September 28, 2006 R. Alarcon @ MIT Symposium

The Electromagnetic Form Factors of the Nucleon

• Introduction

• Proton Form Factors

• Neutron Form Factors

• Summary

Form factor in quantum mechanics

e i k

r e i k r'

Elastic scattering of fast electrons on atoms.Elastic scattering of fast electrons on atoms.

F q dr ri q r( ) ( )= −∫ e ρ

Atomic form factor:Atomic form factor:

σ ( ) ~ ( )q F q2

Fourier transform of diagonalFourier transform of diagonalelements of the density matrix!elements of the density matrix!

The cross section:The cross section:

E.g., the hydrogen atom in the ground state:E.g., the hydrogen atom in the ground state:

F qq

m e( ) = +

⎛⎝⎜

⎞⎠⎟

−

14

2

2 4 2

2

ψπ

( )rr me

=− ⋅e

2 2

ρ ( r ) = ψ (r ) 2

charge densitycharge density

EM Nucleon Form Factors• They are the basic observables that contain important information about the electromagnetic structure of the proton and the neutron in the non-perturbative region.

• Extensively studied by ∼ 40 years now, through electron scattering: SLAC, Saclay, Mainz,NIKHEF, MIT-Bates, JLab, …

• They are required for knowledge of many other things:

structure of nuclei at short distancesProton charge radius and Lamb shiftprecision tests of Weak interaction at low Q2

• They should give clues on how to connect QCD to the NN force

[ ])()()1(

1 2222 QGQGEE

dd

MEMott τετε

σσ+

+′

=Ω

EM Nucleon Form Factors• e-N elastic scattering (Rosenbluth’s formula):

GEp (0) =1 GM

p (0) = μ P

GEn(0) = 0 GM

n (0) = μ n

• e-N elastic scattering does not work for the neutron μ P

GEp

GMp (Q2 ) → 1

Proton

World Data from Rosenbluth’s separation

μ P

GEp

GMp (Q 2 ) → const

Akhiezer+Rekalo, Sov.JPN 3 (1974) 277Arnold,Carlson+Gross, PRC 21 (1980) 1426

Akhiezer+Rekalo, Sov.JPN 3 (1974) 277Arnold,Carlson+Gross, PRC 21 (1980) 1426

Akhiezer+Rekalo, Sov.JPN 3 (1974) 277Arnold,Carlson+Gross, PRC 21 (1980) 1426

Hall A at Jefferson Laboratory

Q2

ln2+

89β Q2

Λ2

F2(Q2)F1(Q

2)→ const

PRL 91 (2003) 092003

A e

Internal Target Physics at MIT-Bates

Ee ≤ 1 GeV, Pe= 40-80 % Im= 200 mA, τ ≥ 10 min

e

South Hall Ring

• pure species• thin• high polarization• thin cell• low holding field

L = 1031-1033 atoms cm-2 s-1

Novosibirsk, AmPS, HERMES, IUCF, COSY

Polarized H/D Target

Left-right symmetric

Large acceptance:0.1 < Q2/(GeV/c)2 < 0.820o < θ < 80o, -15o < φ < 15o

COILS Bmax = 3.8 kG

DRIFT CHAMBERSTracking, PID (charge)δp/p=3%, δθ = 0.5o

CERENKOV COUNTERSe/π separation

SCINTILLATORSTrigger, ToF, PID (π/p)

NEUTRON COUNTERSNeutron tracking (ToF)

DRIFT CHAMBERS

CERENKOVCOUNTERS

SCINTILLATORS

NEUTRON COUNTERS

TARGETBEAM

BEAM

COILS

The BLAST Detector

The BLAST Collaboration

Experimental Program

D-stateT20

Tens-Pol. D

Te11Gn

ED-stateGnM

Vect-Pol. D

N-∆: C2/M1GpE/Gp

MInclusivePol. H

)e',e(p p (e ,e'p) +o+ n)e',e(p ,p)e',e(p n,)e',e(p πππ

d (e ,e') d (e ,e'p) d (e ,e'n) d (e ,e'd)

d (e,e'd) d (e,e'p)

High quality data for nucleon and deuteron structureby means of spin-dependent electron scattering

NC

TOFCC

WC

NC

LADS L20 L15

upstream downstream

1 m

32o

e- left θ* ≈ 90o

“spin-perpendicular”

e- right θ* ≈ 0o

“spin-parallel”

Experimental Technique

C. Crawford (submitted to PRL)

C. Crawford (submitted to PRL)

Neutron

Methods to Determine GEn

Methods to Determine GEn

Methods to Determine GEn

Methods to Determine GEn

Review of GEn world data

Review of GEn world data

Review of GEn world data

Review of GEn world data

Review of GEn world data

Review of GEn world data

Review of GEn world data

Identification of Neutron Events

Very clean quasielastic 2H(e,e’n) spectra

Highly efficient proton veto (drift chambers + TOF)

Extraction of GnE

Quasielastic 2H(e,e’n)

Full Montecarlo simulation of the BLAST experiment

Deuteron electrodisintegrationby H. Arenhövel

Accounted for FSI,MEC,RC,IC

Spin-perpendicular beam-target vector asymmetry AV

ed shows high sensitivity to Gn

E

Compare measured AVed

with BLASTMC, vary GnE

BLASTMC

(e,e’p) (e,e’n)

V. Ziskin (MIT), E. Geis (ASU)

Discussion vs. Nucleon Models

Discussion vs. Nucleon Models

Discussion vs. Nucleon Models

Discussion vs. Nucleon Models

Discussion vs. Nucleon Models

Discussion vs. Nucleon Models

Discussion vs. Nucleon Models

GMn

• Polarized beam + polarized target:

unpol

EMM GGbGaAσ

θθσσσσ )()( *2* +

∝+−

=↑↓↑↑

↑↓↑↑p p

n

d (e e')

)'(3 eeeH→ neutron magnetic ff

Donnelly + Raskin, Ann. Phys. 169 (1986)247

3H e

p

n

d

d(e,e'n)d(e,e' p)

Friedrich & Walcher Parametrization

Expressed form factors as “smooth“ part plus “bump”

smooth

bump

Friedrich & Walcher Parametrization

Extraction of GnM

Quasielastic 2H(e,e’) inclusive

Full Montecarlo simulation of the BLAST experiment

Deuteron electrodisintegrationby H. Arenhövel

Accounted for FSI,MEC,RC,IC

Beam-target vector asymmetry AV

ed spin-parallel + perpendicular show sensitivity to Gn

M

PWIA:BLASTMC

BLASTMC

Neutron Magnetic Form Factor GMn

1. New measurement technique.

2. Includes full deuteron structure.

3. Consistent with recent polarization and other data.

4. Provides a tighter fit to form factor in the low Q2 region.

N. Meitanis (MIT)

Neutron Magnetic Form Factor GMn

Summary• A lot of progress (experimental) in the last few years:

– Polarization techniques– GE

p/GMn biggest surprise (JLab)

– GEn known to 5% at low Q2 (Mainz, Bates) and better

at high Q2 (JLab)– GM

n accurately known at low Q2 and new results expected soon at high Q2 (CLAS)

– Structure at low Q2 (challenge for chiral models and lattice QCD)

• Significant issues: beyond Born Approximation (JLab)

• Bates played a significant role at low Q2 and in the development of the polarization techniques.