Chiral $\pi$-exchange NN-potentials: Results for diagrams proportional to g_A^4 and g_A^6

Abstract

We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by the three-pion exchange diagrams proportional to g_A^4 and g_A^6. Surprisingly, we find that the total isoscalar central $3\pi$-exchange potential vanishes identically. The individually largest $3\pi$-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 $3\pi$-exchange potentials at r=1.0 fm is 4.6 MeV, 2.9 MeV and 1.4 MeV, respectively. Furthermore, we observe that the spin-spin and tensor potentials due to the diagrams proportional to g_A^6 do not exist in the infinite nucleon mass limit.

8 pages, 5 figures

References in corpus (4)

• Nuclear forces from chiral Lagrangians using the method of unitary transformation II: The two-nucleon system
• Chiral two-pion exchange and proton-proton partial-wave analysis
• Chiral $3\pi$-exchange NN-potentials: results for representation invariant classes of diagrams
• Three-pion exchange: a gap in the nucleon-nucleon potential

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