04-0.2 GMn D. Braess et al. Zeit Phys. 198, 527 (1967)reanalysis of Hughes

2H quasielastic 0.39-1.5 GEn, GMn W. Bartel et al. NP B58, 429 (1973)

2H ratio 1.0-1.53 GEn, GMn W. Bartel et al. PL 39B, 407(1972)

2H anticoincidence 0.28-1.8 GEn, GMn K.M. Hanson et al. PR D8, 753 (1973)

2H quasielastic 0.75-2.57 GMn R.G. Arnold et al. PRL 61, 806 (1988)

2H quasielastic 1.75-4.0 GEn, GMn A. Lung et al. PRL 70, 718 (1993)

2H anticoincidence 0.27-4.47 GEn, GMn R.J. Budnitz et al. PR 173, 1357 (1968)

2H quasielastic 2.5-10.0 GMn S. Rock et al. PRL 49, 1139 (1982)

GnM unpolarized

Kubon (02)Anklin (98+94)Bruins (95)Lung (93)Markowitz (93)

Q2(GeV/c)2

GMn/

µ nGD

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

10-1

1

Kubon ratio

Anklin ratio

Bruins ratio

Lung D(e, e′)X

Markowitz D(e, e′n)p

ratio ≡D(e, e′n)p

D(e, e′p)n

GnM unpolarized and polarized

Xu (02+00)Kubon (02)Anklin (98+94)Bruins (95)Lung (93)Markowitz (93)

Q2(GeV/c)2

GMn/

µ nGD

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

10-1

1

Kubon ratio

Anklin ratio

Bruins ratio

Lung D(e, e′)X

Markowitz D(e, e′n)p

Xu−−→3He(~e, e′)X

ratio ≡D(e, e′n)p

D(e, e′p)n

GnE Before Polarization

No free neutron – extract from e − D elastic scattering:

dσ

dΩ= σNS

»

A`

Q2´

+ B`

Q2´

tan2

„

θe

2

«–

small θe approximation

dσ

dΩ= · · · (Gp

E + GnE)2

ˆ

u(r)2 + w(r)2˜

j0(qr

2)dr · · ·

Galster Parametrization: GnE = − τµn

1+5.6τGD

GnE from Elastic Scattering – D(e, e′~d)

Components of the tensor polarization give useful combinations of the form factors,

t20 =1

√2S

8

3τdGCGQ +

8

9τ2d G2

Q +1

3τd

ˆ1 + 2(1 + τd) tan2(θ/2)

˜G2

M

ff

allowing GQ(Q2) to be extracted. Exploiting the fact that GQ(Q2) = (GpE + Gn

E)CQ(q)

suffers less from theoretical uncertainties than A(Q2), GnE can be extracted to larger

momentum transfers.

E94-018!!

GnE at large Q2 through 2H(e, e′)X

PWIA model σ is incoherent sum of p

and n cross section folded with deuteron

structure.

σ = (σp + σn) I (u, w)

= εRL + RT

Extraction of GnE :

Rosenbluth Separation ⇒ RL

Subtraction of proton contribution

Problems:

Unfavorable error propagation

Sensitivity to deuteron structure

SLAC: A. Lung et al, PRL. 70, 718 (1993)

→No indication of non-zero GnE

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5

Q2

(GeV/c)2

(GE

n/

GD

)2

Galster

Lung et al.(1993)

Hanson et al.(1973)

If GnE is small at large Q2 then F n

1must cancel τF n

2,

begging the question, how does F n1

evolve from 0 at

Q2 = 0 to cancel τF n2

at large Q2?

Models of Nucleon Form Factors

VMD F (Q2) =P

i

CγVi

Q2+M2

Vi

FViN (Q2)

breaks down at large Q2

pQCD F2 ∝ F1

“

MQ2

”

helicity conservation

Counting rules: F1 ∝α2

s(Q2)

Q4

Q2F2/F1 → constant

JLAB proton data: QF2/F1 → constant

Hybrid VMD-pQCD GK, Lomon

Lattice Dong .. (1998)

RCQM point form (Wagenbrunn..)

light front (Cardarelli ..)

di-quark Kroll ...

CBM Lu, Thomas, Williams (1998)

LFCBM Miller

Helicity non-conservation pQCD (Ralston..) LF (Miller..)

