Three-pion resonances

We investigate the continuum three-pion problem within a relativistic three-body model that takes into account the ππS and P waves. The dynamical input of the two-body subsystem is given by separable potentials, which yield a good fit to the ππ scattering data and resonance parameters up to a two-body invariant mass of 900MeV. We introduce a parameter ν expressing the ambiguity in the reduction of a fully relativistic theory to a three-dimensional one. The masses and widths of the ω, a₁(1260), and π(1300) mesons, which decay predominantly into three pions, are reasonably well described by our model. The h₁(1170) meson, however, which also decays into three pions, cannot be explained as a three-pion resonance. Some πρ Argand diagrams are shown in those channels where resonances exist.