Measurement of the Neutron Electric Formpeople.virginia.edu/~dbd/NPTalks/fiu-foils.pdf · Models of...

Measurement of the Neutron Electric FormFactor Gn

E in 2−→H(−→e , e′n)p Quasi-elasticScattering

Donal DayUniversity of Virginia

Charlottesville, VA 22904dbd@virginia.edu

March, 28, 2003

Florida International/JLAB Workshop on the Deuteron, March 27–29, 2003

1 IntroductionForm Factors

Interpretation

GnE Models

GnE Measurements

2−→H(−→e , e′n)p Technique

2 Experiment E93026Overview

Moller Polarimeter

Polarized Target

Neutron Detector

3 AnalysisOverview

Simulation

Neutron Identification

Asymmetries

Extracting GnE

4 Results and OutlookResult and Systematics

GnE World Data

Comparison to Models

Outlook

Florida International/JLAB Workshop on the Deuteron, March 27–29, 2003 1

Nucleon Form Factors

dΩ= σMott

h2 (F1 + F2)

2(θe) + (F2)

electron nucleonPSfrag replacements

−→

E ′,

−→

k′ ER,

−→

F p1 = 1 F n

F p2 = 1.79 F n

2 = −1.91

e scatt. angle: θe

pointlike target: σmott =α2 cos2(θe/2)

4E2 sin4(θe/2)

Kin. factor: τ = Q2/4M2

4-momentum transfer:

„−→k −

−→k′«2

−`E − E′

´2= 4EE′ sin2 (θe/2)

“Q2”

= F1(Q2)− τF2

“Q2”

σMott

(1 + τ)

2E + τ(1 + (1 + τ)2 tan

2(θ/2))G

Q2 = 0 limit: GpE = 1 Gn

E = 0 GpM = 2.79 Gn

M = −1.91

GnE Interpretation

In the nonrelativistic limit Q2 = −→q 2 (Breit Frame) GE is Fourier Transform ofthe charge distribution ρ(r):

“q2”

(2π)3

Zd3rρ(r)e(iq·r)

Zd3rρ (r)−

Zd3rρ (r) r2 + ...

= 0−q2

E+ ...

Anomalous magnetic moment of neutron and Yukawa theory of mesons gaverise to the idea of a separated charge distribution in the neutron. The chargeradius was expected to be negative.

E= −6

dGE(0)

dQ2= −6

dF1(0)

2M2F2(0)

r2Foldy

Charge radius, Foldy term

E= −6

dGnE(0)

dQ2= −6

dF n1 (0)

n2 (0)

r2Foldy

EFoldy term, 3µn

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

frame charge distribution.˙r2

¸is measured through neutron-electron scatteringDr

bne = −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 studies have attempted to resolve this issue with theconclusion that Gn

E arises from the neutron’s rest frame chargedistribution.

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

“Interpreting the Neutron’s Electric Form Factor. Rest Frame ChargeDistribution or Foldy Term?”

in relativistic expansion of the constituent quark model the Foldy termcancels against a contribution from F1.

M. Bawin & A.A. Coon Phys. Rev. C. 60, 025207 (1999)

“Neutron charge radius and the Dirac equation”explicit incorporation of the Dirac-Pauli form factors in Dirac equation.The Foldy term is canceled by a contribution from F1.

Why is⟨r2in

⟩< 0?

r (fm)0 0.5 1 1.5 2 2.5 3

ρ2 rπ4

Charge Distribution

r (fm)0 0.5 1 1.5 2 2.5 3

ρ2 rπ4

Hadron Picturepπ− component in neutron wavefunctionπ− cloud on outside

n p n n D+ n

CQMneutron = udd and spin–spin forces create a chargesegregation

Why measure GnE?

Fundamental quantity

• Test of QCD description of the nucleon

Symmetric quark model, with all valence quarks with samewavefunction, Gn

E ≡ 0→ details of the wavefunctions

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

Galster

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

Dong, Liu, Williams, PRD 58 074504

• More sensitive than otherform factors to sea quarkcontributions

• Soliton model Gorski 1992suggests that ρ(r) at large r

due to sea quarks

Necessary for study of nuclear structure.

