Abstract
During the past few decades a large effort has been made toward describing the NN interaction in the framework of chiral Effective Field Theory (EFT). The main idea is to exploit the symmetries of QCD to obtain an effective theory for low energy nuclear systems. In 2003, the first accurate charge-dependent NN potential in this scheme was developed and it has been applied to many ab-initio calculations, opening the possibility to study nuclear systems in a systematic and accurate way. It was shown that the fourth order ((NLO)-L-3) was necessary and sufficient to describe the NN scattering data with a chi(2)/d.o.f on the order of so-called high precision potentials. However the systematics of chiral EFT also allow to relate two- and many-body interactions in a well-defined way. Since many-body forces make their first appearance at higher order, they are substantially smaller than their two-body counterparts, but may never-the-less be crucial for some processes. Thus, there are observables where they can have a big impact and, for example, there are indications that they solve the long standing A(y) puzzle of N-d scattering. The last few years, have also seen substantial progress toward higher orders of chiral EFT which was motivated by the fact that only three-body forces of rather high order may solve some outstanding issues in microscopic nuclear structure and reactions. In this chapter we will review the latest contributions of the authors to development of chiral EFT based potentials up to (NLO)-L-4 as well as first calculations conducted for NN scattering at (NLO)-L-5.