Chiral Lagrangian treatment of πη scattering

We study πη scattering in a model which starts from the tree diagrams of a non-linear chiral Lagrangian including appropriate resonances. Previously, models of this type were applied to ππ and πK scattering and were seen to require the existence of light scalar σ(560) and κ(900) mesons and to be consistent with the f0(980). The present calculation extends this to include the a0(980), thereby completing a possible nonet of light scalars, all ''seen'' in the same manner. We note that, at the initial level, the πη channel is considerably cleaner than the ππ and πK channels for the study of light scalars. This is because the large competing effects of vector meson exchange and ''current-algebra'' contact terms are absent. The simplicity of this channel enables us to demonstrate the closeness of our exactly crossing symmetric amplitude to a related exactly unitary amplitude. The calculation is also extended to higher energies in order to let us discuss the role played by the a0(1450) resonance. (c) 2000 The American Physical Society