Theoretical ModelsVector Meson Dominance

C

F

m +Q

γ∗

ρ,ω

2 2

m2

γ iVe'

e N

N'

Vi

Interaction in terms of coupling strengths of virtual

photon and vector mesons and vector mesons and

nucleon. Success at low and moderate Q2 offset by

failure to accomodate pQCD.

pQCD

High Q2 helicity conservation requires that

Q2F1/F2 → constant as F2 helicity flip arises

from second order corrections and are sup-

pressed by an additional factor of 1/Q2. Fur-

thermore for Q2 ΛQCD counting rules

find F1 ∝ αs(Q2)2/Q4. Thus F1 ∝ 1

Q4and

F2 ∝ 1

Q6⇒ Q2 F2

F1→ constant.

Hybrid Models

Failure to follow the high Q2 behavior sug-

gested by pQCD led GK to incorporate pQCD

at high Q2 with the low VMD behavior. Inclu-

sion of φ by GK had significant effect on GnE .

Lomon has updated with new fits to selected

data.

Lattice calculations of form form factors

Fundamental but limited in stat. accuracy

Dong et al PRD58, 074504 (1998)

QCD based Models

Try to capture aspects of QCD

RCQM, Di-quark model, CBM

Helicity non-conservation shows up in the

light front dynamics analysis of Miller which

predicted QF2

F1→ constant and the viola-

tion of helicity conservation. Ralston’s pQCD

model also predicts that QF2

F1→ constant.

Both models include quark orbital angular mo-

mentum.

Theoretical Models

Spin Correlations in elastic scattering

Dombey, Rev. Mod. Phys. 41 236 (1968): ~p(~e, e′)

Akheizer and Rekalo, Sov. Phys. Doklady 13 572 (1968): p(~e, e′, ~p)

Arnold, Carlson and Gross, Phys. Rev. C 23 363 (1981): 2H(~e, e′~n)p

Essential statement

Exploit spin degrees of freedom

O ∝ GE × GM instead of O ∝ G2E + G2

M

Early work at Bates, Mainz

2H(~e, e′~n)p , Eden et al. (1994)

1H(~e, e′~p) , Milbrath et al. (1998)

3−→He(e, e′), Woodward, Jones, Thompson, Gao (1990 - 1994)

3−→He(e, e′n), Meyerhoff, (1994)

Spin Correlations

Recoil Polarimetry

Beam-Target Asymmetry

Cross Section Measurements

Polarized Beam

Elastic eD

Unpolarized Beam

Ratio Method

Gn

EG

n

E

Gn

MGn

M

Neutron Form Factors

−−→3He(!e, e′)X

−→

D("e, e′n)p

Quasielastic eD

D(e, e′)X

Gn

EG

n

E

−−→3He(!e, e′n)pp

D(e, e′)

D(e, e′−→

d )

D(!e, e′!n)p

Gn

M

Gn

E

D(e, e′n)p

D(e, e′p)n

Gn

M

GnE from spin observables

No free neutron targets – scattering from 2H or 3He– can not avoid

engaging the details of the nuclear physics.

Minimize sensitivity to the how the reaction is treated and maximize the

sensitivity to the neutron form factors by working in quasifree

kinematics. Detect neutron.

Indirect measurements: The experimental asymmetries (ξs′ , AedV ,

Aqeexp) are compared to theoretical calculations.

Theoretical calculations are generated for scaled values of the form

factor.

Form factor is extracted by comparison of the experimental

asymmetry to acceptance averaged theory. Monte Carlo

Polarized targets

The deuteron and 3He only approximate a polarized neutron

Scattering from other unpolarized materials, f dilution factor

Recoil Polarization

n t

l

θe

θ

φ

e

n(p)

e'

Electron scattering plane

Secondary

scattering

plane

I0Pt= − 2p

τ(1 + τ)GEGM tan(θe/2)

I0Pl=1

MN(Ee + Ee′ )

pτ(1 + τ)G2

M tan2(θe/2)

GE

GM= −Pt

Pl

(Ee+Ee′)2MN

tan(θe

2 )Direct measurement of form factor ratio by

measuring the ratio of the transfered

polarization Pt and Pl

Recoil Polarization – Principle and Practice

Interested in transfered polarization, Pl and Pt, at the target

Polarimeters are sensitive to the perpendicular components only,

Ppoln and P

polt

Measuring the ratio Pt/Pl requires the precession of Pl by angle χ

before the polarimeter.

