$J/ψ$-Nucleon Scattering Length and In-medium Mass Shift of $J/ψ$ in QCD Sum Rule Analysis

Abstract

We calculate the spin-averaged $J/ψ$-nucleon scattering length $a_{J/ψ}$ by directly applying QCD sum rule to $J/ψ$-$N$ forward scattering amplitude. Our result $a_{J/ψ} = - 0.10 \pm 0.02$ fm, predicts the possibility of bound states with nuclei, though the force is weaker than that of the light vector mesons ($ρ,ω,ϕ$)-$N$ cases. Up to dimension-4 gluonic operators, we evaluate the scattering length with twist-2 contribution, which increases the absolute value of the scattering length about 30%. If we apply $a_{J/ψ}$ to the effective mass of $J/ψ$ in nuclear matter on the basis of the linear density approximation, it shows very slight decrease ($4 \sim 7$ MeV) at normal matter density.