Resonant $a_0(980)$ state in triangle rescattering $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$ decays

Abstract

We study the $D_s^{+}\to \ddot{I}{€}^{+}(a_0(980{)}^0\to )\ddot{I}{€}^0\hat{I}\cdot$, $\ddot{I}{€}^0(a_0(980{)}^{+}\to )\ddot{I}{€}^{+}\hat{I}\cdot$ decays, which have been recently measured by the BESIII collaboration. We propose that $D_s^{+}\to \ddot{I}{€}^{+(0)}(a_0(980{)}^{0(+)}\to )\ddot{I}{€}^{0(+)}\hat{I}\cdot$ receives the contributions from the triangle rescattering processes, where $M^0$ and $\ddot{I}{}^{+}$ in $D_s^{+}\to M^0\ddot{I}{}^{+}$, by exchanging $\ddot{I}{€}^{0(+)}$, are formed as $a_0(980{)}^{0(+)}$ and $\ddot{I}{€}^{+(0)}$, respectively, with $M^0=(\hat{I}\cdot ,\hat{I}{\cdot }^{\prime })$. Accordingly, we calculate that $\mathcal{B}(D_s^{+}\to a_0(980{)}^{0(+)}\ddot{I}{€}^{+(0)})=(1.7\pm 0.2\pm 0.1)\times 10^{-2}$ and $\mathcal{B}(D_s^{+}\to \ddot{I}{€}^{+(0)}(a_0(980{)}^{0(+)}\to )\ddot{I}{€}^{0(+)}\hat{I}\cdot )=(1.4\pm 0.1\pm 0.1)\times 10^{-2}$, being consistent with the data.

Title changed, 9 pages, 5 diagrams, version published in EPJC