Measurement of the branching fraction of the doubly Cabibbo-suppressed decay $D^0\to K^{+}{\pi }^{-}{\pi }^0$ and search for $D^0\to K^{+}{\pi }^{-}{\pi }^0{\pi }^0$

Abstract

Using $2.93\mathrm{f}{\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at a center-of-mass energy of 3.773\,GeV with the BESIII detector, we present a measurement of the branching fraction of the doubly Cabibbo-suppressed (DCS) decay $D^0\to K^{+}{\pi }^{-}{\pi }^0$ and a search for the DCS decay $D^0\to K^{+}{\pi }^{-}{\pi }^0{\pi }^0$. The branching fraction of $D^0\to K^{+}{\pi }^{-}{\pi }^0$ is determined to be $[3.13_{-0.56}^{+0.60}(\mathrm{stat})\pm 0.09(\mathrm{syst})]\times 10^{-4}$. No signal is observed for $D^0\to K^{+}{\pi }^{-}{\pi }^0{\pi }^0$ and an upper limit of $3.6\times 10^{-4}$ is set on the branching fraction at the 90\% C.L. We combine these results with the world-average branching fractions of their counterpart Cabibbo-favored decays to determine the ratios of the doubly Cabibbo-suppressed over the Cabibbo-favored branching fractions, $\mathcal{B}(D^0\to K^{+}{\pi }^{-}{\pi }^0)/\mathcal{B}(D^0\to K^{-}{\pi }^{+}{\pi }^0)=(0.22\pm 0.04)\%$~and $\mathcal{B}(D^0\to K^{+}{\pi }^{-}{\pi }^0{\pi }^0)/\mathcal{B}(D^0\to K^{-}{\pi }^{+}{\pi }^0{\pi }^0)<0.40\%$ at the 90\% C.L., which correspond to $(0.75\pm 0.14){\tan }^4{\theta }_C$~and $1.37\times {\tan }^4{\theta }_C$, respectively, where ${\theta }_C$ is the Cabibbo angle.