Amplitude analysis and branching fraction measurement of the decay $D_s^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$

Abstract

Using $6.32$ fb${}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at the center-of-mass energies between 4.178 and 4.226 GeV with the BESIII detector, we perform an amplitude analysis of the decay $D_s^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and determine the amplitudes of the various intermediate states. The absolute branching fraction of $D_s^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ is measured to be ($6.11\pm 0.18_{stat.}\pm 0.11_{syst.})\times 10^{-3}$. The branching fractions of the dominant intermediate processes $D_s^{+}\to K^{+}\ddot{I}{}^0,\ddot{I}{}^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $D_s^{+}\to K^{\ast }(892{)}^0\ddot{I}{€}^{+},K^{\ast }(892{)}^0\to K^{+}\ddot{I}{€}^{-}$ are determined to be $(1.96\pm 0.19_{stat.}\pm 0.23_{syst.})\times 10^{-3}$ and $(1.85\pm 0.12_{stat.}\pm 0.13_{syst.})\times 10^{-3}$, respectively. The intermediate resonances $f_0(500)$, $f_0(980)$, and $f_0(1370)$ are observed for the first time in this channel.