Multipole analysis of pion photoproduction based on fixed t dispersion relations and unitarity

Abstract

We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnes and Muskhelishvili. The free parameters were determined by a fit to the most recent data for π^{+} and π^{0} production on the proton as well as π^{-} production on the neutron, in the energy We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnes and Muskhelishvili. The free parameters were determined by a fit to the most recent data for π^{+} and π^{0} production on the proton as well as π^{-} production on the neutron, in the energy range 160 MeV \leq E_γ \leq 420 MeV. The lack of high precision data on the neutron and of polarization observables leads to some limitations of our results. Especially the multipole M_{1-} connected with the Roper resonance P_{11}(1440) cannot be determined to the required precision. Our predictions for the threshold amplitudes are in good agreement with both the data and chiral perturbation theory. In the region of the Δ(1232) we have determined the ratio of electric quadrupole and magnetic dipole excitation. The position of the resonance pole is obtained in excellent agreement with pion-nucleon scattering, and the complex residues of the multipoles are determined with the speed-plot technique.

46 pages LATEX including 29 postscript figures

References in corpus (10)

• Dispersion-Theoretical Analysis of the Nucleon Electromagnetic Formfactors
• Meson-exchange Model for $\pi N$ scattering and $\gamma N->\pi N$ reaction
• Updated analysis of $\pi$N elastic scattering data to 2.1~GeV: The Baryon Spectrum
• Electromagnetic Properties of the Delta(1232)
• Chiral symmetry and the reaction $\gamma p\to {\pi }^{0}p$
• The position and the residues of the delta resonance pole in pion photoproduction
• Chiral corrections to the Kroll-Ruderman theorem
• Observation of a unitary cusp in the threshold γp -> π^{0}p reaction
• A dispersion theoretical approach to the threshold amplitudes of pion photoproduction
• Unitary ambiguity in the extraction of the E2/M1 ratio for the $\gamma N\leftrightarrow \Delta$ transition

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• First measurement of the Gerasimov-Drell-Hearn integral for Hydrogen from 200 to 800 MeV
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