The MAIDDMT Partial Wave Analysis

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The MAID/DMT Partial Wave Analysis
today N-gtN transition form factors at the
Breit-Wigner position and at the T-matrix pole

• S. Kamalov1), D. Drechsel2), L.T.2) and S.N.
  Yang3)
• 1)Dubna, 2)Mainz, 3)Taipei

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N -gt N Transition Form Factors

• In N physics, the existence of a resonance, its
  position and quantum numbers are the primary
  goal.This can be reached with different probes.
• But the electromagnetic probe tells us about the
  structure, how a resonance is built from
  constituents.
• This structure information can be obtained from
  the transition form factors.
• These form factors cannot be directly measured,
  but are obtained in partial wave analysis of
  meson electroproduction.

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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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dynamical approach to pion electroproduction
K-matrix Born approximation
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MAID unitarization procedure
K-matrix unitarization for all background partial
waves up to L3 S11, S31 P11, P13, P31, P33
D13, D15, D33, D35 F15, F17, F35, F37
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MAID unitarization procedure
a correction phase f(W) for all Breit-Wigner
resonance contributions S11 S31 P11 P13
P31 P33 D13 D15 D33 D35 F15 F17 F35
F37
13 nucleon resonances are included in MAID,
7 N 5 D
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in the MAID Ansatz, the fit parameters are
already the reduced multipoles, that are needed
to determine the photon couplings and the
transition form factors
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Definition of the N-N Form Factors
reduced multipoles
different sets of form factors can be defined as
linear combinations of the reduced multipoles
helicity amplitudes
Sachs form factors
covariant (Dirac) form factors
for spin ½ resonances as Roper P11 or S11 we get
only 2 ff
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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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due to Watsons theorem, the background is zero
at the D(1232) position
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N N Transition Form Factors
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Results for the dominant resonances of the proton
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for isospin ½ resonances also neutron form
factors have been analyzed, but the results are
very uncertain, no data after 1988
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transition form factors of the Roper
comparison of MAID and JLab analysis
A1/2
MAID analysis 2007/08
JLab analysis 2008
S1/2
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N-Delta and N-Roper Transition Form Factors on
the Lattice
Huey-Wen Lin et al., 2008
C. Alexandrou et al., 2008
N-Roper quenched with mp720 MeV
N-Delta unquenched with mp360 MeV
F1
GM
F2
pion cloud problem at small Q²
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N -gt S11(1535)
MAID analysis 2007/2008
JLab analysis 2008
longitudinal S1/2
transverse A1/2
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from Breit-Wigner positions
to T-matrix pole positions
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Physics Letters B 385 (1996) 45
residues
phases
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Physical Review C 59 (1999) 1810
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Summary and Conclusions
recent results from pN channel (Maid2007/08)
N-gtN transition form factors for 13 N/D
resonances with PDG
rating reasonably well for I3/2 P33(1232)
I1/2 proton P11(1440), S11(1535),
D13(1520), F15(1680)
S11(1650), D15(1675), P13(1720) also global
fits for S31(1620), D33(1700), I1/2 neutron
for most of these states global fits exist
for the first time we have calculated transition
form factors at the T-matrix pole preliminary
result the complex phase seems to be constant
over a large Q² range
next step new dynamical model for pion
electroproduction DMT2009