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Register a new userRevisiting the $Omega(2012)$ as a hadronic molecule and its strong decays
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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 calculations 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.
We report on a theoretical study of the newly observed $Omega(2012)$ resonance in the nonleptonic weak decays of $Omega_c^0 to pi^+ bar{K}Xi^*(1530) (eta Omega) to pi^+ (bar{K}Xi)^-$ and $pi^+ (bar{K}Xipi)^-$ via final-state interactions of the $bar{K}Xi^*(1530)$ and $eta Omega$ pairs. The weak interaction part is assumed to be dominated by the charm quark decay process: $c(ss) to (s + u + bar{d})(ss)$, while the hadronization part takes place between the $sss$ cluster from the weak decay and a quark-antiquark pair with the quantum numbers $J^{PC} = 0^{++}$ of the vacuum, produces a pair of $bar{K}Xi^*(1530)$ and $eta Omega$. Accordingly, the final $bar{K}Xi^*(1530)$ and $eta Omega$ states are in pure isospin $I= 0$ combinations, and the $Omega_c^0 to pi^+ bar{K}Xi^*(1530)(eta Omega) to pi^+ (bar{K}Xi)^-$ decay is an ideal process to study the $Omega(2012)$ resonance. With the final-state interaction described in the chiral unitary approach, up to an arbitrary normalization, the invariant mass distributions of the final state are calculated, assuming that the $Omega(2012)$ resonance with spin-parity $J^P = 3/2^-$ is a dynamically generated state from the coupled channels interactions of the $bar{K}Xi^*(1530)$ and $eta Omega$ in $s$-wave and $bar{K}Xi$ in $d$-wave. We also calculate the ratio, $R^{bar{K}Xipi}_{bar{K}Xi} = {rm Br}[Omega_c^0 to pi^+ Omega(2012)^- to pi^+ (bar{K}Xi pi)^-] / {rm Br}[Omega_c^0 to pi^+ Omega(2012)^- to pi^+ (bar{K}Xi)^-$]. The proposed mechanism can provide valuable information on the nature of the $Omega(2012)$ and can in principle be tested by future experiments.
Stimulated by the newly discovered $Omega(2012)$ resonance at Belle II, in this work we have studied the OZI allowed strong decays of the low-lying $1P$- and $1D$-wave $Omega$ baryons within the $^3P_0$ model. It is found that $Omega(2012)$ is most likely to be a $1P$-wave $Omega$ state with $J^P=3/2^-$. We also find that the $Omega(2250)$ state could be assigned as a $1D$-wave state with $J^P=5/2^+$. The other missing $1P$- and $1D$-wave $Omega$ baryons may have large potentials to be observed in their main decay channels.
We perform the flavour $SU(3)$ analysis of the recently discovered $Omega(2012)$ hyperon. We find that well known (four star) $Delta(1700)$ resonance with quantum numbers of $J^P=3/2^-$ is a good candidate for the decuplet partner of $Omega(2012)$ if the branching for the three-body decays of the latter is not too large $le 70$%. That implies that the quantum numbers of $Omega(2012)$ are $I(J^P)=0(3/2^-)$. The predictions for the properties of still missing $Sigma$ and $Xi$ decuplet members are made. We also discuss the implications of the ${ overline{ K} Xi(1530)}$ molecular picture of $Omega(2012)$. Crucial experimental tests to distinguish various pictures of $Omega(2012)$ are suggested.
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 ratio 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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