Measurement of the doubly Cabibbo-suppressed decay D+→K+π+π−π0 with semileptonic tags

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We propose a new semileptonic tag method to study the doubly Cabibbo-suppressed $D$ decay in $\ensuremath{\psi}(3770)\ensuremath{\rightarrow}D\overline{D}$ reaction. Utilizing the dataset corresponding to an integrated luminosity of $2.93\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at a center-of-mass energy of 3.773 GeV collected by the BESIII detector, we determine the branching fraction for ${D}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ to be $(1.03\ifmmode\pm\else\textpm\fi{}0.1{2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.0{6}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, in which the contributions from narrow intermediate resonances, ${D}^{+}\ensuremath{\rightarrow}{K}^{+}\ensuremath{\eta}$, ${D}^{+}\ensuremath{\rightarrow}{K}^{+}\ensuremath{\omega}$, and ${D}^{+}\ensuremath{\rightarrow}{K}^{+}\ensuremath{\phi}$ have been excluded. Combining the world average of the branching fraction of ${D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$, we determine $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0})/\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0})=(1.65\ifmmode\pm\else\textpm\fi{}0.21)%$, corresponding to $(5.73\ifmmode\pm\else\textpm\fi{}0.73){\mathrm{tan}}^{4}{\ensuremath{\theta}}_{c}$, where ${\ensuremath{\theta}}_{c}$ 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.

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