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Charmonium-nucleon potential from lattice QCD

We present results for charmonium-nucleon potential $V_{c\bar{c}-N}(r)$ from quenched lattice QCD, which is calculated from the equal-time Bethe-Salpeter amplitude through the effective Schrödinger equation. Detail information of the low-energy interaction between the nucleon and charmonia ($η_c$ and $J/ψ$) is indispensable for exploring the formation of charmonium bound to nuclei. Our simulations are performed at a lattice cutoff of $1/a\approx 2.1$ GeV in a spatial volume of $(3 fm)^3$ with the nonperturbatively $O(a)$ improved Wilson action for the light quarks and a relativistic heavy quark action for the charm quark. We have found that the potential $V_{c\bar{c}-N}(r)$ for either the $η_c$ and $J/ψ$ states is weakly attractive at short distances and exponentially screened at large distances. The spin averaged $J/ψ$-$N$ potential is slightly more attractive than that of the $η_c$-$N$ case.