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Role of the $Λ(1600)$ in the $K^-p \to Λπ^0π^0$ reaction

Role of the $Λ(1600)$ is studied in the $K^- p \to Λπ^0 π^0$ reaction by using the effective Lagrangian approach near the threshold. We perform a calculation for the total and differential cross sections by considering the contributions from the $Λ(1600)$ and $Λ(1670)$ intermediate resonances decaying into $π^0 Σ^{*0}(1385)$ with $Σ^{*0}(1385)$ decaying into $π^0 Λ$. Besides, the non-resonance process from $u$-channel nucleon pole is also taken into account. With our model parameters, the current experimental data on the total cross sections of the $K^- p \to Λπ^0 π^0$ reaction can be well reproduced. It is shown that we really need the contribution from the $Λ(1600)$ with spin-parity $J^P = 1/2^+$, and that these measurements can be used to determine some of the properties of the $Λ(1600)$ resonance. Furthermore, we also plot the $π^0 Λ$ invariant mass distributions which could be tested by the future experimental measurements.