The three-nucleon interaction in pionful and pionless effective field theory

After a brief historical perspective on the three-nucleon (3N) interaction, we will focus on the chiral 3N forces and discuss some of the main present discrepancies with experimental data on low-energy p −d scattering. By including the subleading 3N contact interactions, expected to arise at the fifth order of the chiral expansion (N4LO), these discrepancies can be solved. However, part of the needed contributions can be regarded as of fourth order (N3LO), because they are induced by a unitary transformation devised to absorb redundant NN contact interactions at N3LO. As a result, a satisfactory description in NN and 3N systems can be achieved already at N3LO. Finally, the pionless case will be described, with particular emphasis on the different treatment of the 3N force, and on possible consequences for the chiral series.