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

Abstract

Using $e^{+}{e}^{-}$ annihilation data corresponding to a total integrated luminosity of $6.32$ fb${}^{-1}$ 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 $D_s^{+}\to K^{-}{K}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and determine the relative fractions and phases of different intermediate processes. Absolute branching fraction of $D_s^{+}\to K^{-}{K}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decay is measured to be ($6.60\pm 0.47_{stat.}\pm 0.35_{syst.})\times 10^{-3}$. The dominant intermediate process is $D_s^{+}\to a_1(1260{)}^{+}\ddot{I}•,\ddot{I}•\to K^{-}{K}^{+},a_1(1260{)}^{+}\to \ddot{I}\ddot{I}{€}^{+},\ddot{I}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$, with a branching fraction of $(5.16\pm 0.41_{stat.}\pm 0.27_{syst.})\times 10^{-3}$.