Amplitude analysis of $D^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$

Abstract

We present an amplitude analysis of the decay $D^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ based on a data sample of 2.93 ${\mbox{\,fb}^{-1}}$ acquired by the BESIII detector at the $\ddot{I}ˆ(3770)$ resonance. With a nearly background free sample of about 16000 events, we investigate the substructure of the decay and determine the relative fractions and the phases among the different intermediate processes. Our amplitude model includes the two-body decays $D^0\to {\bar{K}}^{\ast 0}\ddot{I}{}^0$, $D^0\to K^{-}{a}_1^{+}(1260)$ and $D^0\to K_1^{-}(1270)\ddot{I}{€}^{+}$, the three-body decays $D^0\to {\bar{K}}^{\ast 0}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $D^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{}^0$, as well as the four-body decay $D^0\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$. The dominant intermediate process is $D^0\to K^{-}{a}_1^{+}(1260)$, accounting for a fit fraction of $54.6\%$.