Abstract

We conduct a study of the interaction of the $\bar K \Xi^*$, $\eta \Omega$($s$-wave) and $\bar K \Xi$($d$-wave) channels within a coupled channel unitary approach where the transition potential between the $\bar K \Xi^*$ and $\eta \Omega$ channels is obtained from chiral Lagrangians. The transition potential between $\bar K \Xi^*$, $\eta \Omega$ and $\bar K \Xi$ is taken in terms of free parameters, which together with a cut off to regularize the meson-baryon loops are fitted to the $\Omega(2012)$ data. We find that all data including the recent Belle experiment on $\Gamma_{\Omega^* \to \pi \bar K \Xi}/ \Gamma_{\Omega^* \to \bar K \Xi}$, are compatible with the molecular picture stemming from meson baryon interaction of these channels.

Highlights

  • The discovery of the Ωð2012Þ state by the Belle collaboration [1] prompted much theoretical work on the issue, with pictures inspired by quark models and molecular pictures based on the meson-baryon interaction

  • We find that all data including the recent Belle experiment on ΓΩÃ→πK Ξ=ΓΩÃ→K Ξ, are compatible with the molecular picture stemming from meson baryon interaction of these channels

  • In Eq (3) the transition potentials between K ΞÃ and ηΩ are taken from the chiral Lagrangians [20], while the transition potential between K Ξ and K ΞÃ or ηΩ, which proceed in d-wave, are taken in terms of the free parameters α, β

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Summary

INTRODUCTION

The discovery of the Ωð2012Þ state by the Belle collaboration [1] prompted much theoretical work on the issue, with pictures inspired by quark models and molecular pictures based on the meson-baryon interaction. As SU(3) [16], and the algebraic method [17] have contributed to this topic In those models the Ωð2012Þ approximately fits as a JP 1⁄4 3=2− state, yet there is a dispersion of the results for the masses for this state that ranges from 1978 MeV in Ref. The interaction in this case is peculiar since the diagonal potential of the two channels is null, and only the transition potential between these two channels is nonzero This has as a consequence that the mass of the generated bound Ω state depends more strongly on the parameters of the model than in other ordinary molecular states. Anticipating the results, we find that the results are compatible with the molecular picture in coupled channels, but in passing we will learn more about the role played by the ηΩ channel in this problem

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