# Measuring the Neutron Magnetic Form Factor in CLAS12

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## Full text

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nM

2

2

et al.

et al

2

2

### dis-tributions.

2010-05-16 21:36:11 ) 2 (GeV 2 Q 2 4 6 8 10 12 14 D G n µ / M n G 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Green - Previous world data. Red - J.Lachniet et al.

Miller Guidal et al.

Cloet et al.

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### Some Necessary Background

Express the elastic cross section in terms of the elastic electromagnetic form factors (EEFFs): Dirac (F1) and Pauli (F2)

dσ dΩ = σM ott » ` F12 + κ2τ F22´ + 2τ (F1 + κF2)2 tan2 „ θ 2 «–

where κ is the anomalous magnetic moment, E (E′) is the incoming (outgoing) electron energy, θ is the scattered electron angle, τ = 4QM22, and

σM ott =

α2E′ cos2(θ2) 4E3sin4(θ

2)

.

For convenience use the Sachs form factors.

dσ dΩ = σM ott (GnE)2 + τ(GnM)2 1 + τ + 2τ tan 2 θ 2(G n M)2 ! where GE = F1 − τ F2, GM = F1 + F2.

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### Some Necessary Background

Express the elastic cross section in terms of the elastic electromagnetic form factors (EEFFs): Dirac (F1) and Pauli (F2)

dσ dΩ = σM ott » ` F12 + κ2τ F22´ + 2τ (F1 + κF2)2 tan2 „ θ 2 «–

where κ is the anomalous magnetic moment, E (E′) is the incoming (outgoing) electron energy, θ is the scattered electron angle, τ = 4QM22, and

σM ott =

α2E′ cos2(θ2) 4E3sin4(θ

2)

.

For convenience use the Sachs form factors.

dσ dΩ = σM ott (GnE)2 + τ(GnM)2 1 + τ + 2τ tan 2 θ 2(G n M)2 ! where GE = F1 − τ F2, GM = F1 + F2.

An important kinematic quantityθpq for

quasielas-tic (QE) scattering from deuterium.

e

pq

pq

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2

N2

E

M

E

2

−i~q·~r

3

2

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2

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nM

nM

n

D

n k=0

k

k

n+2 k=1

k

k

2

2 p

et al.

### used same ratio method.

) 2 (GeV 2 Q -2 10 10-1 1 10 D G n µ / M n G 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Solid - Published J.Kelly fit (PRC 70, 068202, 2004).

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nM

nM

n

D

n k=0

k

k

n+2 k=1

k

k

2

2 p

et al.

### used same ratio method.

) 2 (GeV 2 Q -2 10 10-1 1 10 D G n µ / M n G 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Solid - Published J.Kelly fit (PRC 70, 068202, 2004). ) 2 (GeV 2 Q -2 10 10-1 1 10 D G n µ / M n G 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Solid - Published J.Kelly fit (PRC 70, 068202, 2004).

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nM

3

3

T′

2

2

### .

M. Jones, 2005 Hall C Workshop.

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dσ dΩ

2

QE

dσ dΩ

2

QE

2

maxpq

max2

### σ

M ott (GnE)2+τ(GnM)2 1+τ

2 θ 2

n M

2 dσ dΩ

1

2

pqmax

max2

pqmax

max2

e.g.

etc.

e.g.

etc.

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dσ dΩ

2

QE

dσ dΩ

2

QE

2

maxpq

max2

### σ

M ott (GnE)2+τ(GnM)2 1+τ

2 θ 2

n M

2 dσ dΩ

1

2

pqmax

max2

pqmax

max2

e.g.

etc.

e.g.

etc.

nM

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### The Experiment - Jefferson Lab

Continuous Electron Beam Accelerator Facility (CEBAF) Superconducting Electron Accelerator (currently 338 cavities), 100% duty cycle.

Emax = 11 GeV in Hall B, ∆E/E ≈ 2 × 10−4, Isummed ≈ 90 µA, Pe ≥ 80%.

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### Target

Forward Detector

Angular Range 5◦ 40(outbenders)

∆p/p < 0.01 @ 5 GeV/c

∆θ (mr) < 1 p > 2.5 GeV/c

∆φ (mr) < 3 p > 2.5 GeV/c

Neutron Detection Nef f = 0.1 − 0.6

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### Target

Forward Detector

Angular Range 5◦ 40(outbenders)

∆p/p < 0.01 @ 5 GeV/c ∆θ (mr) < 1 p > 2.5 GeV/c ∆φ (mr) < 3 p > 2.5 GeV/c Neutron Detection Nef f = 0.1 − 0.6 luminosity ≈ 1035 s−1cm−2. Hydrogen Cell Vacuum Deuterium Cell

The collinear, dual, hydrogen-deuterium target enables us to collect high-precision, in situ

calibration data so systematic uncertainties ≤ 3%.

