Role of N^∗(1535) in the Λ⁺_c → K̄⁰ηp decay and the possible φp state in the Λ⁺_c → π⁰φp decay

The nonleptonic weak decays of Λ⁺_c → K̄⁰ηp and Λ⁺_c → π⁰φp are investigated from the viewpoint of probing the N^∗(1535) resonance and the possible φp state. For the Λ⁺_c → K̄⁰ηp decay, we study the invariant mass distribution of ηp 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 coupled channels. While for the effective Lagrangian model, we take a Breit-Wigner formula for the N^∗(1535) resonance. We found that the behavior of the N^∗(1535) resonance in the Λ⁺_c → K̄⁰N^∗(1535) → K̄⁰ηp decay within the two approaches is different. For the Λ⁺_c → π⁰φp decay, we consider a triangle singularity mechanism, where the Λ⁺_c decays into the K^∗Σ^∗(1385), the Σ^∗(1385) decays into the π⁰Σ/Λ, and then the K^∗Σ/Λ merge to produce the φp in the final state. This mechanism produces a peak structure around 2020 MeV. In addition, the possibility that there is a hidden-strange pentaquark-like state is also considered by taking into account the final state interactions of K^∗Λ, K^∗Σ, and φp. We conclude that it is difficult to search for the hidden-strange state in this decay. However, we do expect nontrivial behavior in the φp invariant mass distribution. The proposed Λ⁺_c decay mechanism here can provide valuable information on the properties of these nuclear resonances and can in principle be tested by experiments such as BESIII, LHCb and Belle-II.