Chiral 3π-exchange NN potentials: Results for diagrams proportional to g⁴_A and g⁶_A

We calculate in (two-loop) chiral perturbation theory the local NN potentials generated by the three-pion exchange diagrams proportional to g⁴_A and g⁶_A. Surprisingly, we find that the total isoscalar central 3 π-exchange potential vanishes identically. The individually largest 3 π-exchange potentials are of isoscalar spin-spin, isovector central, and isoscalar tensor type. For these potentials simple analytical expressions can be given. The strength of these dominant 3 π-exchange potentials at r= 1.0 fm is 3.9 MeV, 2.3 MeV, and 1.2 MeV, respectively. The T-matrix, mass-spectrum, and static potential generated by the crossed three-boson exchange diagrams with a scalar meson-nucleon coupling are derived in the appendix.