Model-independent determination ofK-matrix poles and residues in theΔ(1232)region from the multipole data for pion photoproduction

Using only the analytic structure of the $K$ matrix and the assumption that the Compton-scattering amplitude is small compared to strong and electrostrong amplitudes, we extract the pole position and the residues for the resonant multipoles, in a model-independent and background-free fashion, directly from the experimentally obtained multipole data base in the $\Delta \mathrm{}\left(1232\right)\mathrm{}$ region, posing a challenge for QCD-inspired hadron models.