Measurement of Singly Cabibbo-Suppressed Decays $D^0\to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^0$, $\ddot{I}{€}^0\ddot{I}{€}^0\hat{I}\cdot$, $\ddot{I}{€}^0\hat{I}\cdot \hat{I}\cdot$ and $\hat{I}\cdot \hat{I}\cdot \hat{I}\cdot$

Abstract

Using a data sample of $e^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of 2.93 $f{b}^{-1}$ collected with the BESIII detector at a center-of-mass energy of $\sqrt{s}=3.773GeV$,we search for the singly Cabibbo-suppressed decays $D^0\to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^0$, $\ddot{I}{€}^0\ddot{I}{€}^0\hat{I}\cdot$, $\ddot{I}{€}^0\hat{I}\cdot \hat{I}\cdot$ and $\hat{I}\cdot \hat{I}\cdot \hat{I}\cdot$ using the double tag method. The absolute branching fractions are measured to be $\mathcal{B}(D^0\to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^0)=(2.0\pm 0.4\pm 0.3)\times 10^{-4}$, $\mathcal{B}(D^0\to \ddot{I}{€}^0\ddot{I}{€}^0\hat{I}\cdot )=(3.8\pm 1.1\pm 0.7)\times 10^{-4}$ and $\mathcal{B}(D^0\to \ddot{I}{€}^0\hat{I}\cdot \hat{I}\cdot )=(7.3\pm 1.6\pm 1.5)\times 10^{-4}$ with the statistical significances of $4.8\ddot{I}ƒ$, $3.8\ddot{I}ƒ$ and $5.5\ddot{I}ƒ$, respectively, where the first uncertainties are statistical and the second ones systematic. No significant signal of $D^0\to \hat{I}\cdot \hat{I}\cdot \hat{I}\cdot$ is found, and the upper limit on its decay branching fraction is set to be $\mathcal{B}(D^0\to \hat{I}\cdot \hat{I}\cdot \hat{I}\cdot )<1.3\times 10^{-4}$ at the $90\%$ confidence level.