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arXiv · 1002.0977

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

Sinya Aoki·Janos Balog·Peter Weisz
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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.

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Sinya Aoki, Janos Balog, Peter Weisz. 2010-02-04. Application of the operator product expansion to the short distance behavior of nuclear potentials. https://doi.org/10.1007/jhep05(2010)008

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