Lattice QCD study on nucleon-$Ω_{\rm ccc}$ interaction at the physical point

Abstract

We report the S-wave interactions between the nucleon ($N$) and the triply charmed Omega baryon ($Ω_{\mathrm{ccc}}$) using (2+1)-flavor lattice QCD with a physical pion mass ($m_π\simeq 137.1$ MeV) on a lattice volume $\simeq (8.1~\mathrm{fm})^3$. The charm quark is implemented with a relativistic heavy-quark action at its physical mass. Employing the time-dependent HAL QCD method, the $N-Ω_{\mathrm{ccc}}$ potentials in the spin-1 ($^3\mathrm{S}_1$) and spin-2 ($^5\mathrm{S}_2$) channels are extracted. In both channels, overall attraction is found with the scattering parameters, $a_0 = 0.56(0.13)\left(^{+0.26}_{-0.03}\right)$ fm and $r_{\mathrm{eff}} = 1.60(0.05)\left(^{+0.04}_{-0.12}\right)$ fm for the $^3\mathrm{S}_1$ channel, and $a_0 = 0.38(0.12)\left(^{+0.25}_{-0.00}\right)$ fm and $r_{\mathrm{eff}} = 2.04(0.10)\left(^{+0.03}_{-0.22}\right)$ fm for the $^5\mathrm{S}_2$ channel, indicating the absence of a dibaryon bound state. The extracted potentials are further decomposed into spin-independent and spin-dependent components, which provides a useful handle to investigate the underlying interaction mechanism. The spin-independent potential is a dominant component and features a short-range attractive core and a long-range attractive tail, while the spin-dependent potential shows short-range attraction (repulsion) in the spin-1 (spin-2) channel. Qualitative comparisons with previous studies of the $N$-$J/ψ$ and $N-Ω_{\rm{sss}}$ systems at $m_π\simeq 146$ MeV are provided, emphasizing the role of heavy-hadron chromo-polarizability arising from soft-gluon exchange between the nucleon and flavor-singlet hadrons.

Figures (5)

• Figure 1: $N-\Omega_{\rm ccc}$ potential in the $^3\mathrm{S}_1$ (a) and $^5\mathrm{S}_2$ (b) channels. The potential with staistical errors is extraced from lattice data at $t/a=16$ (yellow), $17$ (green) and $18$ (blue). Two-range Gaussian $V_{\rm fit}$ fits (purple) at $t/a=17$ in the range of $0<r<3$ fm are drawn in both panels. The figure is adapted from our published work, Ref. Zhang:2025zaa.
• Figure 2: Spin-independent $V_0$ (full circles) and spin-dependent $V_s$ (open triangles) potentials of $N-\Omega_{\rm 3c}$, decomposed from the $^3{\rm S}_1$ and $^5{\rm S}_2$ channels, for $t/a=16$ (yellow), $17$ (green) and $18$ (blue). The figure is adapted from Ref. Zhang:2025zaa.
• Figure 3: S-wave $N-\Omega_{\rm 3c}$ scattering phase shifts for $t/a=16$ (yellow), $17$ (green) and $18$ (blue). The solid curves represent the central values, while the shaded bands indicate the statistical uncertainties. Panel (a) shows the $^3{\rm S}_1$ channel, and panel (b) shows the $^5{\rm S}_2$ channel. The figure is adapted from Ref. Zhang:2025zaa.
• Figure 4: Comparison of the $^5{\rm S}_2$$N-\Omega_{\rm 3c}$ potential from F-conf ($t/a=17$) with the $^5{\rm S}_2$$N-\Omega_{\rm 3s}$ potential from K-conf ($t/a=14$) HALQCD:2018qyu. The $N-\Omega_{\rm 3c}$ system exhibits a weaker short-range attraction, in qualitative agreement with phenomenological quark-model expectations Oka:1986fr. The figure is adapted from Ref. Zhang:2025zaa.
• Figure 5: Comparison of the spin-independent potentials for $N-\Omega_{\rm 3c}$ from F-conf (at $t/a=17$) and $N-J/\psi$ from K-conf (at $t/a=13$) Lyu:2024ttm. The lower panels showing their ratio. The interval indicated by the green arrow exhibits a clear plateau, suggesting a same interaction mechanism in the two systems. The figure is adapted from Ref. Zhang:2025zaa.