Effective Range in Doublet S-wave Neutron-Deuteron Scattering

The effective field theory approach is applied to the three-nucleon process of $S=1/2$ neutron-deuteron scattering in the S-wave, including the effective range parameters summed at all orders. This is achieved through a modification of the power counting, following a recent suggestion in the literature. It is shown that with this procedure, while the convergence of the loop integrals improves, one cannot meaningfully include a three-body effective term to describe low-energy data affected by the presence of the triton bound state.