Renormalisation and power counting in effective field theories for nucleon-nucleon scattering

The renormalisation of NN scattering in theories with zero-range interactions is examined using a cut-off regularisation and taking the cut-off to infinity. Inclusion of contact interactions that depend on energy as well as momentum allows the effective range to be fitted to experiment with any desired sign or magnitude. However, power counting breaks down: terms of different orders in the potential can contribute to the scattering amplitude at the same order.