Study of $D_s^{+}\to f_0(980)\ddot{I}{}^{+}$ and $\ddot{I}•\ddot{I}{€}^{+}$ decays through $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$

Abstract

We perform the first amplitude analysis of $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ decays, based on data samples of electron-positron collisions recorded with the BESIII detector at center-of-mass energies between 4.128 and 4.226~GeV, corresponding to an integrated luminosity of 7.33~fb${}^{-1}$. We report the observation of $D_s^{+}\to f_0(980)\ddot{I}(770{)}^{+}$ with a statistical significance greater than 10$\ddot{I}ƒ$ and determine the branching fractions $\mathcal{B}(D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0{|}_{\mathrm{non}-\hat{I}\cdot })=(2.04\pm 0.08_{stat.}\pm 0.05_{syst.})\%$ and $\mathcal{B}(D_s^{+}\to \hat{I}\cdot \ddot{I}{€}^{+})=(1.56\pm 0.09_{stat.}\pm 0.04_{syst.})\%$. Moreover, we measure the relative branching fraction between $\ddot{I}•\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ and $\ddot{I}•\to K^{+}{K}^{-}$ to be $\frac{\mathcal{B}(\ddot{I}•(1020)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0)}{\mathcal{B}(\ddot{I}•(1020)\to K^{+}{K}^{-})}=0.230\pm 0.014_{stat.}\pm 0.010_{syst.}$, which deviates from the world average value by more than $4\ddot{I}ƒ$.