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

N. Kaiser
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Abstract

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 $πN$-scattering amplitude. We also evaluate the one-loop $2π$-exchange diagram with two second order chiral $ππNN$-vertices proportional to the low energy constants $c_{1,2,3,4}$ as well as the first relativistic 1/M-correction to the $2π$-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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N. Kaiser. 2001-07-25. Chiral $2π$-exchange NN-potentials: Two-loop contributions. https://doi.org/10.1103/physrevc.64.057001

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