Theoretical interpretation of the $\Xi (1620)$ and $\Xi (1690)$ resonances seen in ${\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}$ decay

Abstract

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

Comments: 15 pages, 8 figures, 2 tables; v2: discussion added, references added, version to appear in Eur.Phys.J.C