Strangeness $+1$ light multiquark baryons: a jinx?

In view of the renewing experimental interest for searching strangeness $+1$ baryons at J-PARC, we study the existence of light baryon resonances with strangeness +1 generated in the K-(N^*/Δ^*) system, where N^* represents either N^*(1535)/N^*(1650)/N^*(1700), and Δ^* corresponds to Δ(1620). The description of the properties of the aforementioned states requires considering the dynamics involved in the coupled pseudoscalar-baryon and vector-baryon systems with strangeness $S=0$ in the s-wave. For the purpose of our current study, we consider the pseudoscalar-baryon (PB) and vector-baryon channels (VB) to which the mentioned N^* and Δ^* resonances couple and solve the Faddeev equations for the coupled channel system K-PB, K-VB, with all interactions being in the s-wave. Despite some strong attraction present in two of the subsystems, we do not find clear evidence supporting the formation of strangeness +1 states, with spin-parity JP=1/2⁺, in the energy region $2000-2200$ MeV. However, the case of spin-parity JP=3/2⁺ seems more promising, showing the formation of a resonance with a mass around 2167 MeV, with a width of 90-100 MeV. We suggest that a signal of such a state could be found in processes with final states like $KN$, K^*(892) N.