  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.
