O ct 1 99 9 Chiral 3 π - exchange NN - potentials : results for representation - invariant classes of diagrams N . Kaiser

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 3πN N-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 ≥ 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. The longest-range part of the strong nucleon-nucleon interaction is due to the well-established one-pion exchange. Next in range comes the two-pion exchange force, whose formulation has been a longstanding problem in quantum field theory and in dispersion theory. In recent years, it has been argued that the key to the solution is the chiral symmetry of QCD, and that the long-range parts of the two-pion exchange NN-potential can be derived model-independently via a systematic expansion of the effective chiral pion-nucleon Lagrangian. The complete leading and next-to-leading order terms of this chiral two-pion exchange NN-potential have been calculated in ref.[1] (actually most of the contributions have already been obtained in earlier calculations). Recently, the elastic proton-proton scattering data base below 350 MeV laboratory kinetic energy (consisting of 1951 data points) has been analyzed in terms of one-pion exchange and chiral two-pion exchange in ref.[2]. The resulting good χ 2 /dof ≤ 1 constitutes a convincing proof for the presence of the chiral two-pion exchange in the long-range proton-proton strong interaction. Furthermore, it was concluded in ref.[2] that 1π-exchange together with chiral 2π-exchange gives a very good NN-force at least as far inwards as r = 1.4 fm inter-nucleon distance. Naturally, the next question to be answered is whether there are some important effects from chiral three-pion exchange. In a recent work Pupin and Robilotta [3] calculated the potentials generated by one specific two-loop diagram in which the three pions are emitted from a contact vertex at the first nucleon and absorbed on a contact vertex at the second nucleon (first graph in Fig. 1). The resulting isovector spin-spin and tensor potentials were