Measurement of branching fractions and search for $CP$ violation in $D^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot$, $D^0\to K^{+}{K}^{-}\hat{I}\cdot$, and $D^0\to \ddot{I}•\hat{I}\cdot$ at Belle

Abstract

We measure the branching fractions and $CP$ asymmetries for the singly Cabibbo-suppressed decays $D^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot$, $D^0\to K^{+}{K}^{-}\hat{I}\cdot$, and $D^0\to \ddot{I}•\hat{I}\cdot$, using 980 fb${}^{-1}$ of data from the Belle experiment at the KEKB $e^{+}{e}^{-}$ collider. We obtain \begin{eqnarray} \mathcal{B}(D^{0}\toπ^{+}π^{-}η) & = & [1.22\pm 0.02\,({\rm stat})\pm 0.02\,({\rm syst})\pm 0.03\,(\mathcal{B}_{\rm ref})]\times 10^{-3}\,, \nonumber \\ \mathcal{B}(D^{0}\to K^{+}K^{-}η) & = & [1.80\,^{+0.07}_{-0.06}\,({\rm stat})\pm 0.04\,({\rm syst})\pm 0.05\,(\mathcal{B}_{\rm ref})]\times 10^{-4}\,, \nonumber \\ \mathcal{B}(D^{0}\toϕη) & = & [1.84\pm 0.09\,({\rm stat})\pm 0.06\,({\rm syst})\pm 0.05\,(\mathcal{B}_{\rm ref})]\times 10^{-4}\,, \nonumber \end{eqnarray} where the third uncertainty (${\mathcal{B}}_{\mathrm{ref}}$) is from the uncertainty in the branching fraction of the reference mode $D^0\to K^{-}\ddot{I}{€}^{+}\hat{I}\cdot$. The color-suppressed decay $D^0\to \ddot{I}•\hat{I}\cdot$ is observed for the first time, with very high significance. The results for the $CP$ asymmetries are \begin{eqnarray} A_{CP}(D^{0}\toπ^{+}π^{-}η) & = & [0.9\pm 1.2\,({\rm stat})\pm 0.5\,({\rm syst})]\%\,, \nonumber \\ A_{CP}(D^{0}\to K^{+}K^{-}η) & = & [-1.4\pm 3.3\,({\rm stat})\pm 1.1\,({\rm syst})]\%\,, \nonumber \\ A_{CP}(D^{0}\toϕη)&= & [-1.9\pm 4.4\,({\rm stat})\pm 0.6\,({\rm syst})]\%\,. \nonumber \end{eqnarray} The results for $D^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot$ are a significant improvement over previous results. The branching fraction and $A_{CP}$ results for $D^0\to K^{+}{K}^{-}\hat{I}\cdot$, and the $A_{CP}$ result for $D^0\to \ddot{I}•\hat{I}\cdot$, are the first such measurements. No evidence for $CP$ violation is found in any of these decays.

21 pages, 7 figures