Measurements of the branching fractions of ${\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0}$, ${\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+}$, and ${\Xi }_{c}^{+}\to {\Xi }^{0}{K}+$ at Belle and Belle II
Using 983.0 fb β1 and 427.9 fb β1 data samples collected with the Belle and Belle II detectors at the KEKB and SuperKEKB asymmetric energy e + e β 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 Β± 0.010 Β± 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 $\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+})$.