πa1-transitions and the low-energy limit in the linear σ-model with vector and axial-vector mesons

It is discussed a known problem associated with obtaining a correct low-energy limit, which occurs in the extension of the linear σ-model because of vector and axial-vector mesons included. In the naive consideration the three diagrams with intermediate vector (axial-vector) mesons in the low-energy region can reproduce results obtained from the linear σ-model, thus leading to the undesirable double count. Taking the ππ-scattering and the semileptonic τ→ντ3n decay amplitudes as an example, the paper shows that this problem can be solved if πa1-transitions are taken into account in the corresponding meson vertices. 15 refs.; 2 figs