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### Selecting Quasielastic Events

Select e − p events using the CLAS12 tracking system for electrons and protons. Select e − n events with either the TOF or electromagnetic calorimeters;

semi-independent measurements of the neutron production. Apply a θpq cut to isolate quasi-elastic

events plus W2 < 1.2 (GeV /c2)2.

### z

0 0.5 1 1.5 2 2.5 0 5000 10000 15000 20000 25000 30000 35000 ) 2 (GeV 2 W all ep events < 3 degrees pq θ CLAS E5 data 4.2 GeV q and nucleon p. Angle between W cut2

Match acceptances using quasi- elastic electron kinematics to determine if the nucleon lies in CLAS12 acceptance.

Neutrons and protons treated exactly the same whenever possible.

The CLAS GnM measurement at 4 GeV overlaps the proposed measurement to provide a consistency check.

Measure the neutron production in both electromagnetic calorimeters and TOF scintillators; providing an internal consistency check.

Impact of inelastic background will be greater at large Q2

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2

pq cut:

Hermiticity cut:

### No additional particles in the event.

2010-01-21 13:57:48 ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 2000 4000 6000 8000 10000 12000 14000 16000 E = 11 GeV H(e,e’n)X 2 Red - QE Green - Inelastic Black - total 2 = 12.5-14.0 GeV 2 Q ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 500 1000 1500 2000 2500 E = 11 GeV H(e,e’n)X 2 o < 1.5 pq θ Hermiticity OFF 2 Same Q ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 500 1000 1500 2000 2500 E = 11 GeV H(e,e’n)X 2 o < 1.5 pq θ Hermiticity cut ON 2 Same Q

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2

### the dual-cell target shown here.

Hydrogen Cell Vacuum

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### Calibrations - Neutron Detection Efficiency

1. Use the ep → e′π+n reaction from the hydrogen target as a source of tagged neutrons in the TOF and calorimeter.

2. For electrons, use CLAS12 tracking. For π+, use positive tracks, cut on the difference between β measured from tracking and from time-of-flight to reduce photon

background.

3. For neutrons, ep → e′π+X for

0.9 < mX < 0.95 GeV/c2.

4. Use the predicted neutron mo-mentum ~pn to determine the

loca-tion of a hit in the fiducial region and search for that neutron.

5. The CLAS6 GnM results.

6. GSIM12 simulation results for CLAS12 are shown in the inset. Proposed measurement will ex-tend to higher momentum where the efficiency is stable.

Calorimeter efficiency (GeV/c) n p 0 1 2 3 4 5 6 7 8 EC Neutron Efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 o - 25 o = 20 n θ GSIM12 simulation

Simultaneous, in situ calibrations with dual

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### The Ratio Method - Systematic Errors

GnM is related to the e − n/e − p by the following (neutron (n) and proton (p)).

GnM = ± r h R“σ p mott σnmott ” “ 1+τn 1+τp ” “ GpE2 + τεp p G p M 2” − GnE2i εn τn

Upper limits on systematic error from the CLAS6 measurement (∆GnM/GnM = 2.7%).

Quantity δGnM/GnM × 100 Quantity δGnM/GnM × 100

Neutron efficiency parameterization

< 1.5 θpq cut < 1.0

proton σ < 1.5 GnE < 0.7

neutron accidentals < 0.3 Neutron MM cut < 0.5

neutron proximity cut < 0.2 proton efficiency < 0.4

Fermi loss correction < 0.9 Radiative corrections < 0.06

Nuclear Corrections < 0.2

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### Systematic Uncertainty Studies

Systematic uncertainty for proton cross section (∆GnM/GnM ×100) based on differences in the pro-ton reduced cross section pa-rameterizations of Bosted (PRC 51, 409 (1995)) and Arrington-Melnitchouk.

Similar approach to systematic un-certainty (∆GnM/GnM ×100) for GnE

based on differences in GnE pa-rameterizations of Kelly (PRC 70, 068202 (2004))and BBBA05 (hep-ph/0602017).

Neutron Detection Efficiency - Sim-ulate the uncertainty associated with fitting the shape of the mea-sured neutron detection curves.

