Measurements of the branching fractions of $Ξ_{c}^{+}\to Σ^{+}K_{S}^{0}$, $Ξ_{c}^{+}\to Ξ^{0}π^{+}$, and $Ξ_{c}^{+}\to Ξ^{0}K^{+}$ at Belle and Belle II
Using 983.0 $\rm{fb}^{-1}$ and 427.9 $\rm{fb}^{-1}$ 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 $Ξ_c^+$ decays ${Ξ_{c}^{+}\to Σ^{+}K_{S}^{0}}$ and $Ξ_{c}^{+}\to Ξ^{0}π^{+}$, and the singly Cabibbo-suppressed decay $Ξ_{c}^{+}\to Ξ^{0}K^{+}$. The ratios of branching fractions of ${Ξ_{c}^{+}\to Σ^{+}K_{S}^{0}}$ and $Ξ_{c}^{+}\to Ξ^{0}K^{+}$ relative to that of $Ξ_{c}^{+}\toΞ^{-}π^{+}π^{+}$ are measured for the first time, while the ratio ${\cal B}(Ξ_{c}^{+}\toΞ^{0}π^{+})/{\cal B}(Ξ_{c}^{+}\toΞ^{-}π^{+}π^{+}) $ is also determined and improved by an order of magnitude in precision. The measured branching fraction ratios are $\frac{\cal{B}(Ξ_{c}^{+} \to Σ^{+}K_{S}^{0})}{\cal{B}(Ξ_{c}^{+}\to Ξ^{-}π^{+}π^+)}= 0.067 \pm 0.007 \pm 0.003$, $\frac{\cal{B}(Ξ_c^{+} \to Ξ^{0}π^{+})}{\cal{B}(Ξ_{c}^{+}\to Ξ^{-}π^{+}π^+)} = 0.251 \pm 0.005 \pm 0.010$, $\frac{\cal{B}(Ξ_c^{+} \to Ξ^{0}K^{+})}{\cal{B}(Ξ_{c}^{+}\to Ξ^{-}π^{+}π^+)} = 0.017 \pm 0.003 \pm 0.001$. Additionally, the ratio ${\cal B}(Ξ_{c}^{+}\toΞ^{0}K^{+})/{\cal B}(Ξ_{c}^{+}\toΞ^{0}π^{+})$ 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, ${\mathcal B}(Ξ_{c}^{+}\toΞ^{-}π^{+}π^+)= (2.9\pm 1.3)\%$, we obtain the following absolute branching fractions ${\cal B}(Ξ_{c}^{+}\toΣ^{+}K^{0}_{S}) = (0.194 \pm 0.021 \pm 0.009 \pm 0.087 )%$, ${\cal B}(Ξ_{c}^{+}\toΞ^{0}π^{+}) = (0.728 \pm 0.014 \pm 0.027 \pm 0.326 )%$, ${\cal B}(Ξ_{c}^{+}\toΞ^{0}K^{+}) = (0.049 \pm 0.007 \pm 0.003 \pm 0.022 )%$.