Role of $a_0(980)$ in the decays $D^{0} \rightarrow K^{+} K^{-} η$ and $π^{+} π^{-} η$

Abstract: In present work, we study the reactions $D^{0} \rightarrow K^{+} K^{-} \eta$ and $D^0 \rightarrow \pi^{+} \pi^{-} \eta$, and find that the $a_0(980)$ state plays a dominant role. At the quark level, the external and internal $W$-emission mechanisms are taken into account, which can hadronize into the final states, and then the $a_0(980)$ state is generated from the final state interaction. Besides, the contributions of other intermediate resonances, such as $\rho(770)$ and $\phi(1020)$, are also considered. We make a combined fit of the invariant mass spectra measured by the Belle and BESIII Collaborations, where the results are in good agreement with the experiments, and the signal of the $a_0(980)$ shows great significance. Besides, the antisymmetry data for the production of the $a_0(980)^+$ and $a_0(980)^-$ is described well in the combined fit.