Role of the $\Lambda(1600)$ in the $K^-p \to \Lambda \pi^0\pi^0$ reaction

Role of the $\Lambda(1600)$ is studied in the $K^- p \to \Lambda \pi^0 \pi^0$ 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 $\Lambda(1600)$ and $\Lambda(1670)$ intermediate resonances decaying into $\pi^0 \Sigma^{*0}(1385)$ with $\Sigma^{*0}(1385)$ decaying into $\pi^0 \Lambda$. 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 $K^- p \to \Lambda \pi^0 \pi^0$ reaction can be well reproduced. It is shown that we really need the contribution from the $\Lambda(1600)$ with spin-parity $J^P = 1/2^+$, and that these measurements can be used to determine some of the properties of the $\Lambda(1600)$ resonance. Furthermore, we also plot the $\pi^0 \Lambda$ invariant mass distributions which could be tested by the future experimental measurements.