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Regularization and renormalization is discussed in the context of low-energyeffective field theory treatments of two or more heavy particles (such asnucleons). It is desirable to regulate the contact interactions from the outsetby treating them as having a finite range. The low energy physical observablesshould be insensitive to this range provided that the range is of a similar orgreater scale than that of the interaction. Alternative schemes, such asdimensional regularization, lead to paradoxical conclusions such as theimpossibility of repulsive interactions for truly low energy effective theorieswhere all of the exchange particles are integrated out. This difficulty arisesbecause a nonrelativistic field theory with repulsive contact interactions istrivial in the sense that the $S$ matrix is unity and the renormalized couplingconstant zero. Possible consequences of low energy attraction are alsodiscussed. It is argued that in the case of large or small scattering lengths,the region of validity of effective field theory expansion is much larger ifthe contact interactions are given a finite range from the beginning.Comment: 7 page

Regularization, renormalization, and range: The nucleon-nucleon interaction from effective field theory