Symmetry analysis involving meson mixing for charmonium decay

In the light of SU(3) flavor symmetry, the effective interaction Hamiltonian in tensor form is obtained by virtue of group representation theory. The strong and electromagnetic breaking effects are treated as a spurion octet so that the flavor singlet principle can be utilized as the criterion to determine the form of effective Hamiltonian for all charmonium two body decays. Moreover, a synthetical nonet is introduced to include both octet and singlet representations for meson description, and resorting to the mixing angle the pure octet and singlet states are combined into the observable pseudoscalar and vector particles, so that the empirically effective Hamiltonian can be obtained in a concise way. As an application, by virtue of this scenario the relative phase between the strong and electromagnetic amplitudes is studied for vector-pseudoscalar meson final state. In data analysis of samples taken in $e^+e^-$ collider, the details of experimental effects, such as energy spread and initial state radiative correction are taken into consideration in order to make full use of experimental information and acquire the accurate and delicate results.