Using $2.93{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, the first observation of the doubly Cabibbo-suppressed decay $D^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{\pi }^0$ is reported. After removing decays that contain narrow intermediate resonances, including $D^{+}\to K^{+}\eta$, $D^{+}\to K^{+}\omega$, and $D^{+}\to K^{+}\varphi$, the branching fraction of the decay $D^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{\pi }^0$ is measured to be $(1.13\pm 0.08_{\mathrm{stat}}\pm 0.03_{\mathrm{syst}})\times {10}^{-3}$. The ratio of branching fractions of $D^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{\pi }^0$ over $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^0$ is found to be $(1.81\pm 0.15)\%$, which corresponds to $(6.28\pm 0.52){\tan }^4{\theta }_C$, where ${\theta }_C$ is the Cabibbo mixing angle. This ratio is significantly larger than the corresponding ratios for other doubly Cabibbo-suppressed decays. The asymmetry of the branching fractions of charge-conjugated decays $D^{\pm }\to K^{\pm }{\pi }^{\pm }{\pi }^{\mp }{\pi }^0$ is also determined, and no evidence for $CP$ violation is found. In addition, the first evidence for the $D^{+}\to K^{+}\omega$ decay, with a statistical significance of $3.3\sigma$, is presented and the branching fraction is measured to be $\mathcal{B}(D^{+}\to K^{+}\omega )=({5.7_{-2.1}^{+2.5}}_{\mathrm{stat}}\pm 0.2_{\mathrm{syst}})\times {10}^{-5}$.

• Received 15 July 2020
• Accepted 21 August 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.141802

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Published by the American Physical Society