Study of the $D_s^{+}\to a_0(980)\ddot{I}$ and $a_0(980)\ddot{I}‰$ decays

Abstract

We study $D_s^{+}\to \ddot{I}{}^{0(+)}{a}_0^{+(0)}$, $D_s^{+}\to \ddot{I}‰a_0^{+}$, and the resonant $D_s^{+}\to \ddot{I}a_0$,$a_0\to \hat{I}\cdot \ddot{I}€(KK)$ decays. In the final state interaction, where $D_s^{+}\to (\hat{I}{\cdot }^{(\prime )}\ddot{I}{€}^{+},K^{+}{\bar{K}}^0)$ are followed by the $(\hat{I}{\cdot }^{(\prime )}\ddot{I}{€}^{+},K^{+}{\bar{K}}^0)$ to $\ddot{I}{}^{0(+)}{a}_0^{+(0)}$ rescatterings, we predict $\mathcal{B}(D_s^{+}\to \ddot{I}{}^{0(+)}{a}_0^{+(0)})=(3.0\pm 0.3\pm 1.0)\times 10^{-3}$. Due to the cancellation of the rescattering effects and the suppressed short-distance $W$ annihilation contribution, we expect that $\mathcal{B}(D_s^{+}\to \ddot{I}‰a_0^{+})\simeq \mathcal{B}(D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0)<3.4\times 10^{-4}$. In our calculation, $\mathcal{B}(D_s^{+}\to \ddot{I}{}^0(a_0^{+}\to )\hat{I}\cdot \ddot{I}{€}^{+})=(1.6_{-0.3}^{+0.2}\pm 0.6)\times 10^{-3}$ agrees with the data, whereas $\mathcal{B}(D_s^{+}\to \ddot{I}{}^{+}(a_0^0\to )K^{+}{K}^{-})$ is 10 times smaller than the observation, which requires a careful examination.

11 pages, 2 figures, version to appear in EPJC