Structure of the $Ω^{-}(2012)$ with Hamiltonian Effective Field Theory

TL;DR

This paper uses Hamiltonian effective field theory (HEFT) constrained by lattice QCD spectra to study the Ω(2012)^−, considering both $J^P = 1/2^-$ and $3/2^-$ assignments and couplings to the channels $Ξar{K}$ and $Ξ(1530)ar{K}$ via a quark-pair-creation model with a cutoff. By matching finite-volume spectra to lattice data and solving the infinite-volume T-matrix, the authors extract resonance poles and dissect the eigenstate compositions, finding a narrow $J^P = 3/2^-$ state at $M \approx 2012$ MeV with width $ ext{Γ} \approx 3$ MeV, and a broader $J^P = 1/2^-$ partner near $M \approx 2052$ MeV with $ ext{Γ} oughly 13$ MeV; the BESIII observation of Ω(2109) is consistent with a $J^P = 1/2^-$ assignment. The work demonstrates that the near-threshold dynamics and the interplay between a bare three-quark core and coupled-channel meson-baryon states can reproduce both lattice and experimental data, providing insight into the internal structure and spin-parity of excited Ω states. The approach also highlights the importance of channel selection and finite-volume analysis for deciphering resonance properties and motivates future lattice studies with additional interpolators and channels to further refine the spectrum. Overall, the study offers a concrete, first-principles–guided interpretation of the Ω(2012)^− and related excitations, with implications for strange baryon spectroscopy and the role of molecular components in excited hadrons.

Abstract

We investigate the internal structure of the $Ω(2012)^-$ by analyzing lattice QCD simulation and experimental data within Hamiltonian effective field theory, considering both $J^P = 1/2^-$ and $3/2^-$ assignments. The couplings to the dominant decay channel $Ξ\bar{K}$ and the near-threshold channel $Ξ(1530) \bar{K}$ are determined through the quark-pair-creation model. By studying the lattice QCD spectra in these two spin-parity scenarios, we extract the masses and widths of the resonances. We notice that the $J^P = 3/2^-$ resonance is consistent with the observed $Ω(2012)^-$ while the recently reported $Ω(2109)^-$ may be a $J^P = 1/2^-$ $Ω$.

Figures (4)

• Figure 1: Pion-mass dependence of the finite-volume energy for the $J^P=3/2^-$ system with $m_{\Omega}^{0}|_{\mathrm{phys}} = 2.110 \,\text{GeV}$ and the mass slope $\alpha = 0$. The solid red line indicates the largest contribution of the bare basis state in the Hamiltonian model eigenvector. The broken line denotes noninteracting meson-baryon energies. The brown and blue shaded regions represent the impacts on the finite-volume energies induced by $10\%$ and $20\%$ variations of the creation strength $\gamma$ in the ${}^3P_0$ model, respectively. The lattice results are taken from the CSSM group Hockley:2024aym in $2+1$ flavor QCD PACS-CS:2008bkb.
• Figure 2: Pion-mass dependence of the eigenvector components with HEFT for the lowest four eigenstates of the $J^P = 3/2^-$ system.
• Figure 3: Pion-mass dependence of the finite-volume energy for the $J^P=1/2^-$ system with $m_{\Omega}^{0}|_{\mathrm{phys}} = 2.150 \,\text{GeV}$ and the mass slope $\alpha = 0$. The solid red line indicates the largest contribution of the bare basis state within HEFT. The broken line denotes noninteracting meson-baryon energies. The brown and blue shaded regions represent the impacts on the finite-volume energies induced by $10\%$ and $20\%$ variations of the creation strength $\gamma$ in the ${}^3P_0$ model, respectively. The lattice results are taken from the CSSM group Hockley:2024aym in $2+1$ flavor QCD PACS-CS:2008bkb.
• Figure 4: Pion-mass dependence of the eigenvector components with HEFT for the lowest four eigenstates of the $J^P = 1/2^-$ system.