Role of $a_0(980)$ in the decays $D^0\to K^{+}{K}^{-}\eta$ and ${\pi }^{+}{\pi }^{-}\eta$

Abstract

In present work, we study the reactions $D^0\to K^{+}{K}^{-}\eta$ and $D^0\to {\pi }^{+}{\pi }^{-}\eta$, 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 $\varphi (1020)$, 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.

Comments: 19 pages, 8 figures