One-nucleon intermediate-state contribution to the pion-coupled four-quark condensate in the $N$--$J\mathrm{/}\psi$ interaction

The density dependence of four-quark condensates is a major source of uncertainty in operator product expansion analyses of hadrons in nuclear matter. Their determination is particularly relevant to the $N$–$J\mathrm{/}\psi$ interaction, whose long-range attraction appears to be well described by two-pion exchange in lattice QCD. We evaluate the pion-coupled four-quark condensates using one-nucleon intermediate-state insertions and incorporate them into the QCD sum rule analysis for the $J\mathrm{/}\psi$ meson in nuclear matter. At normal nuclear matter density, we find a mass shift of $-1.75$ MeV, which is of the same order as the approximately $-5$ MeV attraction inferred from a two-pion exchange potential fitted to lattice QCD results. A previous factorization-based treatment required the introduction of unnaturally large phenomenological parameters to obtain a comparable shift. Our result shows that one-nucleon intermediate states provide a significant contribution to the in-medium four-quark condensates and improve the connection between the operator product expansion and the long-range $N$–$J\mathrm{/}\psi$ interaction.