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

TL;DR

This paper uses fixed-t dispersion relations and a new partial-wave analysis to separate resonance and nonresonance contributions in pion photoproduction amplitudes, providing improved agreement with quark model predictions and precise transition ratios.

Contribution

It introduces a novel analysis method that successfully separates resonance and nonresonance contributions in pion photoproduction amplitudes, aligning better with theoretical models.

Findings

Resonance and nonresonance contributions are separated successfully.

The amplitudes align better with quark model predictions.

The E2/M1 ratio for the transition is measured as -0.022±0.004.

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: $E2/M1=-0.022\pm 0.004$.