Examination of the $c\bar{c}+n+^{10}$Be bound-state problem within three cluster models based on QCD charmonium-nucleon interactions

TL;DR

This study investigates the potential bound states of a charmonium-nucleus system using a three-cluster model based on lattice QCD-derived interactions, predicting small binding energies and specific nuclear radii.

Contribution

It introduces a three-cluster framework with potentials derived from lattice QCD to analyze charmonium-nucleus bound states, providing new insights into their binding energies and sizes.

Findings

Binding energies are approximately 3.5 MeV for certain spin states.

Predicted nuclear matter radii are around 2.5 fm.

The results suggest possible bound states in the studied system.

Abstract

The possible bound state of the $c\bar{c}+n+^{10}$Be system, representing a hypothetical charmonium-nucleus configuration, is investigated. The analysis is conducted within a three-cluster framework, in which the binary subsystems are treated as $n+^{10}\textrm{Be}$, $^{10}\textrm{Be}+c\bar{c}$, and $c\bar{c}+n$. The hyperspherical harmonics method is employed to provide a convenient description of this three-cluster configuration. The calculations are performed using effective $^{10}\textrm{Be}\textrm{-}c\bar{c}$ potentials constructed via the single-folding procedure. These potentials have been derived recently on the basis of state-of-the-art lattice QCD results from the HAL QCD Collaboration, which provided interactions for the spin-$3/2$ $J/\psi N$, spin-$1/2$ $J/\psi N$, spin-$1/2$ $\eta_{c}N$, and spin-averaged $J/\psi N$ channels, all obtained at nearly physical pion masses. The numerical results indicate that the central binding energies of the spin-$3/2$ $J/\psi+n+^{10}$Be, spin-$1/2$ $J/\psi+n+^{10}$Be, and spin-$1/2$ $\eta_{c}+n+^{10}$Be systems are 3.47, 3.55, and 1.91 MeV, respectively. The corresponding root-mean-square nuclear matter radii are predicted to be approximately 2.49, 2.48, and 2.60 fm.