The aim of this work is to provide a phenomenological analysis of the contribution of [Formula: see text] meson to [Formula: see text], [Formula: see text] and [Formula: see text] quasi-three-body decays. Such that the analysis of mentioned four-body decays is summarized into three-body decay and several channels are observed. Based on the factorization approach, hadronic three-body decays receive both resonant and nonresonant contributions. We compute both contributions of three-body decays. As, there are tree, penguin, emission, and emission annihilation diagrams for these decay modes. Our theoretical model for [Formula: see text] decay is based on the QCD factorization to quasi-two body followed by [Formula: see text]-wave. This model for this decay following experimental information which demonstrated two pion interaction in the [Formula: see text]-wave is introduced by the scalar resonance. The theoretical values are [Formula: see text], [Formula: see text] and [Formula: see text], while the experimental results of them are [Formula: see text], [Formula: see text] and [Formula: see text], respectively. Comparing computation analysis values with experimental values show that our results are in agreement with them.
The annihilation diagram in three-body D-meson decay