l - th / 0 10 70 64 v 1 2 5 Ju l 2 00 1 Chiral 2 π - exchange NN - potentials : Two - loop contributions

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 ¯ d j entering the chiral πN-scattering amplitude. We also evaluate the one-loop 2π-exchange diagram with two second order chiral ππN N-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. Over the past years effective field theory methods have been successfully applied to the two-nucleon system at low and intermediate energies [1, 2, 3, 4, 5, 6]. The idea of constructing the NN-potential from effective field theory was put forward by Weinberg [1] and this was first taken up by van Kolck and collaborators [2] who used " old-fashioned " time-ordered perturbation theory. Later, the systematic method of unitary transformations was employed by Epelbaum, Glöckle and Meißner [4] to construct an energy-independent NN-potential from the effective chiral pion-nucleon Lagrangian at next-to-leading order. Based on one-and two-pion exchange and nine adjustable NN-contact interactions which contribute only to Sand P-waves a good description of the deuteron properties as well as the NN phase-shifts and mixing angles below T lab = 300 MeV was found in that framework [4]. Also recently, the elastic proton-proton scattering data base below 350 MeV laboratory kinetic energy (consisting of 1951 data points) has been analyzed in terms of 1π-exchange and chiral 2π-exchange at next-to-next-to-leading order in ref.[7]. The resulting good χ 2 /dof ≤ 1 constitutes a convincing proof for the presence of the chiral 2π-exchange in the long-range proton-proton strong interaction. It was concluded in ref.[7] that 1π-exchange together with chiral 2π-exchange gives a very good NN-force at least as far inwards as r = 1.4 fm internucleon distance. All shorter range components of the NN-interaction have been effectively parametrized in ref.[7] by 23 boundary condition parameters. At present, there is much interest in extending the calculations of the two-nucleon system [8] (and also the …