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We calculate in (two-loop) chiral perturbation theory the local NN-potentialsgenerated by the three-pion exchange diagrams with one insertion from thesecond order chiral effective pion-nucleon Lagrangian proportional to thelow-energy constants $c_{1,2,3,4}$. The resulting isoscalar central potentialvanishes identically. In most cases these $3\pi$-exchange potentials are largerthan the ones generated by the diagrams involving only leading order verticesdue to the large values of $c_{3,4}$ (which mainly represent virtual$\Delta$-excitation). A similar feature has been observed for the chiral$2\pi$-exchange. We also give suitable (double-integral) representations forthe spin-spin and tensor potentials generated by the leading-order diagramsproportional to $g_A^6$ involving four nucleon propagators. In these cases theCutkosky rule cannot be used to calculate the spectral-functions in theinfinite nucleon mass limit since the corresponding mass-spectra start with anon-vanishing value at the $3\pi$-threshold. Altogether, one finds that chiral$3\pi$-exchange leads to small corrections in the region $r\geq 1.4$ fm where$1\pi$- and chiral $2\pi$-exchange alone provide a very good strong NN-force asshown in a recent analysis of the low-energy pp-scattering data-base.Comment: 11 pages, 7 figures, to be published in The Physical Review

physical review. c. nuclear physics/physical review. c, nuclear physics

Chiral<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mi>π</mml:mi></mml:math>-exchange<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>NN</mml:mi></mml:math>potentials: Results for dominant next-to-leading-order contributions

Chiral3π-exchangeNNpotentials: Results for dominant next-to-leading-order contributions