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

We have analyzed the M1+(32) and E1+(32) 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 Δ (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 RΔ = −0.035 − 0.046i, resulting in an E2/M1 ratio for the “dressed” delta resonance of −3.5%.