• Without GnE almost impossible to extract information in high Q2

few body structure functions

• Large source of error in extraction of strange quark form factorsfrom parity violating experiments

• Explains˙r2ch

¸of 48Ca as compared to 40Ca

Parametrizations of Nucleon Form Factors

The electric form factor, GpE(Q2) = 1

(2π)3

Rd3rρ(r)e(iq·r)

Dipole Parametrization: Good description of early GpE,M data

0.71(GeV/c)2

GpE = GD =

GnE = −τµnGD ; τ =

GD =“1 + Q2

”−2

implies an exponentialcharge distribution:

ρ (r) ∝ e−kr

Galster Parametrization: From e−D elastic scattering

GnE = −

1 + 5.6τGD

Models of Nucleon Form FactorsGround state QCD structure is strong coupling problem: currentlyunsolvable

Vector Meson Dominance

Target

phot onw,r,f

F (Q2) =P

CγViQ2+M2

FViN(Q2)

1Q2+M2

⇒ propagator of meson of mass MVi

CγVi⇒ photon-meson coupling strength

FViN(Q2) ⇒ meson-nucleon form factor.

VMD breaks down at large Q2: Can notreproduce the dipole form factor or reproducethe prediction of pQCD.

pQCDHigh Q2 helicity conservation by γ−quark interaction requiresthat Q2F1/F2 → constant as F2 helicity flip arises from secondorder corrections and are suppressed by an additional factor of1/Q. Furthermore for Q2 ΛQCD counting rules find F1 ∝αs(Q

2)/Q4. Thus F1 ∝ 1Q4 and F2 ∝ 1

Q6 ⇒ Q2F2F1

→constant. Contradicted by JLAB proton data which show thatQ

F2F1→ constant.

Hybrid ModelsFailure to follow the high Q2 behavior suggested by pQCD ledGK to incorporate pQCD at high Q2 with the low VMD behavior.Inclusion of φ by GK had significant effect on Gn

E. Lomon hasupdated with new fits to selected data.

Lattice calculations of form form factors nascentFundamental but currently limited in statistical accuracyDong et al PRD58, 074504 (1998)

QCD based modesModels: try to capture aspects of QCDRCQM P.L. Chung and F. Coester, PR D44, 229 (1991), I.Z. Aznaurian, PL

B316, 39 (1993), M.R. Frank, B.K. Jennings, and G.A. Miller, PRC54, 920

(1996), M. Ivanov, M. Locher, and V. Lyubovitskij, Few Body Systems, 21, 131

(1996).

di-quark model P. Kroll, M.Schurmann, and W. Schweiger, Z. Phys. A432,

429 (1992).

QCD sum rules A.V. Radyushkin, Acta. Phys. Polon. B15, 403 (1984).

Cloudy bag model D.H. Lu, A.W. Thomas, and A.G. Williams, PR C57, 2628

(1998).

Helicity non-conservation shows up in the light front dynamicsanalysis of Miller and collaborators where in the imposition ofPoincare invariance analytic results that predicted Q

F2F1→ constant

and the violation of helicity conservation. Helicity non-conservationalso shows up in the pQCD model of Ralston and collaboratorswhich also predict that Q

→ constant. Both models includequark orbital angular momentum.

light front cloudy bag model Miller has extended the light frontdynamics to include the cloudy bag with a description of theneutron as a bare nucleon and a negative pion cloud with a longtail, giving rise to the negative charge radius.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Q2(GeV/c)2

GalsterG-K (no F)G-K (with F)DipoleVMD - Hohler (fit 8.2)Bag Model - Lu (r=1.0 fm)Quark Model - Ivanov

Soliton→Holzwarth MMD→ Mergell, Meissner and DreschelGBECQM→ Wagenbrum and collaborators

GnE Measurements

No free neutron target =⇒ Use deuteron

• Inclusive cross section measurements on Deuterium:– Elastic e−D scattering at small angles:

depends on N-N potential, subtraction of proton contribution– Quasielastic e−D scattering

