Measurements of the branching fractions of ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}{K}_S^0$, ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{\pi }^{+}$, and ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{K}^{+}$ at Belle and Belle II

Using 983.0 ${\mathrm{f}\mathrm{b}}^{-1}$ and 427.9 ${\mathrm{f}\mathrm{b}}^{-1}$ data samples collected with the Belle and Belle II detectors at the KEKB and SuperKEKB asymmetric energy $e^{+}{e}^{-}$ colliders, respectively, we present studies of the Cabibbo-favored ${\mathrm{\Xi }}_c^{+}$ decays ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}{K}_S^0$ and ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{\pi }^{+}$, and the singly Cabibbo-suppressed decay ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{K}^{+}$. The ratios of branching fractions of ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}{K}_S^0$ and ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{K}^{+}$ relative to that of ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^{-}{\pi }^{+}{\pi }^{+}$ are measured for the first time, while the ratio $\mathcal{B}({\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{\pi }^{+})\mathrm{/}\mathcal{B}({\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^{-}{\pi }^{+}{\pi }^{+})$ is also determined and improved by an order of magnitude in precision. The measured branching fraction ratios are $\frac{\mathcal{B}({\mathcal{\Xi }}_{\mathcal{c}}^{+}\to {\mathcal{\Sigma }}^{+}{\mathcal{K}}_{\mathcal{S}}^{\mathcal{0}})}{\mathcal{B}({\mathcal{\Xi }}_{\mathcal{c}}^{+}\to {\mathcal{\Xi }}^{-}{\mathcal{\pi }}^{+}{\mathcal{\pi }}^{+})}=0.067\pm 0.007\pm 0.003$, $\frac{\mathcal{B}({\mathcal{\Xi }}_{\mathcal{c}}^{+}\to {\mathcal{\Xi }}^{\mathcal{0}}{\mathcal{\pi }}^{+})}{\mathcal{B}({\mathcal{\Xi }}_{\mathcal{c}}^{+}\to {\mathcal{\Xi }}^{-}{\mathcal{\pi }}^{+}{\mathcal{\pi }}^{+})}=0.251\pm 0.005\pm 0.010$, $\frac{\mathcal{B}({\mathcal{\Xi }}_{\mathcal{c}}^{+}\to {\mathcal{\Xi }}^{\mathcal{0}}{\mathcal{K}}^{+})}{\mathcal{B}({\mathcal{\Xi }}_{\mathcal{c}}^{+}\to {\mathcal{\Xi }}^{-}{\mathcal{\pi }}^{+}{\mathcal{\pi }}^{+})}=0.017\pm 0.003\pm 0.001$. Additionally, the ratio $\mathcal{B}({\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{K}^{+})\mathrm{/}\mathcal{B}({\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{\pi }^{+})$ is measured to be $0.068\pm 0.010\pm 0.004$. Here, the first and second uncertainties are statistical and systematic, respectively. Multiplying the ratios by the branching fraction of the normalization mode, $\mathcal{B}({\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^{-}{\pi }^{+}{\pi }^{+})=(2.9\pm 1.3)\mathrm{\%}$, we obtain the following absolute branching fractions $\mathcal{B}({\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}{K}_S^0)=(0.194\pm 0.021\pm 0.009\pm 0.087)$, $\mathcal{B}({\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{\pi }^{+})=(0.728\pm 0.014\pm 0.027\pm 0.326)$, $\mathcal{B}({\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^0{K}^{+})=(0.049\pm 0.007\pm 0.003\pm 0.022)$.