2007-06-09 20:56:27 2 (GeV/c) 2 Q 2 4 6 8 10 12 14 n M /G n M G0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 E = 11 GeV

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### Systematic Uncertainties - Summary

Quantity δGnM/GnM × 100 Quantity δGnM/GnM × 100 Neutron efficiency parameterization < 0.7(1.5) θpq cut < 1.0(1.7) proton σ < 1.5(1.5) GnE < 0.7(0.5) neutron accidentals < 0.3 Neutron MM cut < 0.5

neutron proximity cut < 0.2 proton efficiency < 0.4

Fermi loss correction < 0.9 Radiative corrections < 0.06

Nuclear Corrections < 0.2

Summary of expected systematic uncertainties for CLAS12 GnM measurement

(∆GnM/GnM = 2.4%(2.7)). Red numbers represent the previous upper limits from the CLAS6 measurement.

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et al.

nM

2

2

2

2

2

2

2

### range.

2010-05-18 10:39:38 ) 2 (GeV 2 Q 0 2 4 6 8 10 12 14 n M /G n M G-2 10 -1 10

World’s Data Uncertainty

CLAS12 Anticipated Statistical Uncertainty CLAS12 Anticipated Systematic Uncertainty

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et al.

nM

2

2

2

2

2

2

2

### range.

2010-05-18 10:39:38 ) 2 (GeV 2 Q 0 2 4 6 8 10 12 14 n M /G n M G-2 10 -1 10

World’s Data Uncertainty

CLAS12 Anticipated Statistical Uncertainty CLAS12 Anticipated Systematic Uncertainty

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### CLAS12 Anticipated Results

2010-05-18 00:17:12

2

2

D

n

M n

### 1.2

Red - J.Lachniet et al.

Green - Previous World Data

Miller

Guidal et al.

Cloet et al.

### )

Uncertainty bands are for CLAS6 (Lachniet et al.) (red) and CLAS12 anticipated (black).

Miller - PRC 66, 032201(R) (2002); Guidal - PRD 72, 054013 (2005); Cloët - Few Body Syst., 46:1-36 (2009).

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### CLAS12 Anticipated Results

2010-05-18 00:17:12

2

2

D

n

M n

### 1.2

Red - J.Lachniet et al.

Green - Previous World Data

Miller Guidal et al. Cloet et al. 2010-05-18 00:10:02

2

2

D

n

M n

### 1.2

Red - J.Lachniet et al.

Green - Previous World Data Black - CLAS12 anticipated

Anticipated

Statistical uncertainties only

Miller

Guidal et al.

Cloet et al.

Uncertainty bands are for CLAS6 (Lachniet et al.) (red) and CLAS12 anticipated (black).

Miller - PRC 66, 032201(R) (2002); Guidal - PRD 72, 054013 (2005); Cloët - Few Body Syst., 46:1-36 (2009).

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### Conclusions

The neutron magnetic form factor is a fundamental quantity and extending the Q2

range and coverage will probe deeper into hadronic structure, provide essential constraints on GPDs, and challenge lattice QCD.

With a tested method used in CLAS6, we will significantly expand our understanding of nucleon structure and challenge theory.

The CLAS12 detector will provide wide kinematic acceptance (Q2 = 3 − 15(GeV/c)2) and independent measurements of neutrons with its calorimeters and TOF systems. We propose to use the ratio method on deuterium to reduce our sensitivity to a variety of sources of systematic uncertainty and limit systematic uncertainties to less than 3%. To keep systematic uncertainties small we will measure the detection efficiencies with a unique dual-cell target. Production and calibration data will be taken simultaneously. We have been approved for 30 PAC days of beam time at 11 GeV (A− rating).

Part of a broad effort to measure the EEFFs at JLab and

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nM

pq

pq

### inelastic background.

Effect of θpq and hermiticity cuts. 2010-01-04 13:38:13 ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 2000 4000 6000 8000 10000 12000 14000 16000 E = 11 GeV en events Red - QE Green - Inelastic Black - total 2 = 12.5-14.0 GeV 2 Q ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 500 1000 1500 2000 2500 E = 11 GeV en events o < 1.5 pq θ No hermiticity cut 2 = 12.5-14.0 GeV 2 Q H(e, e’p) 2 ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 500 1000 1500 2000 2500 E = 11 GeV en events o < 1.5 pq θ Hermiticity cut ON 2 = 12.5-14.0 GeV 2 Q

pq

### .

fIN = inelastictotal for W2 < 1.2 GeV2. ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 200 400 600 800 1000 2 = 12.5-14.0 GeV 2 E = 11 GeV, Q en events o < 1.5 pq θ =11% IN f ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 200 400 600 800 1000 2 = 12.5-14.0 GeV 2 E = 11 GeV, Q en events o < 1.0 pq θ =5.5% IN f H(e, e’p) 2 ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 200 400 600 800 1000 2 = 12.5-14.0 GeV 2 E = 11 GeV, Q en events o < 0.5 pq θ =2.3% IN f

