Theoretical interpretation of the $Ξ(1620)$ and $Ξ(1690)$ resonances seen in $Ξ_c^+ \to Ξ^- π^+ π^+$ decay

Abstract

We study the Belle reaction $Ξ_c^+ \to Ξ^- π^+ π^+$ looking at the mass distribution of $π^+ Ξ$, where clear signals for the $Ξ(1620)$ and $Ξ(1690)$ resonances are seen. These two resonances are generated dynamically from the interaction in coupled channels of $πΞ, \bar K Λ, \bar K Σ$ and $ηΞ$ within the chiral unitary approach. Yet, the weak decay process at the quark level, together with the hadronization to produce pairs of mesons, does not produce the $ππΞ$ final state. In order to produce this state one must make transitions from the $\bar K Λ, \bar K Σ$ and $ηΞ$ components to $πΞ$, and this interaction is what produces the resonances. So, the reaction offers a good test for the molecular picture of these resonances. Adding the contribution of the $Ξ^*(1530)$ and some background we are able to get a good reproduction of the mass distribution showing the signatures of the two resonances as found in the experiment.