The position and the residues of the delta resonance pole in pion photoproduction

Abstract

We have analyzed the M (3/2) 1+ and E (3/2) 1+ multipole amplitudes of pion photoproduction in the framework of fixed-t dispersion relations. Applying the speed plot technique to our results for these multipoles, we have determined the position and the residues of the ∆ (1232) resonance pole. The pole is found at total c.m. energy W = (1211 − 50i) MeV on the second Riemann sheet, and the ratio of the electric and magnetic residues is R ∆ = −0.035 − 0.046i, resulting in an E2/M1 ratio for the "dressed" delta resonance of −3.5%.

Direct calculation of the K-matrix for pion electro-production in the delta channel

“…We have explicitly checked that after substituting our matrix elements of V mt in eqs. (21) and (22) by the corresponding bare values the results of ref. [15] are consistent with ours.…”

Pole positions and residues from pion photoproduction using the Laurent-Pietarinen expansion method

“…The numerical values which we find here with the L+P method agree very well with the pole positions and residues from E 3/2 1+ and M 3/2 1+ amplitudes in Refs. [30,31].…”

Dispersion relations and the spin polarizabilities of the nucleon

“…The contributions arising from the contour are expressed in terms of low-mass meson exchanges in the t-channel, as will be discussed in the next section. We use pion photoproduction multipoles from a recent analysis based on fixed t dispersion relations and unitarity by Hanstein, Drechsel and Tiator (HDT) [14]. This analysis is limited to a maximum photon laboratory energy of the order of 500 MeV.…”