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Bound States of $Ω$ Baryons in Light Nuclei

Igor Filikhin, Roman Ya. Kezerashvili, Branislav Vlahovic

TL;DR

The paper investigates bound states of light $Ω$-baryon clusters using a configuration-space Faddeev approach with a short-range regularization of the HAL QCD $V_{ ext{ΩN}}$ potential. A two-range Gaussian form regularizes the short-distance core, preserving two-body observables while reducing unphysically deep three-body binding, and folding procedures generate effective $V_{ ext{Ωα}}$ and $V_{ ext{Ω}_{3c} ext{α}}$ for cluster studies. It extends to $Ω_{3c}$-containing systems by modeling $Ω_{3c}N$ analogously and finds regions in parameter space where bound $Ω_{3c}NN$ and $Ω_{3c}Ω_{3c}N$ states may exist, with mass-polarization effects quantified. Additionally, a short-distance, contact-like repulsive component for the $ΩΩ$ interaction demonstrates regulator independence in two- and three-body energies, highlighting the need to connect quark-level dynamics with hadronic descriptions and to calibrate predictions against experimental data for robust hypernuclear benchmarks.

Abstract

We investigate bound states of light $Ω_{3x}$-clusters ($x = s, c$), motivated by the $Ω_{3s}N$ potential recently developed by the HAL QCD collaboration. To regularize this potential, we remove the deeply attractive core at $r < 0.4~\mathrm{fm}$ and parametrize the long-range component ($r > 0.4~\mathrm{fm}$) using a two-range Gaussian form. This procedure preserves the relevant two-body bound state energy while having a negligible effect on the $Ω_{3s}NN$ and $Ω_{3s}Ω_{3s}N$ systems. An effective $Ω_{3s}α$ potential is then constructed by fitting a two-range Gaussian function to the long-range component of the folding potential, enabling calculations of the bound state energies of the $Ω_{3s}α$, $Ω_{3s}αα$, and $Ω_{3s}Ω_{3s}α$ systems. The regularization procedure leads to a substantial reduction in bound state energies compared to those obtained with the original potential. We further extend the analysis to $Ω_{3c}$-cluster systems by introducing an $Ω_{3c}N$ interaction, derived by comparing the existing $Ω_{3s}Ω_{3s}$ and $Ω_{3c}Ω_{3c}$ potentials. Our results suggest that several parametrizations predict bound states in $Ω_{3c}$-containing clusters. Finally, the $Ω_{3s}Ω_{3s}$ interaction is described using a contact-like potential approach, motivated by the effective field theory.

Bound States of $Ω$ Baryons in Light Nuclei

TL;DR

The paper investigates bound states of light -baryon clusters using a configuration-space Faddeev approach with a short-range regularization of the HAL QCD potential. A two-range Gaussian form regularizes the short-distance core, preserving two-body observables while reducing unphysically deep three-body binding, and folding procedures generate effective and for cluster studies. It extends to -containing systems by modeling analogously and finds regions in parameter space where bound and states may exist, with mass-polarization effects quantified. Additionally, a short-distance, contact-like repulsive component for the interaction demonstrates regulator independence in two- and three-body energies, highlighting the need to connect quark-level dynamics with hadronic descriptions and to calibrate predictions against experimental data for robust hypernuclear benchmarks.

Abstract

We investigate bound states of light -clusters (), motivated by the potential recently developed by the HAL QCD collaboration. To regularize this potential, we remove the deeply attractive core at and parametrize the long-range component () using a two-range Gaussian form. This procedure preserves the relevant two-body bound state energy while having a negligible effect on the and systems. An effective potential is then constructed by fitting a two-range Gaussian function to the long-range component of the folding potential, enabling calculations of the bound state energies of the , , and systems. The regularization procedure leads to a substantial reduction in bound state energies compared to those obtained with the original potential. We further extend the analysis to -cluster systems by introducing an interaction, derived by comparing the existing and potentials. Our results suggest that several parametrizations predict bound states in -containing clusters. Finally, the interaction is described using a contact-like potential approach, motivated by the effective field theory.
Paper Structure (13 sections, 18 equations, 3 figures, 9 tables)

This paper contains 13 sections, 18 equations, 3 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Model
  3. Approaches
  4. $\Omega N$, $\Omega \Omega$, and $\Omega_{3c} \Omega_{3c}$ potentials
  5. $NN$ and $\alpha \alpha$ interactions
  6. Folding $\Omega \alpha$ potential
  7. Numerical Results
  8. Fitting for HAL QCD $\Omega N$ potential
  9. $\Omega_{3c} N$ potential modeling
  10. $\Omega \alpha$ and $\Omega_{3c} \alpha$ potentials
  11. $\Omega_{3x}$-containing $\alpha$-cluster systems
  12. $\Omega\Omega$ potential at short distances
  13. Concluding remarks

Figures (3)

  • Figure 1: $\Omega N$ potentials. The solid curve represents the HAL QCD $\Omega N$ potential ${V}_{\Omega N}$ with parameters P$_1$Iritani2019, while the dashed curve shows the renormalized potential $\widetilde{V}_{\Omega N}$ given by Eq. (\ref{['P1t']}).
  • Figure 2: $\Omega\Omega$ (solid curve) and $\Omega_{3c}\Omega_{3c}$ (dashed curve) potentials $V_{YY}$ ($Y$ means $\Omega$ or $\Omega_{3c}$). The approximation of Eq. (\ref{['Vccc']}) for $\Omega_{3c}\Omega_{3c}$ potential is show for $c_1$=2.3 and $c_2$=1.52 by the doted curve.
  • Figure 3: The $\Omega\Omega$ potential (solid curve) compared with contact-like simulation potentials: $\Lambda = 7.0$ fm$^{-1}$ (dashed curve), $\Lambda = 5.0$ fm$^{-1}$ (dot-dashed curve), and $\Lambda = 3.6$ fm$^{-1}$ (dotted curve).