Measurement of the doubly Cabibbo-suppressed decay $D^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ with semileptonic tags

Abstract

Using an $e^{+}{e}^{-}$ annihilation data sample corresponding to an integrated luminosity of $2.93\mathrm{f}{\mathrm{b}}^{-1}$ collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, the doubly Cabibbo-suppressed decay $D^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ is studied with a semileptonic tag method. After removing the decays containing narrow intermediate resonances, $D^{+}\to K^{+}\hat{I}\cdot$, $D^{+}\to K^{+}\ddot{I}‰$, and $D^{+}\to K^{+}\ddot{I}•$, the branching fraction for the decay $D^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ is determined to be $(1.03\pm 0.12_{\mathrm{stat}}\pm 0.06_{\mathrm{syst}})\times 10^{-3}$. The ratio of the branching fraction for $D^{+}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ to its Cabibbo-favored counterpart $D^{+}\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^0$ is measured to be $(1.65\pm 0.21)\%$, corresponding to $(5.73\pm 0.73){\tan }^4\hat{I}{¸}_C$, where $\hat{I}{¸}_C$ is the Cabibbo mixing angle. These results are consistent with our previous measurement with hadronic tags but are significantly larger than other doubly Cabibbo-suppressed decays in the charm sector.