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Register a new userHadronic molecular assignment for the newly observed $Omega^*$ state
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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.
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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.
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.
The newly observed $Xi(1620)^0$ by the Belle Collaboration inspires our interest in performing a systematic study on the interaction of an anti-strange meson $(bar{K}^{(*)})$ with a strange or doubly strange ground octet baryon $mathcal{B}$ ($Lambda$, $Sigma$, and $Xi$), where the spin-orbit force and the recoil correction are considered in the adopted one-boson-exchange model. Our results indicate that $Xi(1620)^0$ can be explained as a $bar{K}Lambda$ molecular state with $I(J^P)=1/2(1/2^-)$ and the intermediate force from $sigma$ exchange plays an important role. Additionally, we also predict several other possible molecular candidates, i.e., the $bar{K}Sigma$ molecular state with $I(J^P)=1/2(1/2^-)$ and the triply strange $bar{K}Xi$ molecular state with $I(J^P)=0(1/2^-)$.
In the present work, we investigate subsequential production of three kaons and $Omega^-$ baryon based on an effective Lagrangian approach. We only consider the intermediate states with the light mass baryon to suggest the minimum of the total cross section. Coupling constants for verteces of meson-octet baryons are fixed from the empirical data and/or quark models together with SU(3) symmetry considerations and these for meson-decouplet are predicted not only quark model but also Chiral-quark soliton model calculation. Gauge invariance of the resulting amplitude is maintained by introducing the contact currents by extending the gauge-invariant approach of Haberzettl for one-meson photoproduction to two-meson photoproduction.
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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