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Chiral 2π2\pi-exchange NN-potentials: Two-loop contributions

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 62.362.3 MeV at r=1.0r=1.0 fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants dˉj\bar d_j entering the chiral πN\pi N-scattering amplitude. We also evaluate the one-loop 2π2\pi-exchange diagram with two second order chiral ππNN\pi \pi NN-vertices proportional to the low energy constants c1,2,3,4c_{1,2,3,4} as well as the first relativistic 1/M-correction to the 2π2\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.Comment: 6 pages, 2 figure

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    Last time updated on 05/06/2019