\(\Lambda _{c}^{ + } \to \eta \pi ^{ + }\Lambda \) Decay and the Possible \(\Sigma _{1/2^{ - }}^{*}(1380)\)

A possible Σ^* state with spin-parity = 1/2^− [\(\Sigma _{1/2^{ - }}^{*}\text{(1380)}\)] has been predicted in several pentaquark models. In the present work, we discuss how one can employ the \(\Lambda _{c}^{ + } \to \eta \pi ^{ + }\Lambda \) decay to test its existence, as well as to study the \(\Sigma _{3/2^{ + }}^{*}(1385)\) state with J^P = 3/2^+. Because the final π^+Λ system is in a pure isospin I = 1 combination, the \(\Lambda _{c}^{ + } \to \eta \pi ^{ + }\Lambda \) decay can be an ideal process to study these Σ^* resonances. In particular, we show that the decay angle and energy distributions of the π^+ are very different for \(\Sigma _{3/2^{ + }}^{*}(1385)\) and \(\Sigma _{1/2^{ - }}^{*}(1380)\). The proposed decay mechanism as well as the existence of the \(\Sigma _{1/2^{ - }}^{*}(1380)\) state can be checked by future BelleII and BESIII experiments.