the electromagnetic form factors of the nucleon · 2006. 11. 27. · em nucleon form factors •...
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September 28, 2006 R. Alarcon @ MIT Symposium
The Electromagnetic Form Factors of the Nucleon
• Introduction
• Proton Form Factors
• Neutron Form Factors
• Summary
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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
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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
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[ ])()()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
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Proton
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World Data from Rosenbluth’s separation
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μ P
GEp
GMp (Q 2 ) → const
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Akhiezer+Rekalo, Sov.JPN 3 (1974) 277Arnold,Carlson+Gross, PRC 21 (1980) 1426
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Akhiezer+Rekalo, Sov.JPN 3 (1974) 277Arnold,Carlson+Gross, PRC 21 (1980) 1426
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Akhiezer+Rekalo, Sov.JPN 3 (1974) 277Arnold,Carlson+Gross, PRC 21 (1980) 1426
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Hall A at Jefferson Laboratory
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Q2
ln2+
89β Q2
Λ2
F2(Q2)F1(Q
2)→ const
PRL 91 (2003) 092003
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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
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Polarized H/D Target
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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
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The BLAST Collaboration
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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
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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
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C. Crawford (submitted to PRL)
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C. Crawford (submitted to PRL)
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Neutron
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Methods to Determine GEn
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Methods to Determine GEn
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Methods to Determine GEn
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Methods to Determine GEn
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Review of GEn world data
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Review of GEn world data
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Review of GEn world data
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Review of GEn world data
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Review of GEn world data
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Review of GEn world data
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Review of GEn world data
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Identification of Neutron Events
Very clean quasielastic 2H(e,e’n) spectra
Highly efficient proton veto (drift chambers + TOF)
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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)
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V. Ziskin (MIT), E. Geis (ASU)
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Discussion vs. Nucleon Models
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Discussion vs. Nucleon Models
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Discussion vs. Nucleon Models
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Discussion vs. Nucleon Models
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Discussion vs. Nucleon Models
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Discussion vs. Nucleon Models
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Discussion vs. Nucleon Models
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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)
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Friedrich & Walcher Parametrization
Expressed form factors as “smooth“ part plus “bump”
smooth
bump
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Friedrich & Walcher Parametrization
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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
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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.
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N. Meitanis (MIT)
Neutron Magnetic Form Factor GMn
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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.