Contrasting observables related to the $N^*(1535)$ from the molecular or a genuine structure

In this work we compare the predictions for the scattering length and effective range of the channels $K^0 \Sigma^+, K^+ \Sigma^0 , K^+ \Lambda$ and $\eta p$, assuming the $N^*(1535)$ state as a molecular state of these channels, or an original genuine state, made for instance from three quarks. Looking at very different scenarios, what we conclude is that the predictions of these two pictures are drastically different, to the point that we advise the measurement of these magnitudes, accessible for instance by measuring correlation functions, in order to gain much valuable information concerning the nature of this state.