Observation of $D^0\to \ddot{I}{}^0{\hat{I}}^3$ and search for $CP$ violation in radiative charm decays

Abstract

We report the first observation of the radiative charm decay $D^0\to \ddot{I}{}^0{\hat{I}}^3$ and the first search for $CP$ violation in decays $D^0\to \ddot{I}{}^0{\hat{I}}^3$, $\ddot{I}•{\hat{I}}^3$, and $\overline{K}{}^{\ast 0}{\hat{I}}^3$, using a data sample of 943 fb${}^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The branching fraction is measured to be $\mathcal{B}(D^0\to \ddot{I}{}^0{\hat{I}}^3)=(1.77\pm 0.30\pm 0.07)\times 10^{-5}$, where the first uncertainty is statistical and the second is systematic. The obtained $CP$ asymmetries, ${\mathcal{A}}_{CP}(D^0\to \ddot{I}{}^0{\hat{I}}^3)=+0.056\pm 0.152\pm 0.006$, ${\mathcal{A}}_{CP}(D^0\to \ddot{I}•{\hat{I}}^3)=-0.094\pm 0.066\pm 0.001$, and ${\mathcal{A}}_{CP}(D^0\to \overline{K}{}^{\ast 0}{\hat{I}}^3)=-0.003\pm 0.020\pm 0.000$, are consistent with no $CP$ violation. We also present an improved measurement of the branching fractions $\mathcal{B}(D^0\to \ddot{I}•{\hat{I}}^3)=(2.76\pm 0.19\pm 0.10)\times 10^{-5}$ and $\mathcal{B}(D^0\to \overline{K}{}^{\ast 0}{\hat{I}}^3)=(4.66\pm 0.21\pm 0.21)\times 10^{-4}$.