Molecular picture for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2012</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> revisited
Natsumi Ikeno, G. Toledo Sánchez, E. Oset
Abstract
We conduct a study of the interaction of the $\overline{K}{\mathrm{\ensuremath{\Xi}}}^{*}$, $\ensuremath{\eta}\mathrm{\ensuremath{\Omega}}(s\text{\ensuremath{-}}\mathrm{wave})$, and $\overline{K}\mathrm{\ensuremath{\Xi}}(d\text{\ensuremath{-}}\mathrm{wave})$ channels within a coupled channel unitary approach where the transition potential between the $\overline{K}{\mathrm{\ensuremath{\Xi}}}^{*}$ and $\ensuremath{\eta}\mathrm{\ensuremath{\Omega}}$ channels is obtained from chiral Lagrangians. The transition potential between $\overline{K}{\mathrm{\ensuremath{\Xi}}}^{*}$, $\ensuremath{\eta}\mathrm{\ensuremath{\Omega}}$, and $\overline{K}\mathrm{\ensuremath{\Xi}}$ is taken in terms of free parameters, which together with a cutoff to regularize the meson-baryon loops are fitted to the $\mathrm{\ensuremath{\Omega}}(2012)$ data. We find that all data including the recent Belle experiment on ${\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{\ensuremath{\Omega}}}^{*}\ensuremath{\rightarrow}\ensuremath{\pi}\overline{K}\mathrm{\ensuremath{\Xi}}}/{\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{\ensuremath{\Omega}}}^{*}\ensuremath{\rightarrow}\overline{K}\mathrm{\ensuremath{\Xi}}}$, are compatible with the molecular picture stemming from meson baryon interaction of these channels.