Benchmark Calculations for the Triton Binding Energy for Modern NN Forces and the pi-pi Exchange Three-Nucleon Force

We present high precision benchmark calculations for the triton binding energy using the most recent, phase equivalent realistic nucleon-nucleon (NN) potentials and the Tuscon-Melbourne pi-pi three-nucleon force (3NF). That 3NF is included with partial waves up to a total two-body angular momentum of j_max=6. It is shown that the inclusion of the 3NF slows down the convergence in the partial waves and j_max=5 is needed in order to achieve converged results within a few keV. We adjust the cut-off parameter Lambda in the form factors of the Tuscon-Melbourne 3NF separately for the different NN potentials to the triton binding energy. This provides a set of phenomenological three-nucleon Hamiltonians which can be tested in three-nucleon scattering and systems with A>3. A connection between the probability to find two nucleons at short distances in the triton and the effect of that 3NF on the triton binding energy is pointed out.