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Probing Nucleon-$Ω_{\rm ccc}$Interaction via Lattice QCD at Physical Quark Masses

Liang Zhang, Takumi Doi, Yan Lyu, Tetsuo Hatsuda, Yu-Gang Ma

TL;DR

This paper investigates the N-Ωccc interaction in the $^3S_1$ and $^5S_2$ channels using (2+1)-flavor lattice QCD at physical quark masses, extracting the interaction potential via the time-dependent HAL QCD method. It finds attractive interactions in both channels but no bound state, with a dominant spin-independent potential $V_0(r)$ and a short-range spin-dependent term $V_s(r)$, and it quantifies the low-energy scattering parameters $a_0$ and $r_{eff}$ from the effective-range expansion. The results are discussed in the context of heavy-hadron chromo-polarizability by comparing to N-J/psi and N-Ωsss systems, and the charm-mass dependence is explored, showing a weaker $V_0$ for heavier charm mass consistent with roughly $1/m_{Ω_{3c}}$ scaling. These findings provide first-principles constraints on heavy-baryon interactions relevant for hadron spectroscopy and heavy-ion phenomenology.

Abstract

We study 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. 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. The charm quark mass dependence of the $N$-$Ω_{\rm ccc}$ potential is investigated as well.

Probing Nucleon-$Ω_{\rm ccc}$Interaction via Lattice QCD at Physical Quark Masses

TL;DR

This paper investigates the N-Ωccc interaction in the and channels using (2+1)-flavor lattice QCD at physical quark masses, extracting the interaction potential via the time-dependent HAL QCD method. It finds attractive interactions in both channels but no bound state, with a dominant spin-independent potential and a short-range spin-dependent term , and it quantifies the low-energy scattering parameters and from the effective-range expansion. The results are discussed in the context of heavy-hadron chromo-polarizability by comparing to N-J/psi and N-Ωsss systems, and the charm-mass dependence is explored, showing a weaker for heavier charm mass consistent with roughly scaling. These findings provide first-principles constraints on heavy-baryon interactions relevant for hadron spectroscopy and heavy-ion phenomenology.

Abstract

We study the S-wave interactions between the nucleon () and the triply charmed Omega baryon () using (2+1)-flavor lattice QCD with a physical pion mass ( MeV) on a lattice volume . The charm quark is implemented with a relativistic heavy-quark action at its physical mass. Employing the time-dependent HAL QCD method, the - potentials in the spin-1 () and spin-2 () channels are extracted. In both channels, overall attraction is found with the scattering parameters, fm and fm for the channel, and fm and fm for the channel, indicating the absence of a dibaryon bound state. The extracted potentials are further decomposed into spin-independent and spin-dependent components. 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 - and - systems at MeV are provided, emphasizing the role of heavy-hadron chromo-polarizability arising from soft-gluon exchange between the nucleon and flavor-singlet hadrons. The charm quark mass dependence of the - potential is investigated as well.

Paper Structure

This paper contains 11 sections, 8 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. HAL QCD method
  3. Lattice setup
  4. Numerical results
  5. NOmegaccc potential in different spin channels
  6. Phase shifts and scattering parameters
  7. Further discussions
  8. Comparison with N-Jpsi potential
  9. Comparison with N-Omegasss potential
  10. Comparison between different charm masses
  11. Summary

Figures (6)

  • Figure 1: The $N$-$\Omega_{\rm 3c}$ potential in the $S$-wave extracted from lattice data at $t/a$ = 16 (blue), 17 (red) and $18$ (green) with statistical errors. The panel (a) (the panel (b)) shows the potential in the $^3{\rm S}_1$ ($^5{\rm S}_2$) channel. Fits with the two-range Gaussian $V_{\rm fit}(r)$ at $t/a=17$ in the range of $0<r<3$ fm are drawn by the purple.
  • Figure 2: The spin-independent potential $V_0$ (full circle) and spin-dependent potential $V_s$ (open triangle) of $N$-$\Omega_{3c}$, decomposed from the $^3{\rm S}_1$ and $^5{\rm S}_2$ channels, are shown for $t/a$ = 16 (blue), 17 (red) and $18$ (green).
  • Figure 3: S-wave $N$-$\Omega_{\rm 3c}$ scattering phase shifts with central values (solid lines) and statistical errors (bands) for $t/a$ = 16 (blue), 17 (red) and $18$ (green). The panel (a) for the $^3{\rm S}_1$ channel and the panel (b) for the $^5{\rm S}_2$ channel.
  • Figure 4: 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, with the lower panels showing their ratio.
  • Figure 5: Comparison between potentials for $^5{\rm S}_2\ N$-$\Omega_{\rm 3c}$ from F-conf (at $t/a=17$) and $^5{\rm S}_2\ N$-$\Omega_{\rm 3s}$ from K-conf (at $t/a=14$) HALQCD:2018qyu, showing reduced attraction in $N$-$\Omega_{\rm 3c}$ at short distances, consistent with the phenomenological quark model predictions Oka:1986fr.
  • ...and 1 more figures