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

Abstract

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 $3πNN$-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 $4π$-vertex. We find that the resulting isovector spin-spin and tensor NN-potentials are negligibly small for $r\geq 0.8$ fm. One can conclude that the effects of uncorrelated chiral $3π$-exchange in the NN-interaction are very small and therefore of no practical relevance.