If polarization precesses χ (e.g. in a dipole with ~B normal to

scattering plane):

Ppolt = sinχ · Pl + cosχ · Pt

For χ = 90o, Ppolt = Pl and is related to G2

M

For χ = 0o, Ppolt = Pt and is related to GEGM

GnE/Gn

M via 2H(~e, e′~n)p in JLAB’s Hall C - Charybdis and N-Pol

Quality of polarimeter data optimized by taking advantage of proper

flips (helicity reversals).

L1 = No[1 + pAy(θ + α)]

R2 = No[1 − pAy(θ + β)]

R1 = No[1 − pAy(θ + α)]

L2 = No[1 + pAy(θ + β)]

Using the geometric means, L ≡√

L1L2 and R ≡√

R1R2, the false

(instrumental) asymmetries, α and β, cancel.

ξ = pAy =L − R

L + R

GnE in Hall C, E93-038

Recoil polarization, 2H(~e, e′~n)p

In quasifree kinematics, Ps′ is sensitive to GnE and insensitive to

nuclear physics

Up–down asymmetry ξ ⇒ transverse (sideways) polarization

Ps′ = ξs′/PeApol. Requires knowledge of Pe and Apol

Rotate the polarization vector in the scattering plane (with

Charybdis) and measure the longitudinal polarization,

Pl′ = ξl′/PeApol

Take ratio, Ps′

Pl′. Pe and Apol cancel

Three momentum transfers, Q2 = 0.45, 1.13, and 1.45(GeV/c)2.

Data taking 2000/2001.

GnE in Hall C via 2H(~e, e′~n)p

Ee = 0.884 GeV; Ee′ = 0.643 GeV; Θe′ = 52.65°;

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

φnp

c.m. = 0°

φnp

c.m. = 180°

Q2 = 0.45 (GeV/c)

2; Galster Parameterization

PWBA (RC)FULL (RC): FSI+MEC+IC

Quasifree Emission

PX

′

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

φnp

c.m. = 0°

φnp

c.m. = 180°Quasifree Emission

PY

′

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

φnp

c.m. = 0°

φnp

c.m. = 180°

140 160 180 160 140

Quasifree Emission

Θnp

c.m. [deg]

PZ

′

GnE in Hall C via 2H(~e, e′~n)p

To HMS

Charybdis

Front Veto/Tagger

Bottom Rear Array

Rear Veto/Tagger

Front Array

Lead CurtainTarget LD2, LH2

Top Rear Array

e

e

(Momentum Direction)Z

XP+X

= P,

L

PL

, Polarization Vector

PX

−= −PL

,

SP,

+ 90 deg.− 90 deg.

δ

Taking the ratio eliminates the dependence on the analyzing power and

the beam polarization → greatly reduced systematics

GnE

GnM

= K tan δ where tan δ =Ps′

Pl′=

ξs′

ξl′

0

500

1000

1500

2000

2500

3000

-10 0 10 20

cTOF-cTOFcalc

(ns)

Co

un

ts

1.5 ns

0

200

400

600

800

1000

-10 0 10 20

∆TOF-∆TOFcalc

(ns)

Co

un

tsLeft: Coincidence TOF for neutrons. Difference between measured TOF and

calculated TOF assuming quasi-elastic neutron. Right: ∆TOF for neutron in

front array and neutron in rear array.

∆TOF is kept as the four combinations of (-,+) helicity, and (Upper,Lower)

detector and cross ratios formed. False asymmetries cancel.

r =

„

N+U N−

D

N−U N+

D

«1/2

ξ = (r − 1)/(r + 1)

GnE in Hall C via 2H(~e, e′~n)p

Q2 = 1.14 (GeV/c)

2 (n,n) In Front ∆p/p = -3/+5%

-20

-15

-10

-5

0

5

10

15

0 50 100 150 200 250 300 350 400 450

χ2/ndf = 0.90

ξ–

S′ = -1.29 ± 0.13 %χ = 0°

ξ S′ (

%)

-5

-2.5

0

2.5

5

7.5

10

12.5

15

0 10 20 30 40

χ2/ndf = 0.79

ξ–

L′ = 6.21 ± 0.33 %

χ = -90°

Runs

ξ L′ (

%)

