Chiral 3π-exchange [Formula Presented] potentials: Results for diagrams proportional to [Formula Presented] and [Formula Presented]

We calculate in (two-loop) chiral perturbation theory the local [Formula Presented] potentials generated by the three-pion exchange diagrams proportional to [Formula Presented] and [Formula Presented] Surprisingly, we find that the total isoscalar central [Formula Presented]-exchange potential vanishes identically. The individually largest [Formula Presented]-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 [Formula Presented]-exchange potentials at [Formula Presented] 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.