BOUND-STATES AND POWER COUNTING IN EFFECTIVE-FIELD THEORIES

The problem of bound states in effective field theories is studied. A rescaled version of nonrelativistic effective field theory is formulat ed which makes the velocity power counting of operators manifest. Resu lts obtained using the rescaled theory are compared with known results from NRQCD. The same ideas are then applied to study Yukawa bound sta tes in 1+1 and 3+1 dimensions, and to analyze when the Yukawa potentia l can be replaced by a delta-function potential. The implications of t hese results for the study of nucleon- nucleon scattering in chiral pe rturbation theory are discussed.