Measurement of the Resonant and Non-Resonant Branching Ratios in $Ξ_{c}^{0} \rightarrow Ξ^{0} K^+ K^-$
Using the entire data sample of $980$ $fb^{-1}$ integrated luminosity collected with the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider, we present an amplitude analysis measuring the branching fractions of the Cabibbo-allowed, $W$-exchange resonant decay $Ξ_{c}^{0} \rightarrow Ξ^{0} ϕ(\to K^+ K^-)$ with a polarized $ϕ$ and the non-resonant decay via a direct process $Ξ_{c}^{0} \rightarrow Ξ^{0} K^+ K^-$. We present these measurements, relative to the normalization mode $Ξ^{-}π^{+}$, and find branching ratios $\frac{\mathcal{B}(Ξ_{c}^{0} \rightarrow Ξ^{0} ϕ(\rightarrow K^{+}K^{-}))}{\mathcal{B}(Ξ_{c}^{0} \rightarrow Ξ^{-} π^{+})} = 0.036 \pm 0.004 (stat.) \pm 0.002 (syst.)$ and $\frac{\mathcal{B}(Ξ_{c}^{0} \rightarrow Ξ^{0} K^{+} K^{-})}{\mathcal{B}(Ξ_{c}^{0} \rightarrow Ξ^{-} π^{+})} = 0.039 \pm 0.004 (stat.) \pm 0.002 (syst.)$ which suggest that only minor cusping peaks occur in the combinatorial background of $Ω^{*-} \to Ξ^{0}K^{-}$ due to these $Ξ_{c}^{0}$ decays.