Short-range three-nucleon interaction from A=3 data and its hierarchical structure

We construct accurate models of three-nucleon (3N) interaction by fitting, in a hybrid phenomenological approach, the low-energy constants parametrizing the subleading 3N contact operators to the triton binding energy, n-d scattering lengths, cross section and polarization observables of p-d scattering at 2 MeV center-of-mass energy. These models lead to a satisfactory description of polarized p-d scattering data in the whole energy range below the deuteron breakup threshold. In particular, the long-standing $A_y$ puzzle seems to be solved thanks to the new terms considered in the 3N force. Two types of hierarchies among the subleading contact operators are also derived, based on the large-$N_c$ counting and on a recently proposed relativistic counting. We test these hierarchies against the same experimental data and show that they are respected at a reasonable level.