Study of ${\bar{K}}^{\ast }(892{)}^0\hat{I}\cdot$ and $K_S^0{a}_0(980{)}^0$ in the $D^0\to K_S^0\ddot{I}{€}^0\hat{I}\cdot$ decay

Abstract

We perform an amplitude analysis of the decay $D^0\to K_S^0\ddot{I}{€}^0\hat{I}\cdot$ and measure its absolute branching fraction to be $(1.016\pm 0.013_{\text{stat.}}\pm 0.014_{\text{syst.}})\%$. The analysis utilizes $20.3{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector. The branching fraction of the intermediate process $D^0\to {\bar{K}}^{\ast }(892{)}^0\hat{I}\cdot$ is determined to be $(0.73\pm 0.05_{\text{stat.}}\pm 0.03_{\text{syst.}})\%$, which is $5\ddot{I}ƒ$ smaller than the result measured in $D^0\to K^{-}\ddot{I}{€}^{+}\hat{I}\cdot$ by the Belle experiment. As a result, the magnitudes of the $W$-exchange and QCD-penguin exchange amplitudes are found to be less than half of their current estimations. Furthermore, we determine $\mathcal{B}(D^0\to K_S^0{a}_0(980{)}^0,a_0(980{)}^0\to \ddot{I}{€}^0\hat{I}\cdot )=(9.88\pm 0.37_{stat.}\pm 0.42_{syst.})\times 10^{-3}$, with a precision improved by a factor of 4.5 compared to the world average.