Amplitude analysis of the decays And

Using $ e^+e^- $ annihilation data corresponding to an integrated luminosity of 2.93 $ e^+e^- $ taken at the center-of-mass energy $ e^+e^- $ GeV with the BESIII detector, a joint amplitude analysis is performed on the decays $ e^+e^- $ and $ e^+e^- $ (non-η). The fit fractions of individual components are obtained, and large interferences among the dominant components of the decays $ e^+e^- $ , $ e^+e^- $ , $ e^+e^- $ , and $ e^+e^- $ are observed in both channels. With the obtained amplitude model, the $ e^+e^- $ -even fractions of $ e^+e^- $ and $ e^+e^- $ (non-η) are determined to be $ e^+e^- $ % and $ e^+e^- $ %, respectively. The branching fractions of $ e^+e^- $ and $ e^+e^- $ (non-η) are measured to be $ e^+e^- $ % and $ e^+e^- $ %, respectively. The amplitude analysis provides an important model for the binning strategy in measuring the strong phase parameters of $ e^+e^- $ when used to determine the CKM angle $ e^+e^- $ via the $ e^+e^- $ decay.