The Role of Single-Pion Exchange in the Binding of the Omega Meson

The ω meson is the simplest three body hadronic resonance, and as such is crucial to understanding three particle hadron spectroscopy. In this project we assume that the ω meson is generated by pion exchange between two-pion sub-interactions in three-pion scattering. Integral equations governing the three-pion scattering amplitude were solved for the case of the quantum numbers of the ω, which are J P = 1−. These equations do not have analytic solutions, so they were instead discretized and solved numerically. Once a solution was obtained, it was analytically continued into the complex energy plane to search for bound state pole singularities. The results of this process did not yield any poles, suggesting that one-pion-exchange alone cannot account for the binding of the ω. Thus, further analysis is needed to understand the purely three-body interactions which must dominate the formation of the particle.