Observation of ${D}^{0\left(+\right)}\to {K}_{S}^{0}{\pi }^{0\left(+\right)}{\eta }^{\prime }$ and improved measurement of ${D}^{0}\to {K}^{-}{\pi }^{+}{\eta }^{\prime }$

By analyzing an ${e}^{+}{e}^{-}$ data sample corresponding to an integrated luminosity of $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ 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 ${D}^{0}\to {K}^{-}{\pi }^{+}{\eta }^{\prime }$, ${D}^{0}\to {K}_{S}^{0}{\pi }^{0}{\eta }^{\prime }$, and ${D}^{+}\to {K}_{S}^{0}{\pi }^{+}{\eta }^{\prime }$, which are determined to be $\left(6.43±0.1{5}_{\mathrm{stat}}±0.3{1}_{\mathrm{syst}}\right)×{10}^{-3}$, $\left(2.52±0.2{2}_{\mathrm{stat}}±0.1{5}_{\mathrm{syst}}\right)×{10}^{-3}$, and $\left(1.90±0.1{7}_{\mathrm{stat}}±0.1{3}_{\mathrm{syst}}\right)×{10}^{-3}$, respectively. The precision of the branching fraction of ${D}^{0}\to {K}^{-}{\pi }^{+}{\eta }^{\prime }$ is significantly improved, and the processes ${D}^{0}\to {K}_{S}^{0}{\pi }^{0}{\eta }^{\prime }$ and ${D}^{+}\to {K}_{S}^{0}{\pi }^{+}{\eta }^{\prime }$ are observed for the first time.