The $\varphi NN,J/\psi NN,{\eta }_{c}NN$ systems based on HAL QCD interactions

Abstract

We investigate the existence of bound states and resonances in the $\varphi NN,J/\psi NN,{\eta }_{c}NN$ systems using HAL QCD interactions for $\varphi N,J/\psi N$, and ${\eta }_{c}N$. We employ the Gaussian expansion method to solve the complex-scaled Schrödinger equation and find no resonances or bound states in the $J/\psi NN$ and ${\eta }_{c}NN$ systems. We estimate the interaction between charmonium and nuclei, concluding that the $J/\psi$ or ${\eta }_c$ is likely to bind with ${}^3\mathrm{H}$, ${}^3\mathrm{He}$, ${}^4\mathrm{He}$, and heavier nuclei. For the $\varphi NN$ system, the lattice QCD $\varphi N\left({}^2{S}_{1/2}\right)$ interaction is absent. We combine the $\varphi p$ correlation function analysis and HAL QCD results in Model A. We assume the spin-spin interactions for $J/\psi N$ and $\varphi N$ systems are inversely proportional to their masses in Model B. Model A predicts a stronger $\varphi N({}^2{S}_{1/2})$ interaction and permits a two-body bound state, whereas Model B suggests the interaction is attractive but too weak to form a bound state. Both models predict bound states for the $I(J^P)=0(0^{-})$ and $0(1^{-})$ $\varphi NN$ systems. In Model A, these states are deeply bound with binding energies exceeding 15 MeV and remain existent when considering parameter uncertainties. In contrast, these states are very loosely bound in Model B, with binding energies below 1 MeV and an existent probability of about 60\% when parameter uncertainties are considered. In both models, there exist very loosely bound $I(J^P)=0(2^{-})$ three-body states which resemble a $\varphi$-d atom with the $\varphi$ meson surrounding the deuteron, but their existences are sensitive to parameter uncertainties. No bound states or resonances are found in the isovector $I(J^P)=1(1^{-})$ $\varphi NN$ system.

arXiv comment16 pages, 9 figures. Comments are welcome

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