Chiral 2π-exchange nn potentials: Two-loop contributions

We calculate in heavy baryon chiral perturbation theory the local NN potentials generated by the two-pion exchange diagrams at two-loop order. We give explicit expressions for the mass spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN amplitudes. We find from two-loop two-pion exchange, a sizable isoscalar central repulsion that amounts to 62.3 MeV at r= 1.0 fm. There is a similarly strong isovector central attraction that, however, originates mainly from the third-order low-energy constants d̄_j entering the chiral πN-scattering amplitude. We also evaluate the one-loop 2π-exchange diagram with two second-order chiral 2πNN vertices proportional to the low-energy constants c_1,2,3,4 as well as the first relativistic 1/M correction to the 2π-exchange diagrams with one such vertex. The diagrammatic results presented here are relevant components of the chiral NN potential at next-to-next-to-next-to-leading order.