Theoretical interpretation of the $$\Xi (1620)$$ Ξ ( 1620 ) and $$\Xi (1690)$$ Ξ ( 1690 ) resonances seen in $$\Xi _c^+ \rightarrow \Xi ^- \pi ^+ \pi ^+$$ Ξ c + → Ξ - π + π + decay

Abstract

Abstract We study the Belle reaction $$\Xi _c^+ \rightarrow \Xi ^- \pi ^+ \pi ^+$$ Ξ c + → Ξ - π + π + looking at the mass distribution of $$\pi ^+ \Xi $$ π + Ξ , where clear signals for the $$\Xi (1620)$$ Ξ ( 1620 ) and $$\Xi (1690)$$ Ξ ( 1690 ) resonances are seen. These two resonances are generated dynamically from the interaction in coupled channels of $$\pi \Xi , {\bar{K}} \Lambda , {\bar{K}} \Sigma $$ π Ξ , K ¯ Λ , K ¯ Σ and $$\eta \Xi $$ η Ξ 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 $$\pi \pi \Xi $$ π π Ξ final state. In order to produce this state one must make transitions from the $${\bar{K}} \Lambda , {\bar{K}} \Sigma $$ K ¯ Λ , K ¯ Σ and $$\eta \Xi $$ η Ξ components to $$\pi \Xi $$ π Ξ , 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 $$\Xi ^*(1530)$$ 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.