Application of the operator product expansion to the short distance behavior of nuclear potentials

TL;DR

This paper uses the operator product expansion in QCD to analyze the short-distance behavior of nucleon-nucleon potentials, predicting a potential weaker than r^{-2} and suggesting a repulsive force at very short distances.

Contribution

It applies the operator product expansion to derive the short-distance form of NN potentials from QCD, providing analytical insights complementing lattice QCD results.

Findings

Short-distance NN potential is slightly weaker than r^{-2}.

Perturbative analysis suggests the potential is likely repulsive at short distances.

Tensor potential exhibits similar short-distance behavior.

Abstract

We investigate the short distance behavior of nucleon-nucleon (NN) potentials defined through Bethe-Salpeter wave functions, by perturbatively calculating anomalous dimensions of 6-quark operators in QCD. Thanks to the asymptotic freedom of QCD, 1-loop computations give certain exact results for the potentials in the zero distance limit. In particular the functional form of the S-state central NN potential at short distance $r$ is predicted to be a little weaker than $r^{-2}$. On the other hand, due to the intriguing character of the anomalous dimension spectrum, perturbative considerations alone can not determine whether this potential is repulsive or attractive at short distances. A crude estimation suggests that the force at short distance is repulsive, as found numerically in lattice QCD. A similar behavior is found for the tensor potential.