Rutherford - atoms have nuclei
Stern - μp = (1+κp)(e/2M)
Hofstadter - nuclei are not point-like, rather high density core
and sparse surrounding
Mott - light point-like fermion off point-like heavy fermion;
History
2
e(k’)
Manipulate Q and scattering angle to select which G
For constant Q, fit to epsilon: slope gives GE²/τ, intercept gives
GM²
Strategy
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Disadvantages
Rosenbluth Separation more vulnerable to higher order diagrams in
cross-section.
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Proton GE
We see that for high Q², measurements have high errors and utter
inconsistency
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Scattering, like Rosenbluth, but no longer scanning Q and epsilon.
Measure polarizations of proton:
GM known better, so GE/GM determines GE
Polarization Transfer Another aspect: look at asymmetry
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+, - refer to electron beam helicity
For right proton polarization angles θ* and φ*, A approximately
proportional to GE/GM
Very recent asymmetry example from BLAST
Example Polarimeter Proton polarimeters rely on secondary
scattering, in which spin interactions induce known angular
dependences in cross section. In this CEBAF polarimeter, wire
chambers before and after track proton trajectory; carbon target
provides scattering medium. Energy is not determined.
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A Complication We need polarization at target not at polarimeter.
Spin precesses in HRS, so needs to apply spin- rotation matrix,
which comes from Monte Carlo
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Neutron Difficulties There are no free neutrons in these
experiments, so compromise is necessary. Two methods: • Use D–
relatively insensitive to wavefunction FSI, MEC, IC effects • Use
³He– Dominated by S- state wavefunction, so neutron dominates spin.
Bad for low Q²
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Left: Polarization and Rosenbluth Separation data Right:
Polarization data. 17
GMP/μPGD GEP/GD
Neutron GE, GM
Left: D and ³He Asymmetry + D recoil Right: Polarization data
GMP/μPGDGEP/GD
Comparison • Both have trouble with free neutrons • Rosenbluth is
easier and offer more statistics • Polarized experiments require
one measurement per Q², which reduces systematic uncertainties • By
studying ratio of GE/GM, can cancel dependence on systematics of
scale: i.e., beam polarization and polarimeter properties •
Uncertainty due to two-photon processes impact both cross section
and polarization, but the polarization methods rely on
ratios.
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Prevailing interpretation: neutron is positive core surrounded by
negative pion cloud. Proton may virtual strange pair
contribution
Expected to be similar
In the infinite momentum frame, F1→ Transverse distributions
without model dependence, but, use GDP that are model
dependent
Conclusion
• Rosenbluth older, easier and still useful • Polarization
complimentary, better in many ways • Electric form factors harder
to measure • Neutron properties of special interest • No details of
quark momentum, energy, spin contribution; nothing on gluons •
Future FF measurements: RHIC, CEBAF, • Future 2γ contribution
measurements: JLAB, VEPP3, DESY
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References
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• R. Gilman,et al. CEBAF.1995 • Close, Donnachie, Shaw; 2007 •
Predrisat, Punjabi, Vanderhaeghen; 2007 • Arrington, Roberts,
Zanotti; May 2007 • Long Range Nuclear Plan; Dec 2007 • BLAST; July
2008 • Miller, Arrington; Sep 2008 • Ji, McKeown; unpublished •
Hiren; two weeks ago
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