Reanalysis of the newly observed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> state in a hadronic molecule model
Yong-Hui Lin, Fei Wang, B. S. Zou
Abstract
After the recent discovery of the new ${\mathrm{\ensuremath{\Omega}}}^{*}$ state, the ratio of the branching fractions of $\mathrm{\ensuremath{\Omega}}(2012)\ensuremath{\rightarrow}\overline{K}\ensuremath{\pi}\mathrm{\ensuremath{\Xi}}$ relative to the $\overline{K}\mathrm{\ensuremath{\Xi}}$ decay channel was investigated by the Belle Collaboration. The measured 11.9% upper limit to this ratio is in sharp tension with the $S$-wave $\overline{K}\mathrm{\ensuremath{\Xi}}(1530)$ molecule interpretation for $\mathrm{\ensuremath{\Omega}}(2012)$, which indicates the dominant $\overline{K}\ensuremath{\pi}\mathrm{\ensuremath{\Xi}}$ three-body decay. We try to explore the possibility of the $P$-wave molecule assignments for $\mathrm{\ensuremath{\Omega}}(2012)$ [where $\mathrm{\ensuremath{\Omega}}(2012)$ has positive parity]. It is found that the latest experimental measurements are compatible with the $1/{2}^{+}$ and $3/{2}^{+}$ $\overline{K}\mathrm{\ensuremath{\Xi}}(1530)$ molecular pictures, while the $5/{2}^{+}$ $\overline{K}\mathrm{\ensuremath{\Xi}}(1530)$ molecule shows larger $\overline{K}\ensuremath{\pi}\mathrm{\ensuremath{\Xi}}$ three-body decay than $\overline{K}\mathrm{\ensuremath{\Xi}}$ decay as in the case of an $S$-wave molecule. Thus, the newly observed $\mathrm{\ensuremath{\Omega}}(2012)$ can be interpreted as the $1/{2}^{+}$ or $3/{2}^{+}$ $\overline{K}\mathrm{\ensuremath{\Xi}}(1530)$ molecule state according to current experiment data.