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$Omega(2012)$ through the looking glass of flavour SU(3)

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 نشر من قبل Maxim V. Polyakov
 تاريخ النشر 2018
  مجال البحث
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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.



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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.
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