Phenomenological studies on decay *

Abstract

Abstract Within the quasi-two-body decay model, we study the localized CP violation and branching fraction of the four-body decay when the and pair invariant masses are and , with the pairs being dominated by the , , , and , and , , and resonances, respectively. When dealing with the dynamical functions of these resonances, , , and are modeled with the Bugg model, Gounaris-Sakurai function, Flatté formalism and LASS lineshape, respectively, while the others are described by the relativistic Breit-Wigner function. Adopting the end point divergence parameters and , our predicted results are and , based on the hypothetical structures for the scalar mesons in the QCD factorization approach. Meanwhile, we calculate the CP violating asymmetries and branching fractions of the two-body decays and all the individual four-body decays , respectively. Our theoretical results for the two-body decays , , , , and are consistent with the available experimental data, with the remaining predictions await testing in future high precision experiments.