The position and the residues of the delta resonance pole in pion photoproduction

Abstract

We have analyzed the $M_{1+}^{(3/2)}$ and $E_{1+}^{(3/2)}$ multipole amplitudes of pion photoproduction in the framework of fixed-$t$ dispersion relations. Applying the speed plot technique to our results for these multipoles, we have determined the position and the residues of the $\Delta$ (1232) resonance pole. The pole is found at total $c.m.$ energy $W = (1211 - 50i)$ MeV on the second Riemann sheet, and the ratio of the electric and magnetic residues is $R_{\Delta} = - 0.035 - 0.046 i$, resulting in an E2/M1 ratio for the "dressed" delta resonance of $- 3.5 \%$.