Chiral 3 π-exchange NN potentials: Results for representation-invariant classes of diagrams

We calculate in (two-loop) chiral perturbation theory the local NN potentials generated by certain classes of three-pion exchange diagrams. We stress that the chiral 3 πNN-contact vertex depends on the particular choice of the interpolating pion-field and, therefore, one has to consider representation-invariant classes of diagrams by supplementing graphs involving the chiral 4 π vertex. We find that the resulting isovector spin-spin and tensor NN potentials are negligibly small for r ≥ 0.8 fm. One can conclude that the effects of uncorrelated chiral 3 π exchange in the NN interaction are very small and therefore of no practical relevance.