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

We investigate the short distance behavior of the nucleon--nucleon (NN) potential defined through the Bethe-Salpeter wave function, by perturbatively calculating anomalous dimensions of 6--quark operators in QCD. Thanks to the asymptotic freedom of QCD, the 1-loop estimations give exact results for the potential in the zero distance limit. We show that the chiral symmetry of the gauge interaction implies the existence of an operator whose anomalous dimension is zero for a given quantum number. Furthermore we find that non-zero anomalous dimensions of other operators are all negative. These results predict the functional form of the NN potential at short distance, which is a little weaker than $r^{-2}$. On the other hand, the computation of the anomalous dimension spectrum alone can not determine whether the potential is repulsive or attractive at short distance. An additional analytic non-perturbative analysis suggests that the force at short distance is indeed repulsive at low energy as found numerically. Some extensions of the method are briefly discussed.