Chiral coupled channel dynamics of the Lambda(1520) and the K-P -> pi0 pi0 Lambda reaction

We study the $\mathrm{\Lambda }(1520)D_{03}$ in a chiral coupled channel approach. This resonance appears as dynamically generated from the interaction of the decuplet of baryons and the octet of mesons in s-wave, and its treatment is improved here with the phenomenological inclusion of the $\bar{K}N$ and $\pi \mathrm{\Sigma }$ channels in d-wave. Since the most important building block in the $\mathrm{\Lambda }(1520)$ is the $\pi \text{Sgs}(1385)P_{13}$ channel, we study the $K^- p \to \pi \Sgs(1385) (\pi^0 \Lambda)$reactionintheregionofthe$\Lambda(1520)$ and above, and compare the results with recent experimental data. With the coupling of the $\mathrm{\Lambda }(1520)$ to the $\pi \text{Sgs}$ channel predicted by the theory we find a cross section in good agreement with the data and there is as well agreement for the invariant mass distributions which show a neat peak for the $\text{Sgs}(1385)$ in the $({\pi }^0\mathrm{\Lambda })$ spectrum. Predictions are made of a strong $\mathrm{\Lambda }(1520)$ resonant peak of the cross section, as a function of the $K^{-}$ momentum, in the region below the measured data which, if confirmed experimentally, would give a stronger support to the idea of the $\mathrm{\Lambda }(1520)$ as a dynamically generated resonance.