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In effective field theory physical quantities, in particular observables, areexpressed as a power series in terms of a small expansion parameter. Fornon-perturbative systems, for instance nuclear physics, this requires thenon-perturbative treatment of at least a part of the interaction (or thepotential, if we are dealing with a non-relativistic system). This is notentirely trivial and as a consequence different interpretations on how to treatthese systems have appeared. A practical approach is to expand the effectivepotential, where this potential is later fully iterated in the Schr\"odingerequation for obtaining amplitudes and observables. The expectation is that thiswill lead to observables that will have an implicit power counting expansion.Here we explicitly check whether the amplitudes are actually following the samepower counting as the potential. It happens that reality does not necessarilyconform to expectations and the amplitudes will often violate the powercounting with which the potential has been expanded. A more formal approach isto formulate the expansion directly in terms of amplitudes and observables,which is the original aim of the effective field theory idea. Yet this secondapproach is technically complicated. We explore here the possibility ofconstructing potentials that when fully iterated will make sure that amplitudesindeed are expansible in terms of a small expansion parameter.

Scattering amplitudes versus potentials in nuclear effective field theory: is there a potential compromise?