Chiral 3$\pi$-exchange NN-potentials: Results for dominant next-to-leading order contributions

Abstract

We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by the three-pion exchange diagrams with one insertion from the second order chiral effective pion-nucleon Lagrangian proportional to the low-energy constants $c_{1,2,3,4}$. The resulting isoscalar central potential vanishes identically. In most cases these $3\pi$-exchange potentials are larger than the ones generated by the diagrams involving only leading order vertices due 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 for the spin-spin and tensor potentials generated by the leading-order diagrams proportional to $g_A^6$ involving four nucleon propagators. In these cases the Cutkosky rule cannot be used to calculate the spectral-functions in the infinite nucleon mass limit since the corresponding mass-spectra start with a non-vanishing value at the $3\pi$-threshold. Altogether, one finds that chiral $3\pi$-exchange leads to small corrections in the region $r\ge 1.4$ fm where $1\pi$- and chiral $2\pi$-exchange alone provide a very good strong NN-force as shown in a recent analysis of the low-energy pp-scattering data-base.

11 pages, 7 figures, to be published in The Physical Review C

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• Local chiral potentials and the structure of light nuclei
• Renormalization of NN Interaction with Chiral Two Pion Exchange Potential. Central Phases and the Deuteron
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• Two-pion exchange three-nucleon potential: O(q^4) chiral expansion
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• Chiral $2\pi$-exchange NN-potentials: Two-loop contributions
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• Chiral EFT based nuclear forces: Achievements and challenges
• Atomic nuclei from quantum Monte Carlo calculations with chiral EFT interactions
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• The Nucleon-Mass Difference in Chiral Perturbation Theory and Nuclear Forces
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• Microscopic Nuclear Structure Based upon a Chiral NN Potential
• Taking dibaryon fields seriously
• The Nuclear Central Force in the Chiral Limit
• The relativistic self-energy in nuclear dynamics
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Renormalization of chiral two-pion exchange NN interactions with Delta-excitations: Central Phases and the Deuteron
• Renormalization of chiral two pion exchange NN interactions with delta excitations: correlations in the partial wave expansion
• Three-body forces and Efimov physics in nuclei and atoms
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