Chiral [Formula Presented]-exchange [Formula Presented] potentials: Results for representation-invariant classes of diagrams

We calculate in (two-loop) chiral perturbation theory the local [Formula Presented] potentials generated by certain classes of three-pion exchange diagrams. We stress that the chiral [Formula Presented]-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 [Formula Presented] vertex. We find that the resulting isovector spin-spin and tensor [Formula Presented] potentials are negligibly small for [Formula Presented] fm. One can conclude that the effects of uncorrelated chiral [Formula Presented] exchange in the [Formula Presented] interaction are very small and therefore of no practical relevance.