Semileptonic $\Lambda_c$ decay to $\nu l^+$ and $\Lambda(1405)$

We study the semileptonic decay of $\Lambda_c$ to $\nu l^+$ and $\Lambda(1405)$, where the $\Lambda(1405)$ is seen in the invariant mass distribution of $\pi \Sigma$. We perform the hadronization of the quarks produced in the reaction in order to have a meson baryon pair in the final state and then let these hadron pairs undergo final state interaction from where the $\Lambda(1405)$ is dynamically generated. The reaction is particularly suited to study this resonance because we show that it filters I=0. It is also free of tree level $\pi \Sigma$ production, which leads to a clean signal of the resonance with no background. This same feature has as a consequence that one populates the state of the $\Lambda(1405)$ with higher mass around 1420 MeV, predicted by the chiral unitary approach. We make absolute predictions for the invariant mass distributions and find them within measurable range in present facilities. The implementation of this reaction would allow us to gain insight into the existence of the predicted two $\Lambda(1405)$ states and their nature as molecular states.