-17.5

-15

-12.5

-10

-7.5

-5

-2.5

0

2.5

0 10 20 30

χ2/ndf = 0.59

ξ–

L′ = -6.36 ± 0.36 %

χ = +90°

Runs

ξ L′ (

%)

GnE in Hall C via 2H(~e, e′~n)p

Precession Angle, (deg)

Y

2 2Fit to Data for Q = 1.15 (GeV/c)

0

2

4

6

−4

−6

−2

0−50−100 50 100

(nn)

(np)Asym

me

try,

(

%)

χ

ξ δ

= A P sin( + )δχξ

GnE in Hall C via 2H(~e, e′~n)p

Herberg (99)Ostrik (99)

Passchier (99)Golak (01)

Bermuth (03)Sick (01)

Zhu (01)Madey - Preliminary

Q2(GeV/c)

2

GEn

Galster

0

0.02

0.04

0.06

0.08

0.1

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Beam–Target Asymmetry - Principle

Polarized Cross Section:

σ = Σ + h∆

Beam Helicity h ± 1

A =σ+ − σ−

σ+ + σ−

=∆

Σ

θe

e

e'

(q, ω)h = ±1

uy

normal

ux

uz

polarization

axis (θ∗, φ

∗)

φ∗

θ∗

along qxz plane

A =

AT︷ ︸︸ ︷

a cosΘ?(GM )2 +

AT L︷ ︸︸ ︷

b sinΘ? cosΦ?GEGM

c (GM )2

+ d (GE)2 ; ε =

N↑ − N↓

N↑ + N↓= PB · PT ·A

Θ? = 90 Φ? = 0

=⇒ A =bGEGM

c (GM )2 + d (GE)2

Θ? = 0 Φ? = 0

=⇒ A =aG2

M

c (GM )2

+ d (GE)2

Beam–Target Asymmetry in E93-026

2−→H(−→e , e′n)p σ(h, P ) ≈ σ0

(1 + hPAV

ed

)

h: Beam Helicity

P : Vector Target Polarization

T : Tensor Target Polarization T = 2 −√

4 − 3P 2

ATd is suppressed by T ≈ 3%

Theoretical Calculations of electrodisintegration of the deuteron by H.

Arenhövel and co-workers

E93-026−→D(−→e , e′n)p

σ(h, P ) = σ0

(1 + hPAV

ed

)

AVed is sensitive to Gn

E

has low sensitivity to potential models

has low sensitivity to subnuclear degrees of freedom (MEC, IC)

in quasielastic kinematics

Sensitivity to GnE – Insensitivity to Reaction

-0.15

-0.1

-0.05

0

0.05

0.1

0 50 100 150 200 250 300 350

θnpcm (deg)

AedV

GEn=1.0×Galster

GEn=0.5×Galster

GEn=1.5×Galster

-0.15

-0.1

-0.05

0

0.05

0.1

100 120 140 160 180 200 220 240

θnpcm (deg)

AedV

BornNN+MECN+MEC+ICN+MEC+IC+REL

GnE in Hall C

Polarized Target

Chicane to compensate for beam deflection of ≈ 4 degrees

Scattering Plane Tilted

Protons deflected ≈ 17 deg at Q2 = 0.5

Raster to distribute beam over 3 cm2 face of target

Electrons detected in HMS (right)

Neutrons and Protons detected in scintillator array (left)

Beam Polarization measured in coincidence Möller polarimeter

MicrowaveInput

NMRSignal Out

Refrigerator

LiquidHelium

Magnet

Target(inside coil)

1° K

NMR Coil

To Pumps

7656A14-94

LN2LN2

To Pumps

B5T

e–

Beam

Sig

na

l

Frequency

LiquidHelium

Solid Polarized Targets frozen(doped) 15ND3

4He evaporation refrigerator 5T polarizing field remotely movable insert dynamic nuclear polarization

Gen Target Performance, 10Sep01

0 200 400 600 800 10000

10

20

30

40

50

Time (min)

DeuteronPolarization(%)

Neutron Detector

Highly segmented scintillator Rates: 50 - 200 kHz per detector Pb shielding in front to reduce

background 2 thin planes for particle ID (VETO) 6 thick conversion planes 142 elements total, >280 channels

