Dimensional versus cut-off renormalization and the nucleon-nucleon potential of the effective field theory

The role of cut-off and dimensional regularizations is discussed in the context of obtaining a renormalized nucleon-nucleon potential from the chiral Lagrangian formulation of the effective field theory due to Weinberg. Both types of renormalizations are performed for the sum of an attractive delta function and its derivatives. The equivalence between the two forms of regularizations can be established with the use of energy-dependent bare couplings and the explicit forms of these couplings are determined. PACS Numbers 21.30.-x, 03.65.Nk, 11.10.Gh