Using 983.0 fb−1 and 427.9 fb−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 \({\Xi }_{c}^{+}\) decays \({\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0}\) and \({\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+}\) , and the singly Cabibbo-suppressed decay \({\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+}\) . The ratios of branching fractions of \({\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0}\) and \({\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+}\) relative to that of \({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\) are measured for the first time, while the ratio \(\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+})/\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+})\) is also determined and improved by an order of magnitude in precision. The measured branching fraction ratios are
\(\begin{array}{c}\frac{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0}\right)}{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=0.067\pm 0.007\pm 0.003,\\ \frac{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+}\right)}{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=0.251\pm 0.005\pm 0.010,\\ \frac{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+}\right)}{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=0.017\pm 0.003\pm 0.001.\end{array}\)
Additionally, the ratio \(\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+})/\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+})\) is measured to be 0.068 ± 0.010 ± 0.004. Here, the first and second uncertainties are statistical and systematic, respectively. Multiplying the ratios by the branching fraction of the normalization mode, \(\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+})=(2.9\pm 1.3)\%\) , we obtain the following absolute branching fractions
\(\begin{array}{c}\mathcal{B}({\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0})=(0.194\pm 0.021\pm 0.009\pm 0.087)\text{\%},\\ \mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+})=(0.728\pm 0.014\pm 0.027\pm 0.326)\text{\%},\\ \mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+})=(0.049\pm 0.007\pm 0.003\pm 0.022)\text{\%},\end{array}\)
where the third uncertainties are from \(\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+})\) .
