Measurement of the branching fractions of doubly Cabibbo-suppressed $D$ decays

By analyzing $e^{+}{e}^{-}$ collision data collected at the center-of-mass energy of 3.773~GeV with the BESIII detector, corresponding to an integrated luminosity of 20.3~fb${}^{-1}$, we measure the branching fractions of the doubly Cabibbo-suppressed (DCS) decays $D^0\to K^{+}{\pi }^{-}$, $D^0\to K^{+}{\pi }^{-}{\pi }^{-}{\pi }^{+}$, $D^0\to K^{+}{\pi }^{-}{\pi }^0$, $D^0\to K^{+}{\pi }^{-}{\pi }^0{\pi }^0$, $D^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$, and $D^{+}\to K^{+}{K}^{+}{K}^{-}$. We also perform the first searches for $D^0\to K^{+}{\pi }^{-}\eta$, $D^0\to K^{+}{\pi }^{-}{\pi }^0\eta$, $D^{+}\to K^{+}{\pi }^{+}{\pi }^{-}\eta$, $D^{+}\to K^{+}{\left({\pi }^{+}{\pi }^{-}\eta \right)}_{\mathrm{n}\mathrm{o}\mathrm{n}-{\eta }^{\mathrm{\prime }}}$, and $D^{+}\to K^{+}\eta \eta$ and report the first observations and evidence for some of these final states. Combining the measurements with the world averages of the corresponding Cabibbo-favored (CF) decays, the ratios of the DCS/CF branching fractions are obtained. For the $D^{+}\to K^{+}{\left({\pi }^{+}{\pi }^{-}\eta \right)}_{\mathrm{n}\mathrm{o}\mathrm{n}-{\eta }^{\mathrm{\prime }}}$ decay, the ratio is significantly larger than the corresponding ratios of the other DCS decays.