We compare the subtractive renormalization and the Wilsonian renormalization
group approaches in the context of an effective field theory for the
two-nucleon system. Based on an exactly solvable model of contact interactions,
we observe that the standard Wilsonian renormalization group approach with a
single cutoff parameter does not cover the whole space spanned by the
renormalization scale parameters of the subtractive formalism. In particular,
renormalization schemes corresponding to Weinberg's power counting in the case
of an unnaturally large scattering length are beyond the region covered by the
Wilsonian renormalization group approach. In the framework of pionless
effective field theory, also extended by the inclusion of a long-range
interaction of separable type, we demonstrate that Weinberg's power counting
scheme is consistent in the sense that it leads to a systematic order-by-order
expansion of the scattering amplitude.Comment: 23 pages, 2 figure
