Role of a₀(980) in the decays D⁰ → K⁺ K⁻ η and π⁺ π⁻ η

In present work, we study the reactions D⁰ → K⁺ K⁻ η and D⁰ → π⁺ π⁻ η, and find that the a₀(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 a₀(980) state is generated from the final state interaction. Besides, the contributions of other intermediate resonances, such as ρ(770) and φ(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 a₀(980) shows great significance. Besides, the antisymmetry data for the production of the a₀(980)⁺ and a₀(980)⁻ is described well in the combined fit.