Observation of $D^{0(+)}\to K_S^0{\pi }^{0(+)}{\eta }^{\mathrm{\prime }}$ and improved measurement of $D^0\to K^{-}{\pi }^{+}{\eta }^{\mathrm{\prime }}$

By analyzing $2.93\mathrm{f}{\mathrm{b}}^{-1}$ of data taken at a center-of-mass energy of 3.773~GeV with the BESIII detector, we measure the branching fractions of the Cabibbo-favored hadronic decays $D^0\to K^{-}{\pi }^{+}{\eta }^{\mathrm{\prime }}$, $D^0\to K^0_S\pi^0\eta^\prime$and$D^+\to K^0_S\pi^+\eta^\prime$, which are determined to be $(6.43\pm {0.15}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.31}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\times {10}^{-3}$, $(2.52 \pm 0.22_{\rm stat.} \pm 0.15_{\rm syst.})\times 10^{-3}$and$(1.90 \pm 0.17_{\rm stat.} \pm 0.13_{\rm syst.})\times 10^{-3}$, respectively. The precision of the branching fraction of $D^0\to K^{-}{\pi }^{+}{\eta }^{\mathrm{\prime }}$ is significantly improved, and the processes $D^0\to K_S^0{\pi }^0{\eta }^{\mathrm{\prime }}$ and $D^{+}\to K_S^0{\pi }^{+}{\eta }^{\mathrm{\prime }}$ are observed for the first time.