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

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

2010-02-04

arxiv.org/abs/1002.0977v1

Physics

High Energy Physics

High Energy Physics - Lattice

40 pages, no figures

Scientific paper

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.

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