Dispersion Theoretical Analysis of Pion Photoproduction at Threshold and in the Delta Region

Abstract

A new partial wave analysis of pion photoproduction has been obtained in the framework of fixed-t dispersion relations valid form threshold up to 500 MeV. It is based on new Mainz data for \pi^{0} and \pi^{+} production off the proton and both older and more recent data from Bonn, Frascati and TRIUMF for \pi^{+} and \pi^{-}. At threshold we obtain a good agreement with the existing data for both charged and neutral pion production. In the resonance region we have precisely determined the electromagnetic properties of the \Delta(1232) resonance, in particular the E2/M1 ratio R_{EM}=(-2.5 \pm 0.1) %. We show that a model independent resonance background subtraction is possible with the speed-plot technique and obtain the \Delta pole at W =(1211 - 50i) MeV and the E2/M1 ratio of the residues as R_{\Delta} = - 0.035 - 0.046 i.