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

TL;DR

This paper provides a theoretical interpretation of the $\\Xi(1620)$ and $\\Xi(1690)$ resonances observed in a specific decay process, using a chiral unitary approach to explain their dynamical generation and match experimental data.

Contribution

It introduces a novel theoretical framework that explains the origin of the $\\Xi(1620)$ and $\\Xi(1690)$ resonances as dynamically generated states within a coupled-channel chiral unitary model.

Findings

Successfully reproduces the experimental mass distribution of the resonances.

Supports the molecular nature of the $\\Xi(1620)$ and $\\Xi(1690)$ resonances.

Provides a good match to experimental signals including background and other contributions.

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 $\Xi^*(1530)$ 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.