Dispersion relations and the $\Delta$ contributions into the amplitudes $M_{1+}^{3/2},E_{1+}^{3/2}$ from new VPI partial-wave analysis of pion photoproduction

Abstract

Within fixed-t dispersion relations the results of new VPI partial-wave analysis for the multipole amplitudes $M_{1+}^{3/2},E_{1+}^{3/2}$ are successfuly described, and the resonance and nonresonance contributions into these amplitudes are separated in correspondence with the interpretation on the language of diagram approach, dynamical models and effective Lagrangian approach. The amplitudes $A_p^{3/2}$ and $A_p^{1/2}$ corresponding to the $\Delta$ contributions into $M_{1+}^{3/2},E_{1+}^{3/2}$ are obtained. They are in better agreement with quark model predictions than the amplitudes extracted without subtraction of the nonresonance contributions in $M_{1+}^{3/2},E_{1+}^{3/2}$. The obtained value of the ratio $E2/M1$ for the $\gamma N \to P_{33}(1232)$ transition is: $E2/M1=-0.022\pm 0.004$.