Rosenbluth separation, sensitive to deuteron structure

• Double Polarization measurementsasymmetry measurementdetection of neutron in coincidence→ less sensitive to deutron structure→ avoid Rosenbluth separation→ avoid subtraction of proton contribution2H(−→e , e′−→n )p, 2−→H (−→e , e′n)p, 3−→He(−→e , e′n)pp

Other methods

• 2H(e, e′n)p

• 2H(e, e′p)p (anticoincidence)

• Ratio techniquese,e′pe,e′n

e-D Elastic Scattering

Born approximation

dΩ= σNS

»A“

+ B“

„θe

A(Q2) = G2c + 8

9ηG2Q + 2

3η2G2

B(Q2) = 43η(η + 1)G2

η = Q2

small θe approximation

dΩ= · · · (Gp

e + GnE)

2hu(r)

2+ w(r)

2)dr · · ·

1. AIA(Q2) deduced after corrections for relativistic effects andMEC

2. Subtract magnetic dipole using parametrization of data

3. S and D state functions to unfold nuclear structure for variouspotentials to get isoscalar form factor

4. Subtract proton form factor

5. Sensitive to deuteron wavefunction model and MEC

Early measurements of GnE and slope at Q2 = 0

Relativistic corrections and model dependence: Casper and Gross, PR 155, 1607 (1967)

(a) Partovi wave function

(b) Partovi and relativistic corrections

(c) Feshbach-Lomon and relativistic corrections

Elastic, ContinuedIn the case of 2H(e, e′)2

−→H components of the tensor polarization give useful

combinations of the form factors,

t20 =1

3τdGCGQ +

h1 + 2(1 + τd) tan

2(θ/2)

ffallowing GQ(Q2) to be extracted. Exploiting the fact that GQ(Q2)suffersless from theoretical uncertainties than A(Q2), Gn

E can be extracted to largermomentum transfers.

Quasielastic e− d Scattering

PWIA model (Durand and McGee): Cross section is incoherent sum of p and ncross section folded with deuteron structure.

σ =`σp + σn

´I (u, w)

»“G

”2+`G

´2–+

»“G

”2+`G

´2–)I (u, w)

= εRL + RT

ε =h1 + 2 (1 + τ) tan

2(θe/2)

• Extraction of GnE:

Rosenbluth Separation ⇒ RLSubtraction of proton contribution

• Problems:Unfavorable error propagationSensitivity to deuteron structure

SLAC: A. Lung et al, Phys. Rev. Lett. 70, 718 (1993)→Gn

E consistent with zero and Galster.

0 1 2 3 4 5

Q2 (GeV/c) 2

Galster

Lung et al.(1993)Hanson et al.(1973)

Open questions

“Q2”

= F1(Q2)− τF2

“Q2”

If GnE is small at large Q2 then F n

1 must cancel τF n2 , begging the question, how

does F n1 evolve from 0 at Q2 = 0 to cancel τF n

2 at large Q2?

E133 data from SLAC shows the ratio of σn/σp falling with Q2, suggesting that

F n1 ' 0. This implies that Gn

E would dominate GnM at high Q2.

Double polarization measurements

Akhiezer and Rekalo (1968), Dombey (1968)2H(~e, e′~n)p2−→H(~e, e′n)p, ~3He(~e, e′n)pp

Asymmetry measurements→ less sensitive to deuteron structure→ avoid Rosenbluth separation→ avoid subtraction of proton contribution (detect neutron)→ only relative charge measurement needed→ reduced dependence on detector acceptance→ radiative corrections reduced→ understand helicity dependent deadtime→ need absolute beam and target polarization

Target Type Q2(GeV/c)2 Reference2H (−→e , e′−→n ) 0.15 C. Herberg et al., Eur. Phys. J. A 5, 131 (1999)2−→H (−→e , e′n) 0.21 I. Passchier et al., Phys. Rev. Lett. 82, 4988 (1999)2H (−→e , e′−→n ) 0.252 T. Eden et al., Phys. Rev. C 50, R1749 (1994)

3−→He (−→e , e′n) 0.31 M. Meyerhoff et al., Phys. Lett. B 327, 201 (1994)2H (−→e , e′−→n ) 0.33 M. Ostrick et al., Phys. Rev. Lett. 83, 276 (1999)

