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Interpretation of $Ω(2012)$ as a $Ξ(1530)K$ molecular state

Xiang Yu, Jin-Peng Zhang, Xu-Liang Chen, Ding-Kun Lian, Qi-Nan Wang, Wei Chen

Abstract

We investigate the mass and strong decay properties of the $Ω(2012)$ resonance using QCD sum rules, assuming it to be an S-wave $Ξ(1530)K$ molecular pentaquark state with $IJ^{P} = 0\frac{3}{2}^{-}$. A unified interpolating current is constructed, and the two-point and three-point correlation functions are calculated up to dimension-10 condensates in the OPE series. The negative-parity contribution is isolated by employing parity-projected sum rules. The two-body strong decays to $Ξ^0 K^-$ and $Ξ^- K^0$ are studied via their three-point correlation functions. Our analysis yields a mass of $2.00 \pm 0.15~\mathrm{GeV}$ and a total two-body decay width of $Γ= 3.97^{+8.31}_{-1.92}~\mathrm{MeV}$ for the $Ξ(1530)K$ molecular state. The ratios of branching fractions are obtained as $\mathcal{R}^{Ξ^- K^0}_{Ξ^0 K^-} = 0.85$ and $\mathcal{R}^{ΞπK}_{ΞK} = 0.61$. These results are compatible well with the experimental data for the $Ω(2012)$ and support its interpretation as a $Ξ(1530)K$ molecular pentaquark state.

Interpretation of $Ω(2012)$ as a $Ξ(1530)K$ molecular state

Abstract

We investigate the mass and strong decay properties of the resonance using QCD sum rules, assuming it to be an S-wave molecular pentaquark state with . A unified interpolating current is constructed, and the two-point and three-point correlation functions are calculated up to dimension-10 condensates in the OPE series. The negative-parity contribution is isolated by employing parity-projected sum rules. The two-body strong decays to and are studied via their three-point correlation functions. Our analysis yields a mass of and a total two-body decay width of for the molecular state. The ratios of branching fractions are obtained as and . These results are compatible well with the experimental data for the and support its interpretation as a molecular pentaquark state.
Paper Structure (11 sections, 47 equations, 10 figures)

This paper contains 11 sections, 47 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Two-point and three-point QCD sum rules
  3. The $\Xi(1530)K$ molecular interpolating current with $J^{P}=3/2^{-}$
  4. Two-point correlation function
  5. Three-point correlation function
  6. Numerical analyses
  7. The mass of $\Xi(1530)K$ molecular pentaquark
  8. The coupling constant of $\Xi$
  9. The strong decays of $\Omega(2012)\rightarrow \Xi^0 K^-$ and $\Xi^-K^0$
  10. CONCLUSION AND DISCUSSION
  11. The spectral densities for the negative-parity $\Xi(1530)K$ molecular state

Figures (10)

  • Figure 1: The Feynman diagrams involved in our calculations for the $\Xi(1530)K$ molecular pentaquark state. A quark line with dots contains terms proportional to the color factor $\delta^{ij}$ in the propagator $S^{ij}(x)$; consequently, such diagrams effectively subsume multiple Feynman diagrams.
  • Figure 2: The Feynman diagrams which contribute to the theoretical side of the three-point sum rules in the relevant structure for the two-body strong decays of $\Xi(1530)K$ molecular pentaquark state.
  • Figure 3: Behaviors of the spectral densities for different factorization assumption. The solid lines represent the spectral densities for $\kappa=1$, whereas the dashed lines are the corresponding densities considering $\kappa=1.70$.
  • Figure 4: OPE convergence for the $\Xi(1530)K$ molecular pentaquark state considering $\kappa=1.70$.
  • Figure 5: Variation of hadron mass with $s_0$ corresponding to the $\Xi(1530)K$ molecular pentaquark state considering $\kappa=1.70$.
  • ...and 5 more figures