The nature of three-pion enhancements in the minimal K-matrix model

Abstract

The square of the magnitude of the inverse Fredholm determinant associated with the minimal K-matrix integral equations describing three-pion to three-pion scattering was calculated as a function of three-pion mass ¢M from threshold to 1900 MeV for the 0 ≦ I ≦ 2, 0 ≦ J ≦ 2 channels of the three-pion system. The input for these equations consisted of the on-shell π-π t-matrices t 0 0, t 0 2, t 1 1, and t 0 2 obtained from phenomenological phase-shift analyses. For the minimal K-matrix model, the only structure in the natural parity states is an enhancement of kinematical origin at 1284 MeV in the ω-channel. Spurious enhancements appear in all the unnatural parity states considered at roughly 1150 MeV corresponding to the ρπ → ρπ Peierls singularity. In the I = 1 unnatural parity channels, broad enhancements at 1450 MeV ≦ ¢M ≦ 1675 MeV occur. These correspond to the ρπ → fπ fit generalized Peierls singularity.