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Register a new userReanalysis of the newly observed $Omega^*$ state in hadronic molecule model
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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 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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Very recently, a new $Omega^{*}$ state was reported by the Belle Collaboration, with its mass of $2012.4 pm 0.7 text{(stat)}pm 0.6 text{(syst)} mathrm{MeV}$, which locates just below the $KXi^*$ threshold and hence hints to be a possible $KXi^*$ hadronic molecule. Using the effective Lagrangian approach as the same as our previous works for other possible hadronic molecular states, we investigate the decay behavior of this new $Omega^*$ state within the hadronic molecular picture. The results show that the measured decay width can be reproduced well and its dominant decay channel is predicted to be the $KpiXi$ three-body decay. This suggests that the newly observed $Omega^*$ may be ascribed as the $J^P={3/2}^-$ $KXi^*$ hadronic molecular state and can be further checked through its $KpiXi$ decay channel.
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.
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.
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 choose the Reduction Formula, PCAC and Low Energy Theory to reduce the $S$ matrix of a OZI allowed two-body strong decay involving a light pseudoscalar, the covariant transition amplitude formula with relativistic wave functions as input is derived. After confirm this method by the decay $D^*(2010)to Dpi$, we study the state $D^*(2007)$, and the full width $Gamma_{rm{th}}(D^*(2007))=53.8pm0.7$ keV is obtained. Supposing the newly observed $D_{s0}(2590)^{+}$ to be the state $D_s(2^1S_0)^+$, we find its decay width $Gamma$ is highly sensitive to the $D_{s0}(2590)^{+}$ mass, which result in the meaningless comparison of widths by different models with various input masses. Instead of width, we introduce a model independent quantity $X$ and the ratio $Gamma/{|{vec P_f}|^3}$, which are almost mass independent, to give us useful information. The results show that, all the existing theoretical predictions $X_{D_s(2S) to D^*K}=0.25sim 0.41$ and $Gamma/{|{vec P_f}|^3}=0.81sim1.77$ MeV$^{-2}$ are much smaller than experimental data $0.585^{+0.015}_{-0.035}$ and $4.54^{+0.25}_{-0.52}$ MeV$^{-2}$. Further compared with $X^{ex}_{D^*(2010) to Dpi}=0.58$, the current data $X^{ex}_{D_s(2S) to D^*K}=0.585^{+0.015}_{-0.035}$ is too big to be an reasonable value, so to confirm $D_{s0}(2590)^{+}$ as the state $D_s(2^1S_0)^+$, more experimental studies are needed.
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