Amplitude analysis and branching fraction measurement of the decay \boldmath $D_s^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$

Abstract

The singly Cabibbo-suppressed decay $D_s^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ is observed, using a data set corresponding to an integrated luminosity of 6.32 $\mathrm{f}{\mathrm{b}}^{-1}$ recorded by the BESIII detector at the centre-of-mass energies between 4.178 and 4.226 GeV. The first amplitude analysis of $D_s^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ reveals the sub-structures in this decay and determines the fractions and relative phases of different intermediate processes. The dominant intermediate process is $D_s^{+}\to K^{\ast 0}\ddot{I}{}^{+}$, with a fit fraction of $(40.5\pm 2.8_{stat.}\pm 1.5_{syst.})\%$. With the detection efficiency based on our amplitude analysis, the absolute branching fraction for $D_s^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ is measured to be $(9.75\pm 0.54_{stat.}\pm 0.17_{syst.})\times 10^{-3}$.