Probing $NNΩ_{ccc}$ three-body systems with the modern QCD $NΩ_{ccc}$ interaction

TL;DR

The study probes the existence of bound or near-threshold resonant states in the $NNΩ_{ccc}$ three-body system using lattice-QCD–inspired $NΩ_{ccc}$ potentials from HAL QCD, together with a Malfliet-Tjon model for the NN interaction. It employs the Gaussian Expansion Method (GEM) and the Complex Scaling Method (CSM) to analyze bound and resonant states, augmented by a coupling-constant variation to approach the physical point. The main result is a single bound three-body state for the d–Ω_{ccc} system in the $(0)1/2^{+}$ channel at $t/a=16$ with $B_3=-2.255$ MeV, while nnΩ_{ccc}, ppΩ_{ccc}, and pnΩ_{ccc} configurations show no bound states and likely correspond to virtual states near threshold; Coulomb effects were explored but do not qualitatively alter this outcome. These findings inform heavy-baryon interaction physics and motivate experimental and lattice-driven explorations of charmed dibaryons.

Abstract

Newly, first-principles lattice QCD results at the physical pion mass, $ m_π\backsimeq 137.1 $ MeV, have been reported by the HAL QCD Collaboration for the S-wave interaction between the nucleon ($N$) and the triply charmed Omega baryon ($Ω_{ccc}$). The $NΩ_{ccc}$ potentials in the spin-1 $ \left(^{3}S_{1}\right) $ and spin-2 $ \left(^{5}S_{2}\right) $ channels were derived and found to be attractive, though no two-body bound state was supported in these channels. The present work investigates the $NNΩ_{ccc}$ three-body system using the Malfliet-Tjon $NN$ potential. Analyses of spin-1, spin-averaged, and spin-2 $NΩ_{ccc}$ channels (at Euclidean times 16, 17, 18) reveal a three-body bound state only for the d-$Ω_{ccc}$ configuration with spin $(0)1/2^{+}$ and $t/a=16$. Its binding energy ($B_3 = -2.255$ MeV) lies slightly below the deuteron's ($B_d = -2.23$ MeV). Other parameter sets do not yield a bound state, and complex scaling analysis indicates these configurations correspond to virtual states rather than resonances. The Coulomb potential's role was also examined to differentiate charged states.

Figures (6)

• Figure 1: Coupling constant variation for the $nn\Omega_{ccc}$ system.
• Figure 2: Complex-scaled spectrum for the $nn\Omega_{ccc}$ system. No resonance is found. Since this system contains no bound two-body subsystem, there is only a single rotated continuum starting at the origin.
• Figure 3: Coupling constant variation for the $pp\Omega_{ccc}$ system for different $p\Omega_{ccc}$ Coulomb interaction: without (top left), with $V_{\textrm{Coul}}^{\left(1\right)}$ (top right) and with $V_{\textrm{Coul}}^{\left(2\right)}$ (bottom) one.
• Figure 4: Complex-scaled spectrum for the $pp \Omega_{ccc}$ system. No resonance is found. Calculations performed for $V_{\text{Coul}}^{(1)}$. As for the $nn\Omega_{ccc}$ case, this system has no bound two-body subsystem, hence there is only a single rotated continuum starting at the origin.
• Figure 5: Coupling constant variation for the $pn\Omega_{ccc}$ system for different $p\Omega_{ccc}$ Coulomb interaction: without (top left), with $V_{ \text{Coul} }^{\left(1\right)}$ (top right) and with $V_{ \text{Coul} }^{\left(2\right)}$ (bottom) one.