Understanding the properties of $\Xi(1690)$ and $\Xi(2120)$

TL;DR

This study investigates $ ext{Xi}$ resonances using a coupled channel approach, revealing two poles near the real axis that correspond to known states $ ext{Xi}(1690)$ and $ ext{Xi}(2120)$, with results aligning well with experimental data.

Contribution

The paper introduces a relativistic coupled channel formalism treating pseudoscalar-baryon and vector-baryon channels equally, providing new insights into $ ext{Xi}$ resonance properties.

Findings

Identification of two poles related to $ ext{Xi}(1690)$ and $ ext{Xi}(2120)$

Good agreement with BELLE and BABAR experimental data

Relativistic treatment without nonrelativistic approximations

Abstract

In this manuscript we discuss the results of our recent study on $\Xi$ resonances. We have studied meson-baryon interaction with strangeness $-2$ by solving scattering equations in a coupled channel approach and found that the dynamics gives rise to the development of two poles in the complex plane close to the real axis. The corresponding narrow states have isospin half and spin half in one case and spin 3/2 in the other case. We find that the properties of the isospin and spin 1/2 state are strikingly similar to $\Xi(1690)$, while the state with spin 3/2 can be related to $\Xi(2120)$. We find that our results on $\Xi(1690)$ are in good agreement with the data available from the BELLE and BABAR Collaborations. Our formalism consists of treating pseudoscalar-baryon and vector-baryon channels on an equal footing. Since the thresholds of such channels are distributed over a relatively larger energy range, we obtain all interaction kernels needed to solve the Bethe-Salpeter equation without resorting to any nonrelativistic approximation even though the amplitudes are calculated at low energies.