3−→He (−→e , e′n) 0.36 J. Becker et al., Eur. Phys. J . A6, 329 (1999)2−→H (−→e , e′n) 0.5 H. Zhu et al., Phys. Rev. Lett. 87, 081801 (2001)3−→He (−→e , e′n) 0.67 D. Rohe et al., Phys. Rev. Lett. 83, 4257 (1999)2−→H (−→e , e′n) 0.5, 1.0 JLAB E93-026 preliminary 20012H (−→e , e′−→n ) 0.45, 1.15, 1.47 JLAB E93-038 preliminary 2001

3−→He (−→e , e′n) 0.67 Mainz 2003, Bermuth2H (−→e , e′−→n ) 0..3, 0.6, 0.8 Mainz data taking completed 2002

Polarized Electron on Polarized Free Neutron

(q, w)h = ±1

uynormal

polarization axis (q*, f*)

along qxz plane

Neutron Polarization P Beam Helicity h

Polarized Cross Section: σ = σ0 (1 + hPA)

A =a cos θ? (Gn

M)2+ b sin θ? cos Φ?Gn

´2+ d

=⇒ A =

bGnEGn

´2+ d

Polarized Electron on Polarized Deuteron Target

Polarized Cross Section for quasielastic 2−→H(−→e , e′n)p:

σ(h, P ) = σ0

(1 + hAe + PAV

d + TATd + hPAV

ed + hTATed

)h: Beam HelicityP : Vector Target PolarizationT : Tensor Target Polarization T = 2−

√4− 3P 2

Deuteron supports a tensor polarization, T , in addition to the usual vector polarization,P – this can lead to both helicity dependent and helicity independent contributions

– ATed andAe vanish if symmetrically averaged

– AVd vanishes in the scattering plane

– ATd is suppressed by T ≈ 3%

Theoretical Calculations of electrodisintegration of the deuteron:H. Arenhövel, W. Leidemann, and E. L. Tomusiak, Z. Phys. A 331,123 (1988); 334, 363(E) (1989).H. Arenhövel, W. Leidemann, and E. L. Tomusiak, Phys. Rev. C46, 455 (1992).

AVed is sensitive to Gn

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

under certain kinematical conditions....

Sensitivity to GnE – Insensitivity to Reaction

0 50 100 150 200 250 300 350

θnpcm (deg)

GEn=1.0×Galster

GEn=0.5×Galster

GEn=1.5×Galster

100 120 140 160 180 200 220 240

θnpcm (deg)

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

θcmnp : Angle between −→q and relative n-p momentum in cm system; 180 deg corresponds to

neutron in direction of −→q

Experimental Technique for 2−→H(−→e , e′n)p

How to access AVed?

Experiment measures counts for different orientationsof h and P :

NhP ∝ σ (h, P )

Beam-target Asymmetry:

ABT =N++ −N−+ + N−− −N+−

N++ + N−+ + N++ + N++

1 + TATd

' hPAVed

E93026 Collaboration

112 collaborators from 18 institutions

Duke University, Florida International University,Hampton University, Jefferson Lab, Louisiana Tech University,

Mississippi State University, Norfolk State University,North Carolina A&T State University, Old Dominion University,

Ohio University, Southern University at New Orleans,Tel Aviv University, University of Basel,

University of Maryland at College Park, University of Virginia,Virginia Polytechnic Institute & State University,

Vrije Universiteit of Amsterdam, Yerevan Physics Institute

Experiment E93026

• Measured in Hall C at Thomas Jefferson National AcceleratorFacility (Jlab) in Newport News, Virginia, USA

• Measuring periods– Aug 1998 - Oct 1998– July 2001 - Dec 2001

• Kinematics:2.2× 106 neutrons at Q2 = 0.5 (GeV/c)2 (1998)6.5× 106 neutrons at Q2 = 0.5 (GeV/c)2 (2001).75× 106 neutrons at Q2 = 1.0 (GeV/c)2 (1998)1.4× 106 neutrons at Q2 = 1.0 (GeV/c)2 (2001)

Hall Schematic

• 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

net Ta

e– Beam

Signal

Dynamic Nuclear Polarization

Pictorial Representation–Proton Enhancement

M m label

+1/2 +1/2 (c)

