Form Factors from Meson Electroproduction

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Form Factors from Meson Electroproduction
L. Tiator Johannes Gutenberg-Universität Mainz in
collaboration with D. Drechsel (Mainz) and S.
Kamalov (Dubna)

• Introduction
• Inclusive electron scattering
• Inelastic form factors
• The unitary isobar model MAID
• Results
• Nucleon axial ff and pion ff
• Nucleon transition form factors
• Summary and Conclusions

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Inclusive Cross Section for Real and Virtual
Photo Absorption
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Inelastic Electron Scattering in the Resonance
Region
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• in general
• transition form factors can only be obtained by
• partial wave analysis
• and background / resonance separation

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Form Factors in the Electroproduction Process
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Form Factors in MAID2007
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in this analysis the resonances are dressed
dressing and undressing can be studied in
Dynamical Models e.g. Kamalov, Yang and Sato,
Lee more during this workshop
in most cases quark models calculate the bare
resonance couplings a direct comparison with exp.
analysis is not possible, e.g. Giannini on the
hypercentral quark model
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• first application
• axial form factor GA
• pion form factor Fp
• at low Q² near pion threshold

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partial wave analysis
with resonance and background separation
for helicity amplitudes and transition form
factors we need the imaginary parts of the
resonance multipoles
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E/M and S/M ratios for the ND transition
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data base for pion electroproduction
data in the D region up to W 1.3 GeV
data up to the 3rd resonance region up to W 1.7
GeV
older data from SAID data base up W 2 GeV
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Results for the dominant resonances of the proton
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other analysis of the experimental data
Aznauryan and Burkert (JLab) perform an
analysis similar to our MAID analysis and uses
additional constraints from dispersion
relations the data base contains more recent p
data comparisons for P33, P11 and S11 are
possible at Q² gt 1 GeV² deviations are observed
for the Roper A1/2 and the Delta C/M
ratio
MIT-Mainz-Athens collaboration has
intensively studied the ND transition at low
Q² Papanicolas will talk on this workshop
SAID has also started an electroproduction
analysis and tries to extract the transition form
factors this method is still in an early stage it
is more model-independent, but requires much more
data
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theoretical calculations of transition form
factors
nonrel. and relat. quark model calculations exist
and can often describe the photon couplings at
Q²0 quite well, but mostly fail at finite Q² the
Genova Hypercentral Quark Model does quite
well for many resonances in comparison with the
bare resonance form factors, Giannini, later on
this workshop
lattice QCD results have strongly developed over
the last few years and can compare with our
dressed form factors for the D(1232) resonance,
all 3 transition form factors can be
calculated, Alexandrou will talk about it on this
workshop
ChPT calculations have been done for the D(1232)
at low Q² e.g. Gail and Hemmert Pascalutsa,
Vanderhaeghen, also o this workshop
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quark model calculations can be all over the
place in comparison with nucleon-resonance
transition form factors
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Summary

• enter the pole terms of (e,ep)
• a realistic input is important, e.g. GE is
  important for u-channel p(e,ep)n,
• but e,ep cannot give additional information

nucleon e.m. ff
n
is required by LET in the soft-pion limit. near
threshold the slope ltr2gtA can be extracted and
can be compared with ChPT but the variation in
the neutrino data is too large in order to draw a
conclusion
nucleon axial ff
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enters the p-pole term and can be extracted at
high energies and Q²gt 1 GeV² (see H. Blok on the
JLab experiment) at low energy the slope ltr2gtp
can be extracted from Mainz data and is in
agreement with ChPT
pion ff
have only weak sensitivity, commonly described by
the standard dipole ff
vector meson ff
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nucleon transition form factors

• the GM form factor of the D(1232) can be
  extracted directly from the inelastic cross
  section with high accuracy
• all other electric, magnetic and charge form
  factors can only be extracted from partial wave
  analysis
• so far MAID is the only full partial wave
  analysis for electroproduction for Wthr lt W lt
  2 GeV and 0 lt Q² lt 3 GeV²
• mostly due to JLab data on p(e,ep0)p we could
  extract the ffs of

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• recent JLab data on p(e,ep)n help to remove
  correlations between partial waves, e.g. between
  P33 and P11
• the database for the neutron is very
  limited our analysis is based on 890 data points
  from 1971-1988 and most of our neutron ffs are
  not very conclusive new data
  are needed on d(e,ep -p)n

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