ar X iv : n uc l - th / 0 60 70 17 v 1 1 0 Ju l 2 00 6 Partial - Wave Analysis of Single - Pion Production Reactions

We present an overview of our efforts to analyze pion-nucleon elastic scattering data, along with data from related photo-and electroproduction reactions, in order to study the baryon spectrum. We then focus on the ∆(1232) resonance. Fits to pion photo-and electroproduction data have been used to extract values for the R EM = E2/M1 and R SM = S2/M1 ratios as functions of Q 2. These results are compared to other recent determinations. Many of our fits to scattering data have been motivated by ongoing studies of the N * properties [1]. Most of these require, as input, amplitudes extracted from elastic pion-nucleon scattering data [2]. Our pion photoproduction multipoles FIGURE 1. ∆ multipoles from analysis of scattering data − a Road Map. are determined using a K-matrix formalism, based upon pion-nucleon partial-wave amplitudes [3]. The electroproduction analysis is similarly anchored to our Q 2 = 0 photoproduction results, with additional factors intended to account for the Q 2 variation. This relationship is diagrammed in Fig. 1. Most of what we discuss here is confined to an energy region covering the ∆(1232) resonance. Problems associated with the opening of channels beyond πN [4] are avoided. The pion-nucleon amplitudes are determined through a fit to elastic scattering, charge-exchange, and ηN production data, constrained to satisfy forward and fixed-t dispersion relations. A flowchart for this procedure is given in Fig. 2. Two representative results for the partial-wave amplitudes are given in Fig. 3, which shows that the extraction of resonance contributions is difficult for most states. A search of the complex energy plane finds poles which are often far from the physical axis, as shown in Fig. 4, making a simple Breit-Wigner parametrization