REGULARIZATION, RENORMALIZATION, AND RANGE - THE NUCLEON-NUCLEON INTERACTION FROM EFFECTIVE FIELD THEORY

Regularization and renormalization is discussed in the context of low energy effective field theory treatments of two or more heavy particle s (such as nucleons). It is desirable to regulate the contact interact ions from the outset by treating them as having a finite range. The lo w energy physical observables should be insensitive to this range prov ided that the range is of a similar or greater scale than that of the interaction. Alternative schemes, such as dimensional regularization, lead to paradoxical conclusions such as the impossibility of repulsive interactions for truly low energy effective theories where all of the exchange particles are integrated out. This difficulty arises because a nonrelativistic field theory with repulsive contact interactions is trivial in the sense that the S matrix is unity and the renormalized coupling constant zero. Possible consequences of low energy attraction are also discussed. It is argued that in the case of large or small s cattering lengths, the region of validity of effective field theory ex pansion is much larger if the contact interactions are given a finite range from the beginning.