Long-range <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:math> interaction from an operator product expansion perspectiv

A recent lattice QCD study has shown that the $N\ensuremath{-}J/\ensuremath{\psi}$ 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. This is accomplished by extracting the leading-order four-quark operator that couples to two pions and calculating its contribution to the $J/\ensuremath{\psi}$ 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 $J/\ensuremath{\psi}$ and other mesons composed of heavy quarks.