Extended front section forsymmetric proton coverage

PMTs on both ends of scintillator Spatial resolution ' 10 cm Time resolution ' 400 ps Provides 3 space coordinates, time

and energy

Protons

Beam

Height

Neutrons

1.0 cm

11cm

(length:160cm)10 cm

10 cm

1998 2001Coincidence Time (ns)

0

200

400

600

800

1000

1200

1400

-30 -20 -10 0 10 20 30

Experimental Technique for−→D(−→e , e′n)p

For different orientations of h and P : NhP ∝ σ (h, P )

Beam-target Asymmetry:

ε =N↑↑ − N↓↑ + N↓↓ − N↑↓

N↑↑ + N↓↑ + N↓↓ + N↑↑= hPfAV

ed

-0.15

-0.1

-0.05

0

0.05

0.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3

Neutron

Proton

Vertical Slope

Asymmetry

Data and MC Comparison

ypos (cm)

DataMC

E′ (MeV) W (MeV)

Q2, (GeV/c)2 θnq (radian) θnpcm (degree)

0500

1000150020002500300035004000

-80 -26.667 26.667 800

500

1000

1500

2000

2500

3000

3500

2000 21000

1000

2000

3000

4000

5000

6000

800 900 1000

0

500

1000

1500

2000

2500

0.4 0.5 0.60

1000

2000

3000

4000

5000

6000

7000

0 0.20

500

1000

1500

2000

2500

3000

3500

160 180 200

Extracting GnE

0.5 0.80.91.0

1.11.31.5

data

E′, MeV

AedV

ypos, cm

AedV

θnq, radian

AedV

θnpcm, deg

AedV

0

0.02

0.04

0.06

0.08

0.1

2050 2100 21500

0.02

0.04

0.06

0.08

0.1

-20 0 20 40

0

0.02

0.04

0.06

0.08

0.1

0 0.025 0.05 0.075 0.10

0.02

0.04

0.06

0.08

0.1

170 180 190

Scale Factor (× Galster)χ2

E′ ypos θnq θnpcm

2σ

0

10

20

30

40

50

60

70

80

0.6 0.8 1 1.2 1.4

8.68.8

99.29.4

0.90.95 1

Preliminary results

Herberg (99)Ostrik (99)

Passchier (99)Golak (01)

Bermuth (03)Sick (01)

Zhu (01)E93026 - Preliminary

Q2(GeV/c)

2

GEn

Galster

0

0.02

0.04

0.06

0.08

0.1

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

SystematicErrors (included):

Ptarget 3-5%

f 3%

cuts 2%

kinematics 2%

GnM 1.7%

Pbeam 1-3%

other 1%

total 6-8%

Preliminary results

Herberg (99)Ostrik (99)

Passchier (99)Golak (01)

Bermuth (03)Sick (01)

Zhu (01)E93026 - Preliminary

E93038 - Preliminary

Q2(GeV/c)

2

GEn

Galster

0

0.02

0.04

0.06

0.08

0.1

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Laboratory Collaboration Q2(GeV/c)2 Reaction Reported

MIT-Bates E85-05 0.255 2H(e, e′n) 1994

<0.8 2H(e, e′n) Planned

<0.8 3He(e, e′n) Planned

Mainz-MAMI A3 0.31 3He(e, e′n) 1994

A3 0.15, 0.34 2H(e, e′n) 1999

A3 0.385 3He(e, e′n) 1999

A1 0.67 3He(e, e′n) 1999/2003

A1 0.3, 0.6, 0.8 2H(e, e′n) Analysis

NIKHEF 0.21 2H(e, e′n) 1999

Jefferson Lab E93026 0.5, 1.0 2H(e, e′n) 2001/Analysis

E93038 0.45, 1.15, 1.47 2H(e, e′n) Analysis

E02013 1.3, 2.4, 3.4 3He(e, e′n) Approved

Conclusions

GnE remains the poorest known of the four nucleon form factors.

GnE is a fundamental quantity of continued interest.

Significant progress has been made at several laboratories by

exploiting spin correlations

GnE can be described by the Galster parametrization (surprisingly)

and data under analysis is of sufficient quality to test QCD inspired

models.

Future progress likely with new experiments and better theory.