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We investigate the short distance behavior of the nucleon--nucleon (NN)potential defined through the Bethe-Salpeter wave function, by perturbativelycalculating anomalous dimensions of 6--quark operators in QCD. Thanks to theasymptotic freedom of QCD, the 1-loop estimations give exact results for thepotential in the zero distance limit. We show that the chiral symmetry of thegauge interaction implies the existence of an operator whose anomalousdimension is zero for a given quantum number. Furthermore we find that non-zeroanomalous dimensions of other operators are all negative. These results predictthe functional form of the NN potential at short distance, which is a littleweaker than $r^{-2}$. On the other hand, the computation of the anomalousdimension spectrum alone can not determine whether the potential is repulsiveor attractive at short distance. An additional analytic non-perturbativeanalysis suggests that the force at short distance is indeed repulsive at lowenergy as found numerically. Some extensions of the method are brieflydiscussed.

The repulsive core of the NN potential and the operator product expansion