Calculation of theΔ(1236)Resonant Partial Amplitudes in Pion Photoproduction

Abstract

Using an $\frac{N}{D}$-type ansatz, a modified dispersion relation for the partial-wave amplitudes is derived. The equations, if applied to the first resonance in pion photoproduction, allow a fairly complete incorporation of our phenomenological knowledge of the pion-nucleon final state together with a systematic treatment and estimate of the terms to be neglected in practice. Various possibilities of including unknown or uncertain high-energy contributions are discussed and applied. Explicit results for the multipoles $E_{1+}^{}{}_{}{}^{\frac{3}{2}}$, $M_{1+}^{}{}_{}{}^{\frac{3}{2}}$ are presented.