How to extract theP33(1232)resonance contributions from the amplitudesM1+3/2,E1+3/2,S1+3/2of pion electroproduction on nucleons

Within the dispersion relation approach, solutions of integral equations for the multipoles $M_{1+}^{3/2}{,E}_{1+}^{3/2}{,S}_{1+}^{3/2}$ are found at $0<~Q^2<~3{\mathrm{GeV}}^2.$ These solutions should be used as input for the resonance and nonresonance contributions in the analyses of pion electroproduction data in the $P_{33}\mathrm{}\left(1232\right)\mathrm{}$ resonance region. It is shown that the traditional identification of the amplitude $M_{1+}^{3/2}$ (as well as the amplitudes $E_{1+}^{3/2}{,S}_{1+}^{3/2}$) with the $P_{33}\mathrm{}\left(1232\right)\mathrm{}$ resonance contribution is not right; there is a contribution in these amplitudes which has a nonresonance nature and is produced by rescattering effects in the diagrams corresponding to the nucleon and pion poles. This contribution is reproduced by the dispersion relations. Taking into account nonresonance contributions in the amplitudes $M_{1+}^{3/2}{,E}_{1+}^{3/2},$ the helicity amplitudes $A_p^{1/2}{,A}_p^{3/2}$ and the ratio $E2/M1\mathrm{}$ for the $\gamma \overrightarrow{N}{P}_{33}\mathrm{}\left(1232\right)\mathrm{}$ transition are extracted from experiment at $Q^2=0.\mathrm{}$ They are in good agreement with quark model predictions.