Linear σ model, QCD and low-energy Lagrangian for pseudoscalar mesons

The U(3)xU(3) linear σ-model is shown to be compatible with the experimental data on low-energy interactions of pseudoscalar mesons already at the tree level, provided the σ model is supplemented with a Skyrme term, which describes interaction with vector mesons. It is demonstrated that the model not only solves the U(1) problem, but as well correctly reproduces the properties of the QCD Θ-vacuum and provides an entire agreement with the 1/N expansion