Role of the $N^*(1535)$ in the $\Lambda^+_c \to \bar{K}^0 \eta p$ decay

The nonleptonic weak decay of $\Lambda^+_c \to \bar{K}^0 \eta p$ is analyzed from the viewpoint of probing the $N^*(1535)$ resonance, which has a big decay branching ratio to $\eta N$. Up to an arbitrary normalization, the invariant mass distribution of $\eta p$ is calculated with both the chiral unitary approach and an effective Lagrangian model. Within the chiral unitary approach, the $N^*(1535)$ resonance is dynamically generated from the final state interaction of mesons and baryons in the strangeness zero sector. For the effective Lagrangian model, we take a Breit-Wigner formula to describe the distribution of the $N^*(1535)$ resonance. It is found that the behavior of the $N^*(1535)$ resonance in the $\Lambda^+_c \to \bar{K}^0 N^*(1535) \to \bar{K}^0 \eta p$ decay within the two approaches is different. The proposed $\Lambda^+_c$ decay mechanism can provide valuable information on the properties of the $N^*(1535)$ and can in principle be tested by facilities such as BEPC II and SuperKEKB.