Chiral $2π$-exchange NN-potentials: Two-loop contributions

Details Chiral $2π$-exchange NN-potentials: Two-loop contributions Chiral $2π$-exchange NN-potentials: Two-loop contributions

2001-07-25

arxiv.org/abs/nucl-th/0107064v1

Phys.Rev. C64 (2001) 057001

Physics

Nuclear Physics

Nuclear Theory

6 pages, 2 figures

Scientific paper

10.1103/PhysRevC.64.057001

We calculate in heavy baryon chiral perturbation theory the local NN-potentials generated by the two-pion exchange diagrams at two-loop order. We give explicit expressions for the mass-spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN-amplitudes. We find from two-loop two-pion exchange a sizeable isoscalar central repulsion which amounts to $62.3 $MeV at $r=1.0 $fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants $\bar d_j$ entering the chiral $\pi N$-scattering amplitude. We also evaluate the one-loop $2\pi$-exchange diagram with two second order chiral $\pi \pi NN$-vertices proportional to the low energy constants $c_{1,2,3,4}$ as well as the first relativistic 1/M-correction to the $2\pi$-exchange diagrams with one such vertex. The diagrammatic results presented here are relevant components of the chiral NN-potential at next-to-next-to-next-to-leading order.

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