-1/2 +1/2 (a)

213 MHz

140 GHz

+1/2 -1/2 (d)

-1/2 -1/2 (b)

Forbidden

Forbidden transitions (∆mj 6= ±1) allowed

Microwaves of 140Ghz - 213 MHz drive the b → c transition

Relaxation occurs through c → a transition

Target Stick

Deuteron NMR

• Sweep RF frequency-measure absorptive part of response withtuned phase sensitive circuit

• Polarization proportional to signal area

• Fix scale by measuring polarization in thermal equilibrium (TE)

@ (5 Tesla, 1.5 K)

PTE =4tanh(µB/2kT )

3 + tanh2(µB/2kT )≈ 0.07%

Typically can achieve 3 to 5% systematic error (relative)

32.4 32.6 32.8 33

w(MHz)

32.4 32.6 32.8 33

Enhanced

w(MHz)

Gen Target Performance, 10Sep01

0 200 400 600 800 10000

Time (min)

Average polarization ' 25%

Neutron Detector• Highly segmented scintillator

• Rates: 50 - 200 kHz per detector

• Pb shielding in front to reducebackground

• 2 thin planes for particle ID (VETO)

• 6 thick conversion planes forneutron detection

• 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, timeand energy

Protons

BeamHeight

Neutrons

1.0 cm11cm

(length:160cm)10 cm

1998 2001

Analysis

• Event Reconstruction

– HMS standard reconstruction + target magnet + raster– NDET tracking: Particle Identification

⇒ cut variables: W, Ypos, coincidence-time , θnq

• Event Selection and Normalization→ Normalized yields: N↑, N↓

• Experimental asymmetries:

ε = N↑−N↓

N↑+N↓= PB · PT · f · AV

ed⇒`AV

´meas

Dilution factor f =Npolarized

N from 12C

• Radiative corrections, Accidental background subtraction

⇒ measured deuteron asymmetry AVed binned in four variables

• Theoretical calculations of AVed (for different Gn

E = α×Galster)from Arenhövel for a kinematical grid

• Average theoretical AVed over experimental acceptance using

MC and compare with measured`AV

´meas

⇒ GnE

Timing

Coincidence Time (ns)

-30 -20 -10 0 10 20 30

Particle Identification

• Neutrons No paddle hits along trajectory to target

• Veto inefficiency from 2/3 using first bar layer 3% per plane

• Target Field helps, θnq < 0.1 rad

• Protons bent ≈ 17 deg (0.3 rad)

0200400600800

10001200140016001800

0 0.1 0.2 0.3 0.4

MCData

qnq (radian)

0 0.2 0.4 0.6qpq (radian)

Particle Identification

Not typical–most protons above the bulk of the bars

Fired but failed the MT cut.

Experimental Asymmetries

std W θnpcm E’ ypos θpq

lab special

Burger Plot v4

neutron-stdneutron-altproton-stdproton-alt

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3std tbig

Burger Plot v12 -- bins in ntrk_dx (vertical slope)

n - stdn - alt

proton - stdgood p

std ytar x’tar y’tar xfp yfp x’fp y’fp W

Burger Plot v8 -- Electron Kinematics

n-std neutron-alt

proton-stdproton-alt

Dilution factor

Solution: Monte Carlo and experimental data

E, (GeV)

0200400600800

1000120014001600

2.35 2.4 2.45 2.5 2.55

ypos (cm)

0100200300400500600700800900

-50 0 50

θnq (radian)

0200400600800

1000120014001600

0 0.1 0.2 0.3 0.4

θnpcm (degree)

125 150 175 200 225

Structure of AVed

Extracting GnE

0.5 0.80.91.0

1.11.31.5

E¢, MeV

ypos, cm

qnq, radian

qnpcm, deg

Q2, (GeV/c)2

2050 2100 21500

-20 0 20 40

0 0.025 0.05 0.075 0.10

170 180 190

0.45 0.5 0.55 0.6Scale Factor (¥ Galster)

E¢yposqnqqnp

s=6.5%0

0.6 0.8 1 1.2 1.4

Extracting GnE

Scale Factor (× Galster)

E′ ypos θnq θnpcm

0.6 0.8 1 1.2 1.4

8.68.8

99.29.4

0.90.95 1

E′: Energy of the scattered electron

Ypos: Horizontal coordinate of the hadron track in the neutrondetector

θnq: Angle between 3-momentum transfer (−→q ) and hadron track

θcmnp: Angle between neutron and (−→q ) in cm

CEX and multi step processes

Not all good neutrons are generated by quasielastic scattering.Data and asymmetry get contaminated, in the following way.

