Long-Range $N-J/\psi$ Interaction from an Operator Product Expansion Perspective

A recent lattice QCD study has shown that the $N-J/\psi$ potential is attractive at all distances, and its long-range tail is well described by two-pion exchange. Here, we study to what extent the long-range part of the attraction can be reproduced from the perspective of the operator product expansion (OPE). This is accomplished by extracting the leading-order four-quark operator that couples to two pions and calculating its contribution to the $J/\psi$ mass in nuclear matter, to linear order in density, within the QCD sum rule framework. Using previous estimates of the four-quark operators for the chiral symmetric and breaking parts, we obtain a mass decrease that is smaller in magnitude but qualitatively consistent with the attraction obtained in the lattice QCD calculation. By expressing the interaction in terms of four-quark operators, we can analyze the effects of chiral symmetry restoration in dense matter on the masses of the $J/\psi$ and other mesons composed of heavy quarks.