Long-Range $N-J/ψ$ Interaction from an Operator Product Expansion Perspective
Seokwoo Yeo, In Woo Park, Su Houng Lee
TL;DR
The paper addresses the long-range part of the $N$-$J/\\psi$ interaction in nuclear matter, motivated by lattice results showing attraction driven by two-pion exchange. It employs QCD sum rules with an operator-product expansion up to dimension-6, isolating the pion-coupled four-quark condensates via a Fierz transformation and incorporating density dependence through a parameter $\\kappa$. The results yield a small but meaningful in-medium mass decrease for the $J/\\psi$ that qualitatively agrees with lattice findings, with the magnitude and sign depending on $\\kappa$ and $\\alpha_{s,\\mathrm{IR}}$, and vanish or reverse if the pion-coupled component is not isolated. This work links chiral-symmetry restoration effects to heavy-quark systems and underscores the importance of properly accounting for long-distance hadronic contributions in QCD sum-rule analyses of in-medium hadrons.
Abstract
A recent lattice QCD study has shown that the $N-J/ψ$ 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 $J/ψ$ 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 $J/ψ$ and other mesons composed of heavy quarks.