Role of $Σ(1660)$ in the $K^- p \toπ^0π^0Σ^0$ reaction

The processes of $K^-p \to π^0 π^0 Σ^0$ and $K^- p \to π^0 Λ(1405)$ are studied within the effective Lagrangian approach. In addition to the ``background" contribution from the $u$-channel nucleon pole term, contribution from the $Σ(1660)$ resonance with spin-parity $J^P=1/2^+$ is also considered. For the $K^-p \to π^0 π^0 Σ^0$ reaction, we perform a calculation for the total and differential cross sections by considering the contribution from the $Σ(1660)$ intermediate resonance decaying into $π^0 Λ(1405)$ with $Λ(1405)$ decaying into $π^0 Σ^0$. With our model parameters, the available experimental data on both the $K^-p \to π^0 π^0 Σ^0$ and $K^- p \to π^0 Λ(1405)$ reactions can be fairly well reproduced. It is shown that we really need the contribution from the $Σ(1660)$ resonance, and that these experimental measurements could be used to determine some properties of the $Σ(1660)$ resonance.