Understanding the nature of $\mathrm{\Omega }(2012)$ in a coupled-channel approach

We perform a systematic analysis of the mass and strong decays of the $\mathrm{\Omega }(2012)$ resonance in a coupled-channel approach of a bare three-quark state and a composite meson-baryon state. Besides the coupling of the bare state and ${\mathrm{\Xi }}^{*}\overline{K}$ channel, the effective meson-baryon interactions are also included. We find a pole with a mass of 2008 MeV by solving the Bethe-Salpeter equation. The calculated decay widths and its ratios of branching fractions ${\mathcal{R}}_{\mathrm{\Xi }\overline{K}}^{\mathrm{\Xi }\pi \overline{K}}$ agree well with the new experimental measurement by the Belle Collaboration. Our results suggest that both three-quark core and ${\mathrm{\Xi }}^{*}\overline{K}$ channel are essential for the description of the $\mathrm{\Omega }(2012)$ resonance. We expect that present calculations can help us to better understand the nature of $\mathrm{\Omega }(2012)$ resonance.

Figure 1

The Feynman diagram for the effective ${\mathrm{\Xi }}^{*}\overline{K}$ interaction via $\mathrm{\Omega }\eta$ loop.

Figure 2

The tree-level Feynman diagram for the interaction between the bare state and ${\mathrm{\Xi }}^{*}\overline{K}$ channel.

Figure 3

The diagram of sequential decay chain $\mathrm{\Omega }(2012)\to {\mathrm{\Xi }}^{*}\overline{K}\to \mathrm{\Xi }\pi \overline{K}$.

Figure 4

The invariant mass distribution $d\mathrm{\Gamma }[\mathrm{\Omega }(2012)\to {\mathrm{\Xi }}^{*}\overline{K}\to \mathrm{\Xi }\pi \overline{K}]/d{M}_{\mathrm{inv}}(\pi \mathrm{\Xi })$ for a three-body channel. The red solid and blue dashed lines correspond to energy independent and dependent ${\mathrm{\Xi }}^{*}$ widths, respectively. The green vertical line is the lower cut 1.49 GeV as implemented by Belle experiment in 2019 [7].