2πproduction in the Giessen coupled-channels model

Abstract

The coupled channels Lagrangian approach underlying the Giessen model (GiM) is extended to describe the πN → πN , 2πN scattering in the resonance energy region. As a feasibility study we investigate single and double pion production up to the second resonance region. The 2πN production has been significantly improved by using the isobar approximation with σN and π∆(1232) in the intermediate state. The three-body unitarity is maintained up to interference pattern between the isobar subchannels. The scattering amplitudes are obtained as a solution of the Bethe-Salpeter equation in the K matrix approximation. As a first application we perform a partial wave analysis of the πN → πN , π 0 π 0 N reactions in the Roper resonance region. We obtain R σN (1440) = 27 +4 −9 % and R π∆ (1440) = 12 +5 −3 % for the σN and π∆(1232) decay branching ratios of N * (1440) respectively. The extracted πN inelasticities and reaction amplitudes are consistent with the results from other groups.

Production and decay of baryonic resonances in pion induced reactions

“…Considering the large number of resonant and non-resonant mechanisms involved, the combined analysis of various exit channels (coupled channels models, see i.e. [8]) with the partial wave analysis approach is mandatory.…”

Coupled channels approach to photo-meson production on the nucleon

“…Therefore, this production channel had been included from the very beginning into the GiM approach, albeit in a schematic manner. An improved and considerably extended description of double-pion production within our coupled channels scheme was started recently and first results are found in [7]. The inclusion of multi-meson con- figurations into a coupled channels approach is a highly non-trivial exercise in three-body dynamics and beyond.…”

“…In view of the complexities physically meaningful approximations are necessary, retaining the essential dynamical aspects but making numerical calculations feasible. For that goal the ansatz used in [7] relies on an isobar description of intermediate two-pion configurations and their decay into the final double pion states on the mass shell. In Fig.8 the tree-level interactions for two-pion production are displayed diagrammatically.…”

“…The applications range from investigations of the elastic and inelastic πN and πN * channels [1] to ωN [2], ηN [3,4] production as well as the strangeness channels KΛ [5] and KΣ [6]. The 2πN channels were investigated recently in [7]. Here we review central issues of the Giessen approach and present results for selected reactions.…”

“…For stable particles the spectral functions reduce to trivial delta-functions, projecting the integrand on the particles's mass. Since the two-pion discontinuities are taken into account the threebody unitarity in the form of the optical theorem if fulfilled up to interference terms between different isobar subchannels [7]. …”