Low energy expansion in the three body system to all orders and the Triton Channel

We extend and systematize the power counting for the three-body system, in the context of the ''pion-less'' Effective Field Theory approach, to all orders in the low-energy expansion. We show that a sub-leading part of the three-body force appears at the third order and delineate how the expansion proceeds at higher orders. After discussing the renormalization issues in a simple bosonic model, we compute the phase shifts for neutron-deuteron scattering in the doublet S wave (triton) channel and compare our results with phase shift analysis and potential model calculations