• in the lead shielding in front of the neutron detector:– d(e,e’p) followed by Pb(p, n)– d(e,e’p) followed by Pb(p, π0) and π0 → γ + γ

• the 15ND3 target

– d(e,e’p) followed by 15N(p,n)

First estimates of Pb(p,n) revealed that this effect is not neglible.

• A simulation was written using the measured protondistribution in the detector; Pb(p,n) cross section from chargeexchange studies for Gn

• The net contamination in asymmetry due to Pb(p,n) is−3.44± 1.02% for Q2 = 0.5. The error dominated by theuncertainty in the cross section.

• For Q2 = 1 the simulation has not been run. Estimate ofcontamination is −3± 3%.

• The 15N(p,n) contamination is small and is estimated to be−0.3%± 0.3% for Q2 = 0.5 and Q2 = 1.

• Photon contamination is neglible for Q2 = 0.5 and about oneorder of magnitude smaller than from Pb(p,n) for Q2 = 1

based on total cross section of proton induced π0 production.

Preliminary Results

0 1 2Q2 (GeV2/c2)

Sick (01)Bermuth (03)

Ostrik (99)Herberg (99)

Golak (01)

Passchier (99)Zhu (01)Gen01 - Preliminary

Galster

Result for 1998 Q2 = 0.5 (GeV/c)2:

GnE = 0.04632± 0.00616stat ± 0.00341syst

? PRL 87 (2001) 081801

Preliminary Results and Systematics

Final (98)? Q2 = 0.5 (GeV/c)2 GnE = 0.04632± 0.0070

Preliminary (2001) Q2 = 0.5 (GeV/c)2 GnE =' Galster± ' 7.5%(stat.)

Preliminary (2001) Q2 = 1.0 (GeV/c)2 GnE =& Galster± ' 14%(stat.)

Systematics 98 01 (predicted)Target Polarization 5.8% 3-5%

Dilution Factor 3.9% 3%Cut Dependence 2.4% 2%

Kinematics 2.2% 2%Gn

M 1.7% 1.7%Beam Polarization 1.0% 1-3%

Other 1.0% 1%Sum 8.0% 6-8%

1 10Q2 [ GeV2 ]

0 2 4 6 8

Q2 [ GeV2 ]µG

1Q2 [ GeV2 ]

0 0.5 1 1.5 2

Q2 [ GeV2 ]

VMD-pQCD(2002)VMD-pQCD(2001)

Point Form - CQM (2001)

Soliton (2002)Light Front - CQM (2002)

Future GnE Results/ Measurements

Under Analysis

• Jefferson Lab: 2−→H(~e, e′n)p at Q2 = 0.5 and 1.0(GeV/c)2 (E93026)

• Jefferson Lab: D(~e, e′~n)p at Q2 = 0.45, 1.1 and 1.45(GeV/c)2 (E93038)

• Mainz: D(~e, e′~n)p at Q2 =' 0.3, 0.6 and 0.8(GeV/c)2

Future measurements

• Jefferson Lab: 3−→He(~e, e′n)pp up to at Q2 = 3.4(GeV/c)2

• Bates: 2−→H(~e, e′n)p and 3−→He(~e, e′n)pp precisionmeasurements up to Q2 ' 1 (GeV/c)2 with internaltargets and BLAST.

• out to 14 (GeV/c)2 with an upgraded CLAS and the12 GeV upgrade.

Summary

• GnE is related to the charge distribution of the

neutron.

• GnE remains the poorest known of the four nucleon

form factors.

• GnE is a fundamental quantity of continued interest.

