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Revisiting the $Omega(2012)$ as a hadronic molecule and its strong decays

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 نشر من قبل Ju-Jun Xie
 تاريخ النشر 2020
  مجال البحث
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Recently, the Belle collaboration measured the ratios of the branching fractions of the newly observed $Omega(2012)$ excited state. They did not observe significant signals for the $Omega(2012) to bar{K} Xi^*(1530) to bar{K} pi Xi$ decay, and reported an upper limit for the ratio of the three body decay to the two body decay mode of $Omega(2012) to bar{K} Xi$. In this work, we revisit the newly observed $Omega(2012)$ from the molecular perspective where this resonance appears to be a dynamically generated state with spin-parity $3/2^-$ from the coupled channels interactions of the $bar{K} Xi^*(1530)$ and $eta Omega$ in $s$-wave and $bar{K} Xi$ in $d$-wave. With the model parameters for the $d$-wave interaction, we show that the ratio of these decay fractions reported recently by the Belle collaboration can be easily accommodated.

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Strong two- and three-body decays of the new excited hyperon $Omega^*(2012)$ are discussed in the hadronic molecular approach. The $Omega^*(2012)$ state is considered to contain the mixed $Xi bar K$ and $Omega eta$ hadronic components. In our calcula tions we use a phenomenological hadronic Lagrangian describing the coupling of the bound states to its constituents and of the constituents to other hadrons occurring in the final state. Our results show that the decay widths of the two-body decay modes $Omega^*(2012) to Xi bar K$ lie in the few MeV region and are compatible with or dominate over the rates of the three-body modes $Omega^*(2012) to Xi pi bar K$. The sum of two- and three-body decay widths is consistent with a width of the $Omega^*(2012)$ originally measured by the Belle Collaboration. A possible scenario for the suppression of the three-body decay rate recently noticed by the Belle Collaboration is due to the dominant admixture of the $Omega eta$ hadronic component in the $Omega^*(2012)$ state.
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After the discovery of the new $Omega^{*}$ state, the ratio of the branching fractions of $Omega(2012)to bar{K}piXi$ relative to $bar{K}Xi$ decay channel was investigated by the Belle Collaboration recently. The measured $11.9%$ up limit on this rati o is in sharp tension with the $S$-wave $bar{K}Xi(1530)$ molecule interpretation for $Omega(2012)$ which indicates the dominant $bar{K}piXi$ three-body decay. In the present work, we try to explore the possibility of the $P$-wave molecule assignments for $Omega(2012)$ (where $Omega(2012)$ has positive parity). It is found that the latest experimental measurements are compatible with the $1/2^+$ and $3/2^+$ $bar{K}Xi(1530)$ molecular pictures, while the $5/2^+$ $bar{K}Xi(1530)$ molecule shows the larger $bar{K}piXi$ three-body decay compared with the $bar{K}Xi$ decay as the case of $S$-wave molecule. Thus, the newly observed $Omega(2012)$ can be interpreted as the $1/2^+$ or $3/2^+$ $bar{K}Xi(1530)$ molecule state according to current experiment data.
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