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nM

### - QE Scattering Angles

Q2 = 15.0 GeV2 Q2 = 3.5 GeV2 0 10 20 30 40 0 10 20 30 40 Θe HdegL Θn H deg L

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nM

pq

### consistent with CLAS6, E5 data.

2010-01-17 23:14:08 ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 Counts 0 2000 4000 6000 8000 10000 4.2 GeV, E5 epXBlue: eD

Black: epX plus cut

pq

θ

Green: epX plus hermiticity cut cut and pq θ Red: hermiticity cut

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n

n

pn−p0 a0

n

0

n

0

n

n

n

### the difference.

(GeV/c) n p 0 1 2 3 4 5 6 7 8 9 Efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 / ndf = 80.18 / -3 2 χ p0 0.5984 ± 0.001182 p1 1.599 ± 0.001715 p2 0.1496 ± 0.0004325 / ndf = 80.18 / -3 2 χ p0 0.5984 ± 0.001182 p1 1.599 ± 0.001715 p2 0.1496 ± 0.0004325 / ndf = 80.18 / -3 2 χ p0 0.5984 ± 0.001182 p1 1.599 ± 0.001715 p2 0.1496 ± 0.0004325

Neutron Detection Efficiency

2 (GeV/c) 2 Q 2 4 6 8 10 12 14 n M /G n M G0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 E = 11 GeV

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### Update for E12-07-104: Other Elastic Form Factors Uncertainties

Systematic uncertainty (∆GnM/GnM × 100) based on differences in the proton reduced cross section param-eterizations of Bosted and Arrington-Melnitchouk.

Systematic uncertainty (∆GnM/GnM × 100) based on differences in GnE parameteri-zations of Kelly and BBBA05. Future measurements will reduce the uncertainty for

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nE

### Uncertainty

GE,n/GD Kelly

GE,n/GD BBBA05

Q2(GeV2)

World data on GnE. (C.E. Hyde-Wright and K.deJager, Ann. Rev. Nucl. Part. Sci. 54

(2004) 54 and references therein.)

The neutron electric form factor from Kelly and BBBA05 parameterizations as a function of Q2 (J. J. Kelly, PRC 70, 068202 (2004) and R. Bradford et al.,

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### Update for E12-07-104: Systematic Uncertainties

Summary of expected systematic uncertainties for CLAS12 GnM measurement in

percentages (100 × ∆GnM/GnM = 2.5%(2.7)). Red numbers represent the previous upper limits from the CLAS6 measurement.

Quantity δGnM/GnM × 100 Quantity δGnM/GnM × 100

Neutron efficiency < 0.7(1.5) θpq cut < 1.0(1.7)

proton σ < 1.5(1.5) GnE < 0.7(0.5) Background subtraction < 1.0 Fermi loss

correc-tion

< 0.9

neutron accidentals < 0.3 Neutron MM cut < 0.5

neutron proximity cut < 0.2 proton efficiency < 0.4

Nuclear Corrections < 0.2 Radiative correc-tions

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### measurements

2010-05-18 00:10:02

2

2

D

n

M n

### 1.2

Red - J.Lachniet et al.

Green - Previous World Data Black - CLAS12 anticipated

Anticipated

Statistical uncertainties only

Miller

Guidal et al.

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### methods

1. To reduce inelastic background further, reduce the maximum θpq.

fIN = inelastictotal for W2 < 1.2 GeV2. 2010-01-04 13:48:39 ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 200 400 600 800 1000 2 = 12.5-14.0 GeV 2 E = 11 GeV, Q en events o < 1.5 pq θ =11% IN f ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 200 400 600 800 1000 2 = 12.5-14.0 GeV 2 E = 11 GeV, Q en events o < 1.0 pq θ =5.5% IN f H(e, e’p) 2 ) 2 (GeV 2 W -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Counts 0 200 400 600 800 1000 2 = 12.5-14.0 GeV 2 E = 11 GeV, Q en events o < 0.5 pq θ =2.3% IN f

2. In a similar Q2 range, in E12-09-019 only the

θpq cut will be used leaving more inelastic

background contaminating the the QE peak. 3. At higher Q2 (i.e. in PR10-005), the width

of the inelastic component will continue to in-crease.

Updating...

## References

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