• We extracted GnE from beam-target asymmetry

measurements.

• GnE can be described by the Galster parametrization

(surprisingly) and data under analysis is of sufficientquality to test QCD inspired models.

• Future progress likely with new experiments andbetter theory.

Reaction Mechanism Dependence

100 120 140 160 180 200 220 240

θnpcm (deg)

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

Experimental acceptance: 160 deg < θcmnp < 180 deg

Difference between full Calculation andBorn + REL: '8%

From ε to GnE in Detail

The polarized beam and target electron deuteron cross section can beexpressed in the form:

S(h, Pd1 , P

d2 ) = S0

»1 + hAe + P

Vd + P

+ h(Pd1 A

Ved + P

where Ae, AVd , AT

d , AVed, AT

ed are electron asymmetry, vector and tensortarget asymmetries, and electron-deuteron vector and tensor asymmetries.

Comparing with the cross section expression, one can obtain expressions forthe five asymmetries:

2hS0[S(h, 0, 0)− S(−h, 0, 0)] ,

2P d1 S0

hS(0, P

d1 , P

d2 )− S(0,−P

d1 , P

2P d2 S0

hS(0, P

d1 , P

d2 )− S(0,−P

d1 , P

d2 )− 2S0

AV,Ted

4hP d1/2

(hS(h, P

d1 , P

d2 )− S(−h, P

d1 , P

∓hS(h,−P

d1 , P

d2 )− S(−h,−P

d1 , P

d2 )i)

Note that S0 is in the denominator and we never measure S0.

S(+h) + S(−h) 6= S0

ε =(L+ − R+)− (L− − R−)

(L+ + R+) + (L− + R−).

L+ = Φ+nDS(h, P d1 , P d

L− = Φ−nDS(h,−P d1 , P d

R+ = Φ+nDS(−h, P d1 , P d

R− = Φ−nDS(−h,−P d1 , P d

ε =hh(1− β)Ae + (1 + αβ)P d

1 AVed + (1− βγ)P d

2 ATed

i(1 + β) + (1− αβ)P d

+ (1 + βγ)P d2 AT

α = −P1−P1+

β =Φ−Φ+

γ =P2(P1−)

P2(P1+)

P d2 = 2−

h4− 3(P d

1 )2i1/2

AVed =

h(1 + αβ)P d1

(εh(1 + β) + (1− αβ)P

Vd + (1 + βγ)P

−hh(1− β)Ae + (1− βγ)P

With full φ acceptance Ae, AVd and AT

ed have zero contributions.

ATd remains. For P d

1 = 20%, P d2 ' 3%

with ATd ≈ 10−2AT

d can be ignored

AVed =

ε(1 + β)

h(1 + αβ)P d1

With the dilution factor

AVed =

ε(1 + β)

h(1 + αβ)P d1 f

Gen01 Collaboration

A. Aghalaryan, A. Ahmidouch, R. Asaturyan, I. Ben-Dayan, F. Bloch, W. Boeglin, B. Boillat,H. Breuer, J. Brower, C. Carasco, M. Carl, R. Carlini, J. Cha, N. Chant, E. Christy, L. Cole,

L. Coman, M. Coman, D. Crabb, S. Danagoulian, D. Day, K. Duek, J. Dunne, M. Elaasar, R. Ent,J. Farrell, R. Fatemi, D. Fawcett, H. Fenker, T. Forest, K. Garrow, A. Gasparian, I. Goussev,

R. Grima, P. Gueye, M. Harvey, M. Hauger, R. Herrera, B. Hu, I. Jaegle, J. Jourdan, C. Keith,J. Kelly, C. Keppel, M. Khandaker, A. Klein, A. Klimenko, L. Kramer, B. Krusche, S. Kuhn,M. Jones, Y. Liang, J. Lichtenstadt, R. Lindgren, J. Liu, A. Lung, D. Mack, G. Maclachlan,

P. Markowitz, P. McKee, D. McNulty, D. Meekins, J. Mitchell, H. Mkrtchyan, R. Nasseripour,I. Niculescu, K. Normand, B. Norum, A. Opper, E. Piasetzky, J. Pierce, M. Pitt, Y. Prok, B. Raue,

J. Reinhold, J. Roche, D. Rohe, O. Rondon, D. Sacker, N. Savvinov, B. Sawatzky, M. Seely,I. Sick, N. Simicevic, C. Smith, G. Smith, M. Steinacher, S. Stepanyan, J. Stout, V. Tadevosyan,

S. Tajima, L. Tang, G. Testa, R. Trojer, B. Vlahovic, B. Vulcan, K. Wang, G. Warren, S. Wells,F.R. Wesselmann, H. Woehrle, S. Wood, C. Yan, Y. Yanay, L. Yuan, J. Yun, M. Zeier, H. Zhu,

B. ZihlmannDuke University, Florida International University, Hampton University, Jefferson Lab,

Louisiana Tech University, Mississippi State University, Norfolk State University,North Carolina A&T State University, Old Dominion University, Ohio University,Southern University at New Orleans, Tel Aviv University, University of Basel,

University of Maryland at College Park, University of Virginia,Virginia Polytechnic Institute & State University, Vrije Universiteit of Amsterdam,

Yerevan Physics Institute

Impact of GnM

0 0.2 0.4 0.6 0.8 1

Q2(GeV/c)2

/µn G

Mainz(1998)

Mainz(2002)

Jlab(2000)

Dynamic Nuclear Polarization

Pictorial Representation–Deuteron

+1/2 -1 (f)

+1/2 0 (e)

-1/2 0 (b)

-1/2 +1 (a)

32.7 MHz

140 GHz

M m label

-1/2 -1 (c)

+1/2 +1 (d)

For positive enhancement drive the c → e or b → d transition. Relaxationoccurs through e → b and d → a transition

NMR system

Magnetic susceptibility is a function of the frequency

χ(ω) = χ′(ω) + iχ′′(ω) consisting of a dispersive part (χ′) and an absorptivepart (χ′′)

P = 2µ0π~γ2NJ

R∞0 χ′′dω

L(ω) = L0[1 + 4πηχ(ω)]

Measure the impedance of coil to get at χ′′

l/2 Cable

BRM PhaseOut

MagnitudeOut

LengthAdjust

Liverpool Q Meter

RFGenerator

Room TempCryogenic

Target Cavity

Deposited Energy-ADCs

0 2000 4000 60000

0 2000 4000 6000

0 2000 4000 60000

0 2000 4000 6000

0 2000 4000 60000

0 2000 4000 6000

Neutrons do not have definite energy deposit due to conversion mechanism.12-14 MeVee

Dilution Factor and Packing Fraction

df =Rpolarized

Rpolarized + RunpolarizedPf =

Material Source Ni/ND

Nitrogen ND3 0.333Helium (1− Pf) 0.240Helium external 0.080Aluminum Cell in/out 0.015Copper NMR Coil 0.003Nickel NMR Coil 0.001∗∗Carbon Calibration 0.286∗∗Helium Calibration 0.560

ρi ∗ thickness/Ai

Current Asymmetry

Cut Optimization

θnq (radian)

x 10 2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

SumDNHeAl

Invariant Mass (MeV/c2)

x 10 3

750 800 850 900 950 1000 1050 1100 1150 1200 1250

SumDNHeAl

Balancing count rate and dilution factor

Accidental Background

proton cointime

x 10 2

-5 0 5 10

neutron cointime

-5 0 5 10

• Shape of background is determined by fact that TDC acceptsonly one hit– Randoms/Reals ≈ 4% for neutrons– Acts like dilution for unpolarized randoms

MC vs Data ND 3

Neutron

ypos (cm)

DataMC

xpos (cm)

E′ (MeV) W (MeV)

θnq (radian) θnpcm (degree)

-50 0 500

-50 0 50 100

2000 2050 2100 21500

800 900 1000 1100

0 0.1 0.2 0.30

160 170 180 190 200

Proton

ypos (cm)

DataMC

x (cm)

E¢ (MeV) W (MeV)

1000015000200002500030000

-50 0 500

500010000150002000025000300003500040000

-200 -100 0 100

1000015000200002500030000

2000 2050 2100 21500

100002000030000400005000060000

800 900 1000 1100

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