Anomalous quark diagrams in the virtual V → P+P', P → V+P' decays and in the related processes

Form factors of the virtual decays V→P+P' and P→V+P' are calculated assuming that the anomaly due to the corresponding quark diagram dominates in the VPP' vertex, where V and P are a vector meson and a pseudoscalar meson. An effect of the obtained form factors upon the electromagnetic and weak P- meson form factors is considered. It is shown that the results coincide with predictions of the standard vector-meson dominance model, if the interactions of the photon and of the W-boson with the pseudoscalar meson are determined by the quark-diagram anomaly in the vertices γPP and WPP. The effect of the rho→ππ decay form factors for a virtual rho-meson on the superconvergency of the dispersion relations for the rhoπ→rhoπ scattering amplitude, as well as on the rho-meson contribution to the ππ-scattering lengths, is discussed. Rules for calculation of quark graphs with an arbitrary number of mesons are formulated for the examples of the decays ω→π+π-π0 and eta(eta')→π+π-γ