MAID Analysis Techniques

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MAIDAnalysis Techniques

• introduction
• a dynamical approach to meson electroproduction
• the unitary isobar model MAID
• comparison of multipoles between MAID and SAID
• resonance parameters and transition form factors
• summary and outlook

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why partial wave analysis

• learn about nucleon resonancesin particular
  about their e.m. structuretransition moments,
  form factors GE, GM, GC
• study threshold amplitudesto compare with ChPT
• obtain cross sections and amplitudes over a wide
  range of energies for dispersive studies- sum
  rules GDH, FFR, etc.- two-photon reactions
  Compton, VCS, SSA, etc.
• find missing or exotic resonances

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part of the resonance dressing in K-matrix and
isobar models - as well as in PDG definition -
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MAID
the Mainz-Dubna Unitary Isobar Model
K-matrix unitarization
unitarization phase determined by the Watson
theorem, below 2p threshold relaxed above 2p
threshold

• the Resonances in MAID are dressed resonances

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Results on photo- and electroproduction of
nucleon resonances
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(MAID uses SAID pion nucleon analysis)
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comparison between MAID and SAID
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comparison between MAID and SAID
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electroproduction analysis of nucleon resonances
with MAID
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Delta P33(1232) and D13(1520) resonances
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Roper P11(1440) and S11(1535) resonances
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some results from Eta-MAID
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Resonance Parameters from h-MAID
10-3 GeV-1/2
MeV
Numbers in green are fitting parameters
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D15(1675) mainly a neutron resonance with large
branching into hN
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summary on MAID techniques

• field theoretical background in tree
  approximation
• pion loop contributions in K-matrix
  approximationguarantees a unitarized background
• non-Born bg terms account for missing loop
  contributions a) empirical terms near threshold
  for E0, S0b) PS-PV mixing at higher energies
  in E0, S0, M1-, S1-
• nucleon resonance excitation in s-channel
  Breit-Wigner parametrization(MAID strategy as
  few as necessary, in Maid05 13 res.)
• Q2 dependent transition form factorslead to
  superglobal energy- and Q2 dependent solutions
• Outlook PWA groups should work together in order
  todetermine and eventually to reduce model
  dependence