Can the nature of $a_0(980)$ be tested in the $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$ decay?

Abstract

From the amplitude analysis of the $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$ decay, the BESIII Collaboration firstly observed the $D_s^{+}\to a_0(980{)}^{+}\ddot{I}{€}^0$ and $D_s^{+}\to a_0(980{)}^0\ddot{I}{€}^{+}$ decay modes, which are expected to occur through the pure $W$-annihilation processes. The measured branching fraction $\mathcal{B}[D_s^{+}\to a_0(980{)}^{+(0)}\ddot{I}{€}^{0(+)},a_0(980{)}^{+(0)}\to \ddot{I}{€}^{+(0)}\hat{I}\cdot ]$ is, however, found to be larger than those of known $W$-annihilation decays by one order of magnitude. This apparent contradiction can be reconciled if the two decays are induced by internal $W$-conversion or external $W$-emission mechanisms instead of $W$-annihilation mechanism. In this work, we propose that the $D_s^{+}$ decay proceeds via both the external and internal $W$-emission instead of $W$-annihilation mechanisms. In such a scenario, we perform a study of the $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$ decay by taking into account the contributions from the tree diagram $D_s^{+}\to \ddot{I}{}^{+}\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$ and the intermediate $\ddot{I}{}^{+}\hat{I}\cdot$ and $K^{\ast }\bar{K}/K{\bar{K}}^{\ast }$ triangle diagrams. The intermediate $a_0(980)$ state can be dynamically generated from the final state interactions of coupled $K\bar{K}$ and $\ddot{I}€\hat{I}\cdot$ channels, and it is shown that the experimental data can be described fairly well, which supports the interpretation of $a_0(980)$ as a molecular